diff --git a/changelog b/changelog index 5d27d71..d1d6548 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100620 tpd src/axiom-website/patches.html 20100620.05.tpd.patch +20100620 tpd src/input/richtrig100-199.input remove useless derivatives +20100620 tpd src/input/richtrig000-099.input remove useless derivatives 20100620 tpd src/axiom-website/patches.html 20100620.04.tpd.patch 20100620 tpd src/input/Makefile integral function integration 20100620 tpd src/input/richspecfunc000-022.input special function integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 8324fcd..4f1462b 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2934,6 +2934,8 @@ src/input/richerror000-078.input error function integration
src/input/richintfunc000-032.input integral function integration
20100620.04.tpd.patch src/input/richspecfunc000-022.input special function integration
+20100620.05.tpd.patch +src/input/richtrig000-099, richtrig100-199 remove useless derivatives
diff --git a/src/input/richtrig000-099.input.pamphlet b/src/input/richtrig000-099.input.pamphlet index ac8505d..9097fb8 100644 --- a/src/input/richtrig000-099.input.pamphlet +++ b/src/input/richtrig000-099.input.pamphlet @@ -72,7 +72,8 @@ t0001:= sin(a+b*x)^(3/2) --E 6 --S 7 of 520 -r0001:= -2/3*(-EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)+cos(a+b*x)*sin(a+b*x)^(1/2))/b +r0001:= -2/3*(-EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)+_ + cos(a+b*x)*sin(a+b*x)^(1/2))/b --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -118,7 +119,8 @@ t0002:= sin(a+b*x)^(5/2) --E 11 --S 12 of 520 -r0002:= -2/5*(-3*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)+cos(a+b*x)*sin(a+b*x)^(3/2))/b +r0002:= -2/5*(-3*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)+_ + cos(a+b*x)*sin(a+b*x)^(3/2))/b --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -215,7 +217,8 @@ t0004:= 1/sin(a+b*x)^(3/2) --E 21 --S 22 of 520 -r0004:= -2*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)/b-2*cos(a+b*x)/b/sin(a+b*x)^(1/2) +r0004:= -2*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)/b-_ + 2*cos(a+b*x)/b/sin(a+b*x)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -264,7 +267,8 @@ t0005:= 1/sin(a+b*x)^(5/2) --E 26 --S 27 of 520 -r0005:= 2/3*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)/b-2/3*cos(a+b*x)/b/sin(a+b*x)^(3/2) +r0005:= 2/3*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)/b-_ + 2/3*cos(a+b*x)/b/sin(a+b*x)^(3/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -358,7 +362,8 @@ t0007:= (a*sin(x)^3)^(1/2) --E 36 --S 37 of 520 -r0007:= 2/3*(EllipticF(-1/4*%pi+1/2*x,2)-cos(x)*sin(x)^(1/2))*(a*sin(x)^3)^(1/2)/sin(x)^(3/2) +r0007:= 2/3*(EllipticF(-1/4*%pi+1/2*x,2)-_ + cos(x)*sin(x)^(1/2))*(a*sin(x)^3)^(1/2)/sin(x)^(3/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -404,7 +409,8 @@ t0008:= (a*sin(x))^(3/2) --E 41 --S 42 of 520 -r0008:= 2/3*a^2*(EllipticF(-1/4*%pi+1/2*x,2)*sin(x)^(1/2)-cos(x)*sin(x))/(a*sin(x))^(1/2) +r0008:= 2/3*a^2*(EllipticF(-1/4*%pi+1/2*x,2)*sin(x)^(1/2)-_ + cos(x)*sin(x))/(a*sin(x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -451,7 +457,8 @@ t0009:= (a*sin(x)^3)^(3/2) --E 46 --S 47 of 520 -r0009:= 2/45*a*(a*sin(x)^3)^(1/2)*(21*EllipticE(-1/4*%pi+1/2*x,2)-7*cos(x)*sin(x)^(3/2)-5*cos(x)*sin(x)^(7/2))/sin(x)^(3/2) +r0009:= 2/45*a*(a*sin(x)^3)^(1/2)*(21*EllipticE(-1/4*%pi+1/2*x,2)-_ + 7*cos(x)*sin(x)^(3/2)-5*cos(x)*sin(x)^(7/2))/sin(x)^(3/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -615,7 +622,8 @@ t0012:= 1/(a*sin(x)^3)^(1/2) --E 61 --S 62 of 520 -r0012:= -2*(cos(x)+EllipticE(-1/4*%pi+1/2*x,2)*sin(x)^(1/2))*sin(x)/(a*sin(x)^3)^(1/2) +r0012:= -2*(cos(x)+EllipticE(-1/4*%pi+1/2*x,2)*sin(x)^(1/2))*_ + sin(x)/(a*sin(x)^3)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -665,7 +673,8 @@ t0013:= 1/(a+b*sin(c+d*x))^2 --E 66 --S 67 of 520 -r0013:= 2*a*atan((b+a*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)/d+b*cos(c+d*x)/(a^2-b^2)/d/(a+b*sin(c+d*x)) +r0013:= 2*a*atan((b+a*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)/d+_ + b*cos(c+d*x)/(a^2-b^2)/d/(a+b*sin(c+d*x)) --R --R --R (31) @@ -1013,7 +1022,9 @@ t0014:= 1/(a+b*sin(c+d*x))^3 --E 73 --S 74 of 520 -r0014:= (2*a^2+b^2)*atan((b+a*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)/d+1/2*b*cos(c+d*x)/(a^2-b^2)/d/(a+b*sin(c+d*x))^2+3/2*a*b*cos(c+d*x)/(a^2-b^2)^2/d/(a+b*sin(c+d*x)) +r0014:= (2*a^2+b^2)*atan((b+a*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/_ + (a^2-b^2)^(5/2)/d+1/2*b*cos(c+d*x)/(a^2-b^2)/d/(a+b*sin(c+d*x))^2+_ + 3/2*a*b*cos(c+d*x)/(a^2-b^2)^2/d/(a+b*sin(c+d*x)) --R --R --R (38) @@ -3824,7 +3835,10 @@ t0015:= 1/(a+b*sin(c+d*x))^4 --E 80 --S 81 of 520 -r0015:= a*(2*a^2+3*b^2)*atan((b+a*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(7/2)/d+1/3*b*cos(c+d*x)/(a^2-b^2)/d/(a+b*sin(c+d*x))^3+5/6*a*b*cos(c+d*x)/(a^2-b^2)^2/d/(a+b*sin(c+d*x))^2+1/6*b*(11*a^2+4*b^2)*cos(c+d*x)/(a^2-b^2)^3/d/(a+b*sin(c+d*x)) +r0015:= a*(2*a^2+3*b^2)*atan((b+a*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/_ + (a^2-b^2)^(7/2)/d+1/3*b*cos(c+d*x)/(a^2-b^2)/d/(a+b*sin(c+d*x))^3+_ + 5/6*a*b*cos(c+d*x)/(a^2-b^2)^2/d/(a+b*sin(c+d*x))^2+_ + 1/6*b*(11*a^2+4*b^2)*cos(c+d*x)/(a^2-b^2)^3/d/(a+b*sin(c+d*x)) --R --R --R (45) @@ -6270,7 +6284,8 @@ t0017:= 1/(1+sin(c+d*x))^3 --E 92 --S 93 of 520 -r0017:= 1/15/cos(c+d*x)^5*(12*sin(c+d*x)+cos(c+d*x)^2*sin(c+d*x)-12+5*cos(c+d*x)^2+2*cos(c+d*x)^4*sin(c+d*x))/d +r0017:= 1/15/cos(c+d*x)^5*(12*sin(c+d*x)+cos(c+d*x)^2*sin(c+d*x)-_ + 12+5*cos(c+d*x)^2+2*cos(c+d*x)^4*sin(c+d*x))/d --R --R --R (56) @@ -6432,7 +6447,9 @@ t0018:= 1/(1+sin(c+d*x))^4 --E 97 --S 98 of 520 -r0018:= 1/35/cos(c+d*x)^7*(40*sin(c+d*x)-8*cos(c+d*x)^2*sin(c+d*x)-40+28*cos(c+d*x)^2+cos(c+d*x)^4*sin(c+d*x)+2*cos(c+d*x)^6*sin(c+d*x))/d +r0018:= 1/35/cos(c+d*x)^7*(40*sin(c+d*x)-8*cos(c+d*x)^2*sin(c+d*x)-_ + 40+28*cos(c+d*x)^2+cos(c+d*x)^4*sin(c+d*x)+_ + 2*cos(c+d*x)^6*sin(c+d*x))/d --R --R --R (61) @@ -6764,7 +6781,8 @@ t0020:= 1/(1-sin(c+d*x))^3 --E 107 --S 108 of 520 -r0020:= 1/15/cos(c+d*x)^5*(12*sin(c+d*x)+cos(c+d*x)^2*sin(c+d*x)+12-5*cos(c+d*x)^2+2*cos(c+d*x)^4*sin(c+d*x))/d +r0020:= 1/15/cos(c+d*x)^5*(12*sin(c+d*x)+cos(c+d*x)^2*sin(c+d*x)+12-_ + 5*cos(c+d*x)^2+2*cos(c+d*x)^4*sin(c+d*x))/d --R --R --R (71) @@ -6925,7 +6943,8 @@ t0021:= 1/(1-sin(c+d*x))^4 --E 112 --S 113 of 520 -r0021:= 1/35/cos(c+d*x)^7*(40*sin(c+d*x)-8*cos(c+d*x)^2*sin(c+d*x)+40-28*cos(c+d*x)^2+cos(c+d*x)^4*sin(c+d*x)+2*cos(c+d*x)^6*sin(c+d*x))/d +r0021:= 1/35/cos(c+d*x)^7*(40*sin(c+d*x)-8*cos(c+d*x)^2*sin(c+d*x)+40-_ + 28*cos(c+d*x)^2+cos(c+d*x)^4*sin(c+d*x)+2*cos(c+d*x)^6*sin(c+d*x))/d --R --R --R (76) @@ -7138,7 +7157,8 @@ t0022:= (a+b*sin(c+d*x))^(1/2) --E 117 --S 118 of 520 -r0022:= 2*EllipticE(1/2*c-1/4*%pi+1/2*d*x,2*b/(a+b))*(a+b*sin(c+d*x))^(1/2)/d/((a+b*sin(c+d*x))/(a+b))^(1/2) +r0022:= 2*EllipticE(1/2*c-1/4*%pi+1/2*d*x,2*b/(a+b))*_ + (a+b*sin(c+d*x))^(1/2)/d/((a+b*sin(c+d*x))/(a+b))^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -7184,7 +7204,11 @@ t0023:= (a+b*sin(x))^(3/2) --E 122 --S 123 of 520 -r0023:= 2/3*(4*a*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))-a*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))-b*cos(x)*((a+b*sin(x))/(a+b))^(1/2)+b*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b)))*(a+b*sin(x))^(1/2)/((a+b*sin(x))/(a+b))^(1/2) +r0023:= 2/3*(4*a*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))-_ + a*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))-_ + b*cos(x)*((a+b*sin(x))/(a+b))^(1/2)+b*_ + EllipticF(-1/4*%pi+1/2*x,2*b/(a+b)))*(a+b*sin(x))^(1/2)/_ + ((a+b*sin(x))/(a+b))^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -7232,7 +7256,8 @@ t0024:= 1/(a+b*sin(x))^(1/2) --E 127 --S 128 of 520 -r0024:= 2*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))*((a+b*sin(x))/(a+b))^(1/2)/(a+b*sin(x))^(1/2) +r0024:= 2*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))*((a+b*sin(x))/(a+b))^(1/2)/_ + (a+b*sin(x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -7281,7 +7306,9 @@ t0025:= 1/(a+b*sin(x))^(3/2) --E 132 --S 133 of 520 -r0025:= 2*b*cos(x)/(a^2-b^2)/(a+b*sin(x))^(1/2)+2*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))*(a+b*sin(x))^(1/2)/(a^2-b^2)/((a+b*sin(x))/(a+b))^(1/2) +r0025:= 2*b*cos(x)/(a^2-b^2)/(a+b*sin(x))^(1/2)+_ + 2*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))*(a+b*sin(x))^(1/2)/_ + (a^2-b^2)/((a+b*sin(x))/(a+b))^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -7330,7 +7357,12 @@ t0026:= 1/(a+b*sin(x))^(5/2) --E 137 --S 138 of 520 -r0026:= 2/3*b*cos(x)/(a^2-b^2)/(a+b*sin(x))^(3/2)+8/3*a*b*cos(x)/(a^2-b^2)^2/(a+b*sin(x))^(1/2)+8/3*a*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))*(a+b*sin(x))^(1/2)/(a^2-b^2)^2/((a+b*sin(x))/(a+b))^(1/2)-2/3*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))*((a+b*sin(x))/(a+b))^(1/2)/(a^2-b^2)/(a+b*sin(x))^(1/2) +r0026:= 2/3*b*cos(x)/(a^2-b^2)/(a+b*sin(x))^(3/2)+_ + 8/3*a*b*cos(x)/(a^2-b^2)^2/(a+b*sin(x))^(1/2)+_ + 8/3*a*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))*_ + (a+b*sin(x))^(1/2)/(a^2-b^2)^2/((a+b*sin(x))/(a+b))^(1/2)-_ + 2/3*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))*_ + ((a+b*sin(x))/(a+b))^(1/2)/(a^2-b^2)/(a+b*sin(x))^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -7379,7 +7411,8 @@ t0027:= 1/(a+a*sin(c+d*x))^(1/2) --E 142 --S 143 of 520 -r0027:= -2*atanh(cos(1/2*c+1/4*%pi+1/2*d*x))*sin(1/2*c+1/4*%pi+1/2*d*x)/d/(a+a*sin(c+d*x))^(1/2) +r0027:= -2*atanh(cos(1/2*c+1/4*%pi+1/2*d*x))*_ + sin(1/2*c+1/4*%pi+1/2*d*x)/d/(a+a*sin(c+d*x))^(1/2) --R --R --R 2d x + %pi + 2c 2d x + %pi + 2c @@ -8460,7 +8493,9 @@ t0028:= 1/(a+a*sin(c+d*x))^(3/2) --E 149 --S 150 of 520 -r0028:= -1/2*cos(c+d*x)/d/(a+a*sin(c+d*x))^(3/2)-1/2*atanh(cos(1/2*c+1/4*%pi+1/2*d*x))*sin(1/2*c+1/4*%pi+1/2*d*x)/a/d/(a+a*sin(c+d*x))^(1/2) +r0028:= -1/2*cos(c+d*x)/d/(a+a*sin(c+d*x))^(3/2)-_ + 1/2*atanh(cos(1/2*c+1/4*%pi+1/2*d*x))*_ + sin(1/2*c+1/4*%pi+1/2*d*x)/a/d/(a+a*sin(c+d*x))^(1/2) --R --R --R (98) @@ -11563,7 +11598,10 @@ t0029:= 1/(a+a*sin(c+d*x))^(5/2) --E 156 --S 157 of 520 -r0029:= -1/4*cos(c+d*x)/d/(a+a*sin(c+d*x))^(5/2)-3/16*cos(c+d*x)/a/d/(a+a*sin(c+d*x))^(3/2)-3/16*atanh(cos(1/2*c+1/4*%pi+1/2*d*x))*sin(1/2*c+1/4*%pi+1/2*d*x)/a^2/d/(a+a*sin(c+d*x))^(1/2) +r0029:= -1/4*cos(c+d*x)/d/(a+a*sin(c+d*x))^(5/2)-_ + 3/16*cos(c+d*x)/a/d/(a+a*sin(c+d*x))^(3/2)-_ + 3/16*atanh(cos(1/2*c+1/4*%pi+1/2*d*x))*_ + sin(1/2*c+1/4*%pi+1/2*d*x)/a^2/d/(a+a*sin(c+d*x))^(1/2) --R --R --R (105) @@ -11732,7 +11770,8 @@ t0030:= 1/(a-a*sin(c+d*x))^(1/2) --E 163 --S 164 of 520 -r0030:= 2*atanh(sin(1/2*c+1/4*%pi+1/2*d*x))*cos(1/2*c+1/4*%pi+1/2*d*x)/d/(a-a*sin(c+d*x))^(1/2) +r0030:= 2*atanh(sin(1/2*c+1/4*%pi+1/2*d*x))*_ + cos(1/2*c+1/4*%pi+1/2*d*x)/d/(a-a*sin(c+d*x))^(1/2) --R --R --R 2d x + %pi + 2c 2d x + %pi + 2c @@ -12875,7 +12914,9 @@ t0031:= 1/(a-a*sin(c+d*x))^(3/2) --E 170 --S 171 of 520 -r0031:= 1/2*cos(c+d*x)/d/(a-a*sin(c+d*x))^(3/2)+1/2*atanh(sin(1/2*c+1/4*%pi+1/2*d*x))*cos(1/2*c+1/4*%pi+1/2*d*x)/a/d/(a-a*sin(c+d*x))^(1/2) +r0031:= 1/2*cos(c+d*x)/d/(a-a*sin(c+d*x))^(3/2)+_ + 1/2*atanh(sin(1/2*c+1/4*%pi+1/2*d*x))*_ + cos(1/2*c+1/4*%pi+1/2*d*x)/a/d/(a-a*sin(c+d*x))^(1/2) --R --R --R (115) @@ -15841,7 +15882,10 @@ t0032:= 1/(a-a*sin(c+d*x))^(5/2) --E 177 --S 178 of 520 -r0032:= 1/4*cos(c+d*x)/d/(a-a*sin(c+d*x))^(5/2)+3/16*cos(c+d*x)/a/d/(a-a*sin(c+d*x))^(3/2)+3/16*atanh(sin(1/2*c+1/4*%pi+1/2*d*x))*cos(1/2*c+1/4*%pi+1/2*d*x)/a^2/d/(a-a*sin(c+d*x))^(1/2) +r0032:= 1/4*cos(c+d*x)/d/(a-a*sin(c+d*x))^(5/2)+_ + 3/16*cos(c+d*x)/a/d/(a-a*sin(c+d*x))^(3/2)+_ + 3/16*atanh(sin(1/2*c+1/4*%pi+1/2*d*x))*_ + cos(1/2*c+1/4*%pi+1/2*d*x)/a^2/d/(a-a*sin(c+d*x))^(1/2) --R --R --R (122) @@ -16006,7 +16050,8 @@ t0033:= (b*sin(c+d*x))^(1/2) --E 184 --S 185 of 520 -r0033:= 2*EllipticE(1/2*c-1/4*%pi+1/2*d*x,2)*(b*sin(c+d*x))^(1/2)/d/sin(c+d*x)^(1/2) +r0033:= 2*EllipticE(1/2*c-1/4*%pi+1/2*d*x,2)*_ + (b*sin(c+d*x))^(1/2)/d/sin(c+d*x)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -16035,23 +16080,11 @@ a0033:= integrate(t0033,x) --E 186 --S 187 of 520 -m0033:= a0033-r0033 ---R ---R ---R x ---R ++ +---------------+ ---R (126) | \|b sin(%R d + c) d%R - r0033 ---R ++ ---R Type: Expression Integer +--m0033:= a0033-r0033 --E 187 --S 188 of 520 -d0033:= D(m0033,x) ---R ---R ---R +--------------+ ---R (127) \|b sin(d x + c) ---R Type: Expression Integer +--d0033:= D(m0033,x) --E 188 --S 189 of 520 @@ -16059,12 +16092,13 @@ t0034:= (b*sin(c+d*x))^(3/2) --R --R --R +--------------+ ---R (128) b sin(d x + c)\|b sin(d x + c) +--R (126) b sin(d x + c)\|b sin(d x + c) --R Type: Expression Integer --E 189 --S 190 of 520 -r0034:= -2/3*b^2*(-EllipticF(1/2*c-1/4*%pi+1/2*d*x,2)*sin(c+d*x)^(1/2)+cos(c+d*x)*sin(c+d*x))/d/(b*sin(c+d*x))^(1/2) +r0034:= -2/3*b^2*(-EllipticF(1/2*c-1/4*%pi+1/2*d*x,2)*sin(c+d*x)^(1/2)+_ + cos(c+d*x)*sin(c+d*x))/d/(b*sin(c+d*x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -16087,7 +16121,7 @@ a0034:= integrate(t0034,x) --R --R x --R ++ +---------------+ ---R (129) | b sin(%R d + c)\|b sin(%R d + c) d%R +--R (127) | b sin(%R d + c)\|b sin(%R d + c) d%R --R ++ --R Type: Union(Expression Integer,...) --E 191 @@ -16105,12 +16139,13 @@ t0035:= (b*sin(c+d*x))^(5/2) --R --R --R 2 2 +--------------+ ---R (130) b sin(d x + c) \|b sin(d x + c) +--R (128) b sin(d x + c) \|b sin(d x + c) --R Type: Expression Integer --E 194 --S 195 of 520 -r0035:= 2/5*b^2*(b*sin(c+d*x))^(1/2)*(3*EllipticE(1/2*c-1/4*%pi+1/2*d*x,2)-cos(c+d*x)*sin(c+d*x)^(3/2))/d/sin(c+d*x)^(1/2) +r0035:= 2/5*b^2*(b*sin(c+d*x))^(1/2)*(3*EllipticE(1/2*c-1/4*%pi+1/2*d*x,2)-_ + cos(c+d*x)*sin(c+d*x)^(3/2))/d/sin(c+d*x)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -16133,7 +16168,7 @@ a0035:= integrate(t0035,x) --R --R x --R ++ 2 2 +---------------+ ---R (131) | b sin(%R d + c) \|b sin(%R d + c) d%R +--R (129) | b sin(%R d + c) \|b sin(%R d + c) d%R --R ++ --R Type: Union(Expression Integer,...) --E 196 @@ -16151,14 +16186,15 @@ t0036:= 1/(b*sin(c+d*x))^(1/2) --R --R --R 1 ---R (132) ----------------- +--R (130) ----------------- --R +--------------+ --R \|b sin(d x + c) --R Type: Expression Integer --E 199 --S 200 of 520 -r0036:= 2*EllipticF(1/2*c-1/4*%pi+1/2*d*x,2)*sin(c+d*x)^(1/2)/d/(b*sin(c+d*x))^(1/2) +r0036:= 2*EllipticF(1/2*c-1/4*%pi+1/2*d*x,2)*_ + sin(c+d*x)^(1/2)/d/(b*sin(c+d*x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -16181,7 +16217,7 @@ a0036:= integrate(t0036,x) --R --R x --R ++ 1 ---R (133) | ------------------ d%R +--R (131) | ------------------ d%R --R ++ +---------------+ --R \|b sin(%R d + c) --R Type: Union(Expression Integer,...) @@ -16200,14 +16236,16 @@ t0037:= 1/(b*sin(c+d*x))^(3/2) --R --R --R 1 ---R (134) ------------------------------- +--R (132) ------------------------------- --R +--------------+ --R b sin(d x + c)\|b sin(d x + c) --R Type: Expression Integer --E 204 --S 205 of 520 -r0037:= -2/b*(sin(c+d*x)^(1/2)*cos(c+d*x)+EllipticE(1/2*c-1/4*%pi+1/2*d*x,2)*sin(c+d*x))/d/(b*sin(c+d*x))^(1/2)/sin(c+d*x)^(1/2) +r0037:= -2/b*(sin(c+d*x)^(1/2)*cos(c+d*x)+_ + EllipticE(1/2*c-1/4*%pi+1/2*d*x,2)*sin(c+d*x))/d/_ + (b*sin(c+d*x))^(1/2)/sin(c+d*x)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -16230,7 +16268,7 @@ a0037:= integrate(t0037,x) --R --R x --R ++ 1 ---R (135) | --------------------------------- d%R +--R (133) | --------------------------------- d%R --R ++ +---------------+ --R b sin(%R d + c)\|b sin(%R d + c) --R Type: Union(Expression Integer,...) @@ -16249,14 +16287,16 @@ t0038:= 1/(b*sin(c+d*x))^(5/2) --R --R --R 1 ---R (136) -------------------------------- +--R (134) -------------------------------- --R 2 2 +--------------+ --R b sin(d x + c) \|b sin(d x + c) --R Type: Expression Integer --E 209 --S 210 of 520 -r0038:= 2/3*(-cos(c+d*x)+EllipticF(1/2*c-1/4*%pi+1/2*d*x,2)*sin(c+d*x)^(3/2))/b^2/d/sin(c+d*x)/(b*sin(c+d*x))^(1/2) +r0038:= 2/3*(-cos(c+d*x)+_ + EllipticF(1/2*c-1/4*%pi+1/2*d*x,2)*_ + sin(c+d*x)^(3/2))/b^2/d/sin(c+d*x)/(b*sin(c+d*x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -16279,7 +16319,7 @@ a0038:= integrate(t0038,x) --R --R x --R ++ 1 ---R (137) | ---------------------------------- d%R +--R (135) | ---------------------------------- d%R --R ++ 2 2 +---------------+ --R b sin(%R d + c) \|b sin(%R d + c) --R Type: Union(Expression Integer,...) @@ -16299,13 +16339,20 @@ t0039:= x^2/(a+b*sin(x)) --R --R 2 --R x ---R (138) ------------ +--R (136) ------------ --R b sin(x) + a --R Type: Expression Integer --E 214 --S 215 of 520 -r0039:= -(%i*x^2*log(-%i*(-%i*a+%i*(a^2-b^2)^(1/2)-b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-%i*x^2*log(-%i*(%i*a+%i*(a^2-b^2)^(1/2)+b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+2*x*polylog(2,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-2*x*polylog(2,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+2*%i*polylog(3,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-2*%i*polylog(3,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +r0039:= -(%i*x^2*log(-%i*(-%i*a+%i*(a^2-b^2)^(1/2)-_ + b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-_ + %i*x^2*log(-%i*(%i*a+%i*(a^2-b^2)^(1/2)+_ + b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+_ + 2*x*polylog(2,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 2*x*polylog(2,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+_ + 2*%i*polylog(3,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 2*%i*polylog(3,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -16328,7 +16375,7 @@ a0039:= integrate(t0039,x) --R --R x 2 --R ++ %R ---R (139) | ------------- d%R +--R (137) | ------------- d%R --R ++ b sin(%R) + a --R Type: Union(Expression Integer,...) --E 216 @@ -16347,13 +16394,21 @@ t0040:= x^3/(a+b*sin(x)) --R --R 3 --R x ---R (140) ------------ +--R (138) ------------ --R b sin(x) + a --R Type: Expression Integer --E 219 --S 220 of 520 -r0040:= -(%i*x^3*log(-%i*(-%i*a+%i*(a^2-b^2)^(1/2)-b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-%i*x^3*log(-%i*(%i*a+%i*(a^2-b^2)^(1/2)+b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+3*x^2*polylog(2,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-3*x^2*polylog(2,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+6*%i*x*polylog(3,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-6*%i*x*polylog(3,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))-6*polylog(4,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))+6*polylog(4,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +r0040:= -(%i*x^3*log(-%i*(-%i*a+%i*(a^2-b^2)^(1/2)-b*exp(%i*x))/_ + (-a+(a^2-b^2)^(1/2)))-%i*x^3*log(-%i*(%i*a+%i*(a^2-b^2)^(1/2)+_ + b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+_ + 3*x^2*polylog(2,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 3*x^2*polylog(2,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+_ + 6*%i*x*polylog(3,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 6*%i*x*polylog(3,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))-_ + 6*polylog(4,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))+_ + 6*polylog(4,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -16376,7 +16431,7 @@ a0040:= integrate(t0040,x) --R --R x 3 --R ++ %R ---R (141) | ------------- d%R +--R (139) | ------------- d%R --R ++ b sin(%R) + a --R Type: Union(Expression Integer,...) --E 221 @@ -16394,7 +16449,7 @@ t0041:= x/(a+a*sin(x)) --R --R --R x ---R (142) ------------ +--R (140) ------------ --R a sin(x) + a --R Type: Expression Integer --E 224 @@ -16406,7 +16461,7 @@ r0041:= 2*log(cos(-1/4*%pi+1/2*x))/a-x*cot(1/4*%pi+1/2*x)/a --R 2x - %pi 2x + %pi --R 2log(cos(--------)) - x cot(--------) --R 4 4 ---R (143) ------------------------------------- +--R (141) ------------------------------------- --R a --R Type: Expression Integer --E 225 @@ -16415,7 +16470,7 @@ r0041:= 2*log(cos(-1/4*%pi+1/2*x))/a-x*cot(1/4*%pi+1/2*x)/a a0041:= integrate(t0041,x) --R --R ---R (144) +--R (142) --R sin(x) + cos(x) + 1 --R (2sin(x) + 2cos(x) + 2)log(-------------------) --R cos(x) + 1 @@ -16432,7 +16487,7 @@ a0041:= integrate(t0041,x) m0041:= a0041-r0041 --R --R ---R (145) +--R (143) --R sin(x) + cos(x) + 1 --R (2sin(x) + 2cos(x) + 2)log(-------------------) --R cos(x) + 1 @@ -16457,7 +16512,7 @@ m0041:= a0041-r0041 d0041:= D(m0041,x) --R --R ---R (146) +--R (144) --R 2x - %pi 3 --R 2cos(--------)sin(x) --R 4 @@ -16576,7 +16631,7 @@ t0042:= x/(a-a*sin(x)) --R --R --R x ---R (147) - ------------ +--R (145) - ------------ --R a sin(x) - a --R Type: Expression Integer --E 229 @@ -16588,7 +16643,7 @@ r0042:= 2*log(cos(1/4*%pi+1/2*x))/a+x*tan(1/4*%pi+1/2*x)/a --R 2x + %pi 2x + %pi --R 2log(cos(--------)) + x tan(--------) --R 4 4 ---R (148) ------------------------------------- +--R (146) ------------------------------------- --R a --R Type: Expression Integer --E 230 @@ -16597,7 +16652,7 @@ r0042:= 2*log(cos(1/4*%pi+1/2*x))/a+x*tan(1/4*%pi+1/2*x)/a a0042:= integrate(t0042,x) --R --R ---R (149) +--R (147) --R sin(x) - cos(x) - 1 --R (2sin(x) - 2cos(x) - 2)log(-------------------) --R cos(x) + 1 @@ -16614,7 +16669,7 @@ a0042:= integrate(t0042,x) m0042:= a0042-r0042 --R --R ---R (150) +--R (148) --R sin(x) - cos(x) - 1 --R (2sin(x) - 2cos(x) - 2)log(-------------------) --R cos(x) + 1 @@ -16639,7 +16694,7 @@ m0042:= a0042-r0042 d0042:= D(m0042,x) --R --R ---R (151) +--R (149) --R 2x + %pi 2x + %pi 2 --R (- x cos(--------)cos(x) - x cos(--------))sin(x) --R 4 4 @@ -16752,14 +16807,19 @@ t0043:= x/(a+b*sin(x))^2 --R --R --R x ---R (152) ---------------------------- +--R (150) ---------------------------- --R 2 2 2 --R b sin(x) + 2a b sin(x) + a --R Type: Expression Integer --E 234 --S 235 of 520 -r0043:= -%i*a*x*log(1-%i*b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+%i*a*x*log(1-%i*b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-log(a+b*sin(x))/(a^2-b^2)-a*polylog(2,%i*b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+a*polylog(2,%i*b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+b*x*cos(x)/(a^2-b^2)/(a+b*sin(x)) +r0043:= -%i*a*x*log(1-%i*b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/_ + (a^2-b^2)^(3/2)+%i*a*x*log(1-%i*b*exp(1)^(%i*x)/_ + (a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-log(a+b*sin(x))/(a^2-b^2)-_ + a*polylog(2,%i*b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+_ + a*polylog(2,%i*b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+_ + b*x*cos(x)/(a^2-b^2)/(a+b*sin(x)) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -16782,7 +16842,7 @@ a0043:= integrate(t0043,x) --R --R x --R ++ %R ---R (153) | ------------------------------ d%R +--R (151) | ------------------------------ d%R --R ++ 2 2 2 --R b sin(%R) + 2a b sin(%R) + a --R Type: Union(Expression Integer,...) @@ -16801,15 +16861,17 @@ t0044:= x*(a+a*sin(c+d*x))^(1/2) --R --R --R +------------------+ ---R (154) x\|a sin(d x + c) + a +--R (152) x\|a sin(d x + c) + a --R Type: Expression Integer --E 239 --S 240 of 520 -r0044:= 2*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*csc(1/2*c+1/4*%pi+1/2*d*x)*(2*sin(1/2*c+1/4*%pi+1/2*d*x)-d*x*cos(1/2*c+1/4*%pi+1/2*d*x))/d^2 +r0044:= 2*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + csc(1/2*c+1/4*%pi+1/2*d*x)*(2*sin(1/2*c+1/4*%pi+1/2*d*x)-_ + d*x*cos(1/2*c+1/4*%pi+1/2*d*x))/d^2 --R --R ---R (155) +--R (153) --R +-+ 2d x + %pi + 2c 2d x + %pi + 2c --R 4\|2 csc(---------------)sin(---------------) --R 4 4 @@ -16840,65 +16902,11 @@ a0044:= integrate(t0044,x) --E 241 --S 242 of 520 -m0044:= a0044-r0044 ---R ---R ---R (156) ---R +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R - 4\|2 csc(---------------)sin(---------------) ---R 4 4 ---R + ---R +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R 2d x\|2 cos(---------------)csc(---------------) ---R 4 4 ---R * ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R |a sin(---------------) ---R \| 4 ---R + ---R 2 ---R a0044 d ---R / ---R 2 ---R d ---R Type: Expression Integer +--m0044:= a0044-r0044 --E 242 --S 243 of 520 -d0044:= D(m0044,x) ---R ---R ---R (157) ---R +-+ 2d x + %pi + 2c +-+ 2d x + %pi + 2c ---R (2a\|2 cot(---------------) - a d x\|2 )csc(---------------) ---R 4 4 ---R * ---R 2d x + %pi + 2c 3 ---R sin(---------------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R - a d x\|2 cos(---------------)cot(---------------) ---R 4 4 ---R + ---R +-+ 2d x + %pi + 2c ---R - 2a\|2 cos(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c 2d x + %pi + 2c 2 ---R csc(---------------)sin(---------------) ---R 4 4 ---R + ---R +-+ 2d x + %pi + 2c 2 2d x + %pi + 2c 2d x + %pi + 2c ---R a d x\|2 cos(---------------) csc(---------------)sin(---------------) ---R 4 4 4 ---R / ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R d |a sin(---------------) ---R \| 4 ---R Type: Expression Integer +--d0044:= D(m0044,x) --E 243 --S 244 of 520 @@ -16906,15 +16914,17 @@ t0045:= x^2*(a+a*sin(c+d*x))^(1/2) --R --R --R 2 +------------------+ ---R (158) x \|a sin(d x + c) + a +--R (154) x \|a sin(d x + c) + a --R Type: Expression Integer --E 244 --S 245 of 520 -r0045:= 2*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*csc(1/2*c+1/4*%pi+1/2*d*x)*(4*d*x*sin(1/2*c+1/4*%pi+1/2*d*x)+(8-d^2*x^2)*cos(1/2*c+1/4*%pi+1/2*d*x))/d^3 +r0045:= 2*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + csc(1/2*c+1/4*%pi+1/2*d*x)*(4*d*x*sin(1/2*c+1/4*%pi+1/2*d*x)+_ + (8-d^2*x^2)*cos(1/2*c+1/4*%pi+1/2*d*x))/d^3 --R --R ---R (159) +--R (155) --R +-+ 2d x + %pi + 2c 2d x + %pi + 2c --R 8d x\|2 csc(---------------)sin(---------------) --R 4 4 @@ -16945,69 +16955,11 @@ a0045:= integrate(t0045,x) --E 246 --S 247 of 520 -m0045:= a0045-r0045 ---R ---R ---R (160) ---R +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R - 8d x\|2 csc(---------------)sin(---------------) ---R 4 4 ---R + ---R 2 2 +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R (2d x - 16)\|2 cos(---------------)csc(---------------) ---R 4 4 ---R * ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R |a sin(---------------) ---R \| 4 ---R + ---R 3 ---R a0045 d ---R / ---R 3 ---R d ---R Type: Expression Integer +--m0045:= a0045-r0045 --E 247 --S 248 of 520 -d0045:= D(m0045,x) ---R ---R ---R (161) ---R +-+ 2d x + %pi + 2c 2 2 +-+ 2d x + %pi + 2c ---R (4a d x\|2 cot(---------------) - a d x \|2 )csc(---------------) ---R 4 4 ---R * ---R 2d x + %pi + 2c 3 ---R sin(---------------) ---R 4 ---R + ---R 2 2 +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R (- a d x + 8a)\|2 cos(---------------)cot(---------------) ---R 4 4 ---R + ---R +-+ 2d x + %pi + 2c ---R - 4a d x\|2 cos(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c 2d x + %pi + 2c 2 ---R csc(---------------)sin(---------------) ---R 4 4 ---R + ---R 2 2 +-+ 2d x + %pi + 2c 2 2d x + %pi + 2c ---R (a d x - 8a)\|2 cos(---------------) csc(---------------) ---R 4 4 ---R * ---R 2d x + %pi + 2c ---R sin(---------------) ---R 4 ---R / ---R +-----------------------+ ---R 2 | 2d x + %pi + 2c 2 ---R d |a sin(---------------) ---R \| 4 ---R Type: Expression Integer +--d0045:= D(m0045,x) --E 248 --S 249 of 520 @@ -17015,15 +16967,17 @@ t0046:= x*(a-a*sin(c+d*x))^(1/2) --R --R --R +--------------------+ ---R (162) x\|- a sin(d x + c) + a +--R (156) x\|- a sin(d x + c) + a --R Type: Expression Integer --E 249 --S 250 of 520 -r0046:= 2*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/4*%pi+1/2*d*x)*(2*cos(1/2*c+1/4*%pi+1/2*d*x)+d*x*sin(1/2*c+1/4*%pi+1/2*d*x))/d^2 +r0046:= 2*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + sec(1/2*c+1/4*%pi+1/2*d*x)*(2*cos(1/2*c+1/4*%pi+1/2*d*x)+_ + d*x*sin(1/2*c+1/4*%pi+1/2*d*x))/d^2 --R --R ---R (163) +--R (157) --R +-+ 2d x + %pi + 2c 2d x + %pi + 2c --R 2d x\|2 sec(---------------)sin(---------------) --R 4 4 @@ -17054,70 +17008,11 @@ a0046:= integrate(t0046,x) --E 251 --S 252 of 520 -m0046:= a0046-r0046 ---R ---R ---R (164) ---R +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R - 2d x\|2 sec(---------------)sin(---------------) ---R 4 4 ---R + ---R +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R - 4\|2 cos(---------------)sec(---------------) ---R 4 4 ---R * ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R |a cos(---------------) ---R \| 4 ---R + ---R 2 ---R a0046 d ---R / ---R 2 ---R d ---R Type: Expression Integer +--m0046:= a0046-r0046 --E 252 --S 253 of 520 -d0046:= D(m0046,x) ---R ---R ---R (165) ---R - ---R +-+ 2d x + %pi + 2c 2 2d x + %pi + 2c ---R a d x\|2 cos(---------------) sec(---------------) ---R 4 4 ---R * ---R 2d x + %pi + 2c ---R sin(---------------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c 3 2d x + %pi + 2c ---R - 2a\|2 cos(---------------) sec(---------------) ---R 4 4 ---R * ---R 2d x + %pi + 2c ---R tan(---------------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c 2d x + %pi + 2c 2d x + %pi + 2c 2 ---R a d x\|2 cos(---------------)sec(---------------)sin(---------------) ---R 4 4 4 ---R + ---R +-+ 2d x + %pi + 2c 2 2d x + %pi + 2c 2d x + %pi + 2c ---R 2a\|2 cos(---------------) sec(---------------)sin(---------------) ---R 4 4 4 ---R + ---R +-+ 2d x + %pi + 2c 3 2d x + %pi + 2c ---R - a d x\|2 cos(---------------) sec(---------------) ---R 4 4 ---R / ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R d |a cos(---------------) ---R \| 4 ---R Type: Expression Integer +--d0046:= D(m0046,x) --E 253 --S 254 of 520 @@ -17125,15 +17020,17 @@ t0047:= x^2*(a-a*sin(c+d*x))^(1/2) --R --R --R 2 +--------------------+ ---R (166) x \|- a sin(d x + c) + a +--R (158) x \|- a sin(d x + c) + a --R Type: Expression Integer --E 254 --S 255 of 520 -r0047:= 2*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/4*%pi+1/2*d*x)*(4*d*x*cos(1/2*c+1/4*%pi+1/2*d*x)-(8-d^2*x^2)*sin(1/2*c+1/4*%pi+1/2*d*x))/d^3 +r0047:= 2*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + sec(1/2*c+1/4*%pi+1/2*d*x)*(4*d*x*cos(1/2*c+1/4*%pi+1/2*d*x)-_ + (8-d^2*x^2)*sin(1/2*c+1/4*%pi+1/2*d*x))/d^3 --R --R ---R (167) +--R (159) --R 2 2 +-+ 2d x + %pi + 2c 2d x + %pi + 2c --R (2d x - 16)\|2 sec(---------------)sin(---------------) --R 4 4 @@ -17164,73 +17061,11 @@ a0047:= integrate(t0047,x) --E 256 --S 257 of 520 -m0047:= a0047-r0047 ---R ---R ---R (168) ---R 2 2 +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R (- 2d x + 16)\|2 sec(---------------)sin(---------------) ---R 4 4 ---R + ---R +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R - 8d x\|2 cos(---------------)sec(---------------) ---R 4 4 ---R * ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R |a cos(---------------) ---R \| 4 ---R + ---R 3 ---R a0047 d ---R / ---R 3 ---R d ---R Type: Expression Integer +--m0047:= a0047-r0047 --E 257 --S 258 of 520 -d0047:= D(m0047,x) ---R ---R ---R (169) ---R 2 2 +-+ 2d x + %pi + 2c 2 2d x + %pi + 2c ---R (- a d x + 8a)\|2 cos(---------------) sec(---------------) ---R 4 4 ---R * ---R 2d x + %pi + 2c ---R sin(---------------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c 3 2d x + %pi + 2c ---R - 4a d x\|2 cos(---------------) sec(---------------) ---R 4 4 ---R * ---R 2d x + %pi + 2c ---R tan(---------------) ---R 4 ---R + ---R 2 2 +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R (a d x - 8a)\|2 cos(---------------)sec(---------------) ---R 4 4 ---R * ---R 2d x + %pi + 2c 2 ---R sin(---------------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c 2 2d x + %pi + 2c 2d x + %pi + 2c ---R 4a d x\|2 cos(---------------) sec(---------------)sin(---------------) ---R 4 4 4 ---R + ---R 2 2 +-+ 2d x + %pi + 2c 3 2d x + %pi + 2c ---R - a d x \|2 cos(---------------) sec(---------------) ---R 4 4 ---R / ---R +-----------------------+ ---R 2 | 2d x + %pi + 2c 2 ---R d |a cos(---------------) ---R \| 4 ---R Type: Expression Integer +--d0047:= D(m0047,x) --E 258 --S 259 of 520 @@ -17239,16 +17074,18 @@ t0048:= (a+a*sin(c+d*x))^(1/2)/x --R --R +------------------+ --R \|a sin(d x + c) + a ---R (170) --------------------- +--R (160) --------------------- --R x --R Type: Expression Integer --E 259 --S 260 of 520 -r0048:= 2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*csc(1/2*c+1/4*%pi+1/2*d*x)*(sin(1/2*c+1/4*%pi)*Ci(1/2*d*x)+cos(1/2*c+1/4*%pi)*Si(1/2*d*x)) +r0048:= 2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + csc(1/2*c+1/4*%pi+1/2*d*x)*(sin(1/2*c+1/4*%pi)*Ci(1/2*d*x)+_ + cos(1/2*c+1/4*%pi)*Si(1/2*d*x)) --R --R ---R (171) +--R (161) --R +-+ d x 2d x + %pi + 2c %pi + 2c --R \|2 Ci(---)csc(---------------)sin(--------) --R 2 4 4 @@ -17276,74 +17113,11 @@ a0048:= integrate(t0048,x) --E 261 --S 262 of 520 -m0048:= a0048-r0048 ---R ---R ---R (172) ---R +-+ d x 2d x + %pi + 2c %pi + 2c ---R - \|2 Ci(---)csc(---------------)sin(--------) ---R 2 4 4 ---R + ---R +-+ d x %pi + 2c 2d x + %pi + 2c ---R - \|2 Si(---)cos(--------)csc(---------------) ---R 2 4 4 ---R * ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R |a sin(---------------) ---R \| 4 ---R + ---R a0048 ---R Type: Expression Integer +--m0048:= a0048-r0048 --E 262 --S 263 of 520 -d0048:= D(m0048,x) ---R ---R ---R (173) ---R +-+ %pi + 2c 2d x + %pi + 2c d x ---R - 2a\|2 cos(--------)csc(---------------)sin(---) ---R 4 4 2 ---R + ---R +-+ d x 2d x + %pi + 2c +-+ d x ---R (a d x\|2 Ci(---)cot(---------------) - 2a\|2 cos(---)) ---R 2 4 2 ---R * ---R 2d x + %pi + 2c %pi + 2c ---R csc(---------------)sin(--------) ---R 4 4 ---R + ---R +-+ d x %pi + 2c 2d x + %pi + 2c 2d x + %pi + 2c ---R a d x\|2 Si(---)cos(--------)cot(---------------)csc(---------------) ---R 2 4 4 4 ---R * ---R 2d x + %pi + 2c 2 ---R sin(---------------) ---R 4 ---R + ---R - ---R +-+ d x 2d x + %pi + 2c 2d x + %pi + 2c ---R a d x\|2 Ci(---)cos(---------------)csc(---------------) ---R 2 4 4 ---R * ---R %pi + 2c ---R sin(--------) ---R 4 ---R + ---R +-+ d x %pi + 2c 2d x + %pi + 2c 2d x + %pi + 2c ---R - a d x\|2 Si(---)cos(--------)cos(---------------)csc(---------------) ---R 2 4 4 4 ---R * ---R 2d x + %pi + 2c ---R sin(---------------) ---R 4 ---R / ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R 2x |a sin(---------------) ---R \| 4 ---R Type: Expression Integer +--d0048:= D(m0048,x) --E 263 --S 264 of 520 @@ -17352,17 +17126,19 @@ t0049:= (a+a*sin(c+d*x))^(1/2)/x^2 --R --R +------------------+ --R \|a sin(d x + c) + a ---R (174) --------------------- +--R (162) --------------------- --R 2 --R x --R Type: Expression Integer --E 264 --S 265 of 520 -r0049:= -1/2*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*csc(1/2*c+1/4*%pi+1/2*d*x)*(2*sin(1/2*c+1/4*%pi+1/2*d*x)/x-d*Ci(1/2*d*x)*cos(1/2*c+1/4*%pi)+d*sin(1/2*c+1/4*%pi)*Si(1/2*d*x)) +r0049:= -1/2*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + csc(1/2*c+1/4*%pi+1/2*d*x)*(2*sin(1/2*c+1/4*%pi+1/2*d*x)/x-_ + d*Ci(1/2*d*x)*cos(1/2*c+1/4*%pi)+d*sin(1/2*c+1/4*%pi)*Si(1/2*d*x)) --R --R ---R (175) +--R (163) --R +-+ 2d x + %pi + 2c 2d x + %pi + 2c --R - 2\|2 csc(---------------)sin(---------------) --R 4 4 @@ -17396,101 +17172,11 @@ a0049:= integrate(t0049,x) --E 266 --S 267 of 520 -m0049:= a0049-r0049 ---R ---R ---R (176) ---R +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R 2\|2 csc(---------------)sin(---------------) ---R 4 4 ---R + ---R +-+ d x 2d x + %pi + 2c %pi + 2c ---R d x\|2 Si(---)csc(---------------)sin(--------) ---R 2 4 4 ---R + ---R +-+ d x %pi + 2c 2d x + %pi + 2c ---R - d x\|2 Ci(---)cos(--------)csc(---------------) ---R 2 4 4 ---R * ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R |a sin(---------------) ---R \| 4 ---R + ---R 2a0049 x ---R / ---R 2x ---R Type: Expression Integer +--m0049:= a0049-r0049 --E 267 --S 268 of 520 -d0049:= D(m0049,x) ---R ---R ---R (177) ---R +-+ 2d x + %pi + 2c +-+ 2d x + %pi + 2c ---R (- 2a d x\|2 cot(---------------) - 4a\|2 )csc(---------------) ---R 4 4 ---R * ---R 2d x + %pi + 2c 3 ---R sin(---------------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c %pi + 2c d x ---R 2a d x\|2 csc(---------------)sin(--------)sin(---) ---R 4 4 2 ---R + ---R - ---R 2 2 +-+ d x 2d x + %pi + 2c 2d x + %pi + 2c ---R a d x \|2 Si(---)cot(---------------)csc(---------------) ---R 2 4 4 ---R * ---R %pi + 2c ---R sin(--------) ---R 4 ---R + ---R 2 2 +-+ d x %pi + 2c 2d x + %pi + 2c ---R a d x \|2 Ci(---)cos(--------)cot(---------------) ---R 2 4 4 ---R + ---R +-+ 2d x + %pi + 2c +-+ %pi + 2c d x ---R 4a d x\|2 cos(---------------) - 2a d x\|2 cos(--------)cos(---) ---R 4 4 2 ---R * ---R 2d x + %pi + 2c ---R csc(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c 2 ---R sin(---------------) ---R 4 ---R + ---R 2 2 +-+ d x 2d x + %pi + 2c 2d x + %pi + 2c ---R a d x \|2 Si(---)cos(---------------)csc(---------------) ---R 2 4 4 ---R * ---R %pi + 2c ---R sin(--------) ---R 4 ---R + ---R - ---R 2 2 +-+ d x %pi + 2c 2d x + %pi + 2c ---R a d x \|2 Ci(---)cos(--------)cos(---------------) ---R 2 4 4 ---R * ---R 2d x + %pi + 2c ---R csc(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c ---R sin(---------------) ---R 4 ---R / ---R +-----------------------+ ---R 2 | 2d x + %pi + 2c 2 ---R 4x |a sin(---------------) ---R \| 4 ---R Type: Expression Integer +--d0049:= D(m0049,x) --E 268 --S 269 of 520 @@ -17499,17 +17185,20 @@ t0050:= (a+a*sin(c+d*x))^(1/2)/x^3 --R --R +------------------+ --R \|a sin(d x + c) + a ---R (178) --------------------- +--R (164) --------------------- --R 3 --R x --R Type: Expression Integer --E 269 --S 270 of 520 -r0050:= -1/8*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*csc(1/2*c+1/4*%pi+1/2*d*x)*(4*sin(1/2*c+1/4*%pi+1/2*d*x)/x^2+d^2*sin(1/2*c+1/4*%pi)*Ci(1/2*d*x)+2*d*cos(1/2*c+1/4*%pi+1/2*d*x)/x+d^2*cos(1/2*c+1/4*%pi)*Si(1/2*d*x)) +r0050:= -1/8*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + csc(1/2*c+1/4*%pi+1/2*d*x)*(4*sin(1/2*c+1/4*%pi+1/2*d*x)/x^2+_ + d^2*sin(1/2*c+1/4*%pi)*Ci(1/2*d*x)+_ + 2*d*cos(1/2*c+1/4*%pi+1/2*d*x)/x+d^2*cos(1/2*c+1/4*%pi)*Si(1/2*d*x)) --R --R ---R (179) +--R (165) --R +-+ 2d x + %pi + 2c 2d x + %pi + 2c --R - 4\|2 csc(---------------)sin(---------------) --R 4 4 @@ -17548,117 +17237,11 @@ a0050:= integrate(t0050,x) --E 271 --S 272 of 520 -m0050:= a0050-r0050 ---R ---R ---R (180) ---R +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R 4\|2 csc(---------------)sin(---------------) ---R 4 4 ---R + ---R 2 2 +-+ d x 2d x + %pi + 2c %pi + 2c ---R d x \|2 Ci(---)csc(---------------)sin(--------) ---R 2 4 4 ---R + ---R +-+ 2d x + %pi + 2c 2 2 +-+ d x %pi + 2c ---R (2d x\|2 cos(---------------) + d x \|2 Si(---)cos(--------)) ---R 4 2 4 ---R * ---R 2d x + %pi + 2c ---R csc(---------------) ---R 4 ---R * ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R |a sin(---------------) ---R \| 4 ---R + ---R 2 ---R 8a0050 x ---R / ---R 2 ---R 8x ---R Type: Expression Integer +--m0050:= a0050-r0050 --E 272 --S 273 of 520 -d0050:= D(m0050,x) ---R ---R ---R (181) ---R +-+ 2d x + %pi + 2c 2 2 +-+ ---R (- 4a d x\|2 cot(---------------) + (- 2a d x - 16a)\|2 ) ---R 4 ---R * ---R 2d x + %pi + 2c 2d x + %pi + 2c 3 ---R csc(---------------)sin(---------------) ---R 4 4 ---R + ---R 2 2 +-+ %pi + 2c 2d x + %pi + 2c d x ---R 2a d x \|2 cos(--------)csc(---------------)sin(---) ---R 4 4 2 ---R + ---R 3 3 +-+ d x 2d x + %pi + 2c 2 2 +-+ d x ---R (- a d x \|2 Ci(---)cot(---------------) + 2a d x \|2 cos(---)) ---R 2 4 2 ---R * ---R 2d x + %pi + 2c %pi + 2c ---R csc(---------------)sin(--------) ---R 4 4 ---R + ---R 2 2 +-+ 2d x + %pi + 2c ---R - 2a d x \|2 cos(---------------) ---R 4 ---R + ---R 3 3 +-+ d x %pi + 2c ---R - a d x \|2 Si(---)cos(--------) ---R 2 4 ---R * ---R 2d x + %pi + 2c ---R cot(---------------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c ---R 4a d x\|2 cos(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c ---R csc(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c 2 ---R sin(---------------) ---R 4 ---R + ---R 3 3 +-+ d x 2d x + %pi + 2c 2d x + %pi + 2c ---R a d x \|2 Ci(---)cos(---------------)csc(---------------) ---R 2 4 4 ---R * ---R %pi + 2c ---R sin(--------) ---R 4 ---R + ---R 2 2 +-+ 2d x + %pi + 2c 2 ---R 2a d x \|2 cos(---------------) ---R 4 ---R + ---R 3 3 +-+ d x %pi + 2c 2d x + %pi + 2c ---R a d x \|2 Si(---)cos(--------)cos(---------------) ---R 2 4 4 ---R * ---R 2d x + %pi + 2c ---R csc(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c ---R sin(---------------) ---R 4 ---R / ---R +-----------------------+ ---R 3 | 2d x + %pi + 2c 2 ---R 16x |a sin(---------------) ---R \| 4 ---R Type: Expression Integer +--d0050:= D(m0050,x) --E 273 --S 274 of 520 @@ -17667,16 +17250,18 @@ t0051:= (a-a*sin(c+d*x))^(1/2)/x --R --R +--------------------+ --R \|- a sin(d x + c) + a ---R (182) ----------------------- +--R (166) ----------------------- --R x --R Type: Expression Integer --E 274 --S 275 of 520 -r0051:= 2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/4*%pi+1/2*d*x)*(cos(1/2*c+1/4*%pi)*Ci(1/2*d*x)-sin(1/2*c+1/4*%pi)*Si(1/2*d*x)) +r0051:= 2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/4*%pi+_ + 1/2*d*x)*(cos(1/2*c+1/4*%pi)*Ci(1/2*d*x)-_ + sin(1/2*c+1/4*%pi)*Si(1/2*d*x)) --R --R ---R (183) +--R (167) --R +-+ d x 2d x + %pi + 2c %pi + 2c --R - \|2 Si(---)sec(---------------)sin(--------) --R 2 4 4 @@ -17704,83 +17289,11 @@ a0051:= integrate(t0051,x) --E 276 --S 277 of 520 -m0051:= a0051-r0051 ---R ---R ---R (184) ---R +-+ d x 2d x + %pi + 2c %pi + 2c ---R \|2 Si(---)sec(---------------)sin(--------) ---R 2 4 4 ---R + ---R +-+ d x %pi + 2c 2d x + %pi + 2c ---R - \|2 Ci(---)cos(--------)sec(---------------) ---R 2 4 4 ---R * ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R |a cos(---------------) ---R \| 4 ---R + ---R a0051 ---R Type: Expression Integer +--m0051:= a0051-r0051 --E 277 --S 278 of 520 -d0051:= D(m0051,x) ---R ---R ---R (185) ---R +-+ d x 2d x + %pi + 2c 2 2d x + %pi + 2c ---R a d x\|2 Si(---)cos(---------------) sec(---------------) ---R 2 4 4 ---R * ---R %pi + 2c ---R sin(--------) ---R 4 ---R + ---R - ---R +-+ d x %pi + 2c 2d x + %pi + 2c 2 ---R a d x\|2 Ci(---)cos(--------)cos(---------------) ---R 2 4 4 ---R * ---R 2d x + %pi + 2c ---R sec(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c ---R tan(---------------) ---R 4 ---R + ---R - ---R +-+ d x 2d x + %pi + 2c 2d x + %pi + 2c ---R a d x\|2 Si(---)cos(---------------)sec(---------------) ---R 2 4 4 ---R * ---R %pi + 2c ---R sin(--------) ---R 4 ---R + ---R +-+ d x %pi + 2c 2d x + %pi + 2c 2d x + %pi + 2c ---R a d x\|2 Ci(---)cos(--------)cos(---------------)sec(---------------) ---R 2 4 4 4 ---R * ---R 2d x + %pi + 2c ---R sin(---------------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c 2 2d x + %pi + 2c %pi + 2c d x ---R 2a\|2 cos(---------------) sec(---------------)sin(--------)sin(---) ---R 4 4 4 2 ---R + ---R +-+ %pi + 2c d x 2d x + %pi + 2c 2 2d x + %pi + 2c ---R - 2a\|2 cos(--------)cos(---)cos(---------------) sec(---------------) ---R 4 2 4 4 ---R / ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R 2x |a cos(---------------) ---R \| 4 ---R Type: Expression Integer +--d0051:= D(m0051,x) --E 278 --S 279 of 520 @@ -17789,17 +17302,19 @@ t0052:= (a-a*sin(c+d*x))^(1/2)/x^2 --R --R +--------------------+ --R \|- a sin(d x + c) + a ---R (186) ----------------------- +--R (168) ----------------------- --R 2 --R x --R Type: Expression Integer --E 279 --S 280 of 520 -r0052:= -1/2*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/4*%pi+1/2*d*x)*(2*cos(1/2*c+1/4*%pi+1/2*d*x)/x+d*Ci(1/2*d*x)*sin(1/2*c+1/4*%pi)+d*cos(1/2*c+1/4*%pi)*Si(1/2*d*x)) +r0052:= -1/2*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + sec(1/2*c+1/4*%pi+1/2*d*x)*(2*cos(1/2*c+1/4*%pi+1/2*d*x)/x+_ + d*Ci(1/2*d*x)*sin(1/2*c+1/4*%pi)+d*cos(1/2*c+1/4*%pi)*Si(1/2*d*x)) --R --R ---R (187) +--R (169) --R +-+ d x 2d x + %pi + 2c %pi + 2c --R - d x\|2 Ci(---)sec(---------------)sin(--------) --R 2 4 4 @@ -17833,104 +17348,11 @@ a0052:= integrate(t0052,x) --E 281 --S 282 of 520 -m0052:= a0052-r0052 ---R ---R ---R (188) ---R +-+ d x 2d x + %pi + 2c %pi + 2c ---R d x\|2 Ci(---)sec(---------------)sin(--------) ---R 2 4 4 ---R + ---R +-+ 2d x + %pi + 2c +-+ d x %pi + 2c ---R (2\|2 cos(---------------) + d x\|2 Si(---)cos(--------)) ---R 4 2 4 ---R * ---R 2d x + %pi + 2c ---R sec(---------------) ---R 4 ---R * ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R |a cos(---------------) ---R \| 4 ---R + ---R 2a0052 x ---R / ---R 2x ---R Type: Expression Integer +--m0052:= a0052-r0052 --E 282 --S 283 of 520 -d0052:= D(m0052,x) ---R ---R ---R (189) ---R 2 2 +-+ d x 2d x + %pi + 2c 2 2d x + %pi + 2c ---R a d x \|2 Ci(---)cos(---------------) sec(---------------) ---R 2 4 4 ---R * ---R %pi + 2c ---R sin(--------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c 3 ---R 2a d x\|2 cos(---------------) ---R 4 ---R + ---R 2 2 +-+ d x %pi + 2c 2d x + %pi + 2c 2 ---R a d x \|2 Si(---)cos(--------)cos(---------------) ---R 2 4 4 ---R * ---R 2d x + %pi + 2c ---R sec(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c ---R tan(---------------) ---R 4 ---R + ---R - ---R 2 2 +-+ d x 2d x + %pi + 2c 2d x + %pi + 2c ---R a d x \|2 Ci(---)cos(---------------)sec(---------------) ---R 2 4 4 ---R * ---R %pi + 2c ---R sin(--------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c 2 ---R - 4a d x\|2 cos(---------------) ---R 4 ---R + ---R 2 2 +-+ d x %pi + 2c 2d x + %pi + 2c ---R - a d x \|2 Si(---)cos(--------)cos(---------------) ---R 2 4 4 ---R * ---R 2d x + %pi + 2c ---R sec(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c ---R sin(---------------) ---R 4 ---R + ---R +-+ %pi + 2c 2d x + %pi + 2c 2 2d x + %pi + 2c d x ---R 2a d x\|2 cos(--------)cos(---------------) sec(---------------)sin(---) ---R 4 4 4 2 ---R + ---R +-+ d x 2d x + %pi + 2c 2 2d x + %pi + 2c %pi + 2c ---R 2a d x\|2 cos(---)cos(---------------) sec(---------------)sin(--------) ---R 2 4 4 4 ---R + ---R +-+ 2d x + %pi + 2c 3 2d x + %pi + 2c ---R - 4a\|2 cos(---------------) sec(---------------) ---R 4 4 ---R / ---R +-----------------------+ ---R 2 | 2d x + %pi + 2c 2 ---R 4x |a cos(---------------) ---R \| 4 ---R Type: Expression Integer +--d0052:= D(m0052,x) --E 283 --S 284 of 520 @@ -17939,17 +17361,20 @@ t0053:= (a-a*sin(c+d*x))^(1/2)/x^3 --R --R +--------------------+ --R \|- a sin(d x + c) + a ---R (190) ----------------------- +--R (170) ----------------------- --R 3 --R x --R Type: Expression Integer --E 284 --S 285 of 520 -r0053:= -1/8*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/4*%pi+1/2*d*x)*(4*cos(1/2*c+1/4*%pi+1/2*d*x)/x^2+d^2*cos(1/2*c+1/4*%pi)*Ci(1/2*d*x)-2*d*sin(1/2*c+1/4*%pi+1/2*d*x)/x-d^2*sin(1/2*c+1/4*%pi)*Si(1/2*d*x)) +r0053:= -1/8*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + sec(1/2*c+1/4*%pi+1/2*d*x)*(4*cos(1/2*c+1/4*%pi+1/2*d*x)/x^2+_ + d^2*cos(1/2*c+1/4*%pi)*Ci(1/2*d*x)-_ + 2*d*sin(1/2*c+1/4*%pi+1/2*d*x)/x-d^2*sin(1/2*c+1/4*%pi)*Si(1/2*d*x)) --R --R ---R (191) +--R (171) --R +-+ 2d x + %pi + 2c 2d x + %pi + 2c --R 2d x\|2 sec(---------------)sin(---------------) --R 4 4 @@ -17988,132 +17413,11 @@ a0053:= integrate(t0053,x) --E 286 --S 287 of 520 -m0053:= a0053-r0053 ---R ---R ---R (192) ---R +-+ 2d x + %pi + 2c 2d x + %pi + 2c ---R - 2d x\|2 sec(---------------)sin(---------------) ---R 4 4 ---R + ---R 2 2 +-+ d x 2d x + %pi + 2c %pi + 2c ---R - d x \|2 Si(---)sec(---------------)sin(--------) ---R 2 4 4 ---R + ---R +-+ 2d x + %pi + 2c 2 2 +-+ d x %pi + 2c ---R (4\|2 cos(---------------) + d x \|2 Ci(---)cos(--------)) ---R 4 2 4 ---R * ---R 2d x + %pi + 2c ---R sec(---------------) ---R 4 ---R * ---R +-----------------------+ ---R | 2d x + %pi + 2c 2 ---R |a cos(---------------) ---R \| 4 ---R + ---R 2 ---R 8a0053 x ---R / ---R 2 ---R 8x ---R Type: Expression Integer +--m0053:= a0053-r0053 --E 287 --S 288 of 520 -d0053:= D(m0053,x) ---R ---R ---R (193) ---R - ---R 2 2 +-+ 2d x + %pi + 2c 2 2d x + %pi + 2c ---R 2a d x \|2 cos(---------------) sec(---------------) ---R 4 4 ---R * ---R 2d x + %pi + 2c ---R sin(---------------) ---R 4 ---R + ---R - ---R 3 3 +-+ d x 2d x + %pi + 2c 2 2d x + %pi + 2c ---R a d x \|2 Si(---)cos(---------------) sec(---------------) ---R 2 4 4 ---R * ---R %pi + 2c ---R sin(--------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c 3 ---R 4a d x\|2 cos(---------------) ---R 4 ---R + ---R 3 3 +-+ d x %pi + 2c 2d x + %pi + 2c 2 ---R a d x \|2 Ci(---)cos(--------)cos(---------------) ---R 2 4 4 ---R * ---R 2d x + %pi + 2c ---R sec(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c ---R tan(---------------) ---R 4 ---R + ---R 2 2 +-+ 2d x + %pi + 2c 2d x + %pi + 2c 2d x + %pi + 2c 2 ---R 2a d x \|2 cos(---------------)sec(---------------)sin(---------------) ---R 4 4 4 ---R + ---R 3 3 +-+ d x 2d x + %pi + 2c 2d x + %pi + 2c ---R a d x \|2 Si(---)cos(---------------)sec(---------------) ---R 2 4 4 ---R * ---R %pi + 2c ---R sin(--------) ---R 4 ---R + ---R +-+ 2d x + %pi + 2c 2 ---R - 4a d x\|2 cos(---------------) ---R 4 ---R + ---R 3 3 +-+ d x %pi + 2c 2d x + %pi + 2c ---R - a d x \|2 Ci(---)cos(--------)cos(---------------) ---R 2 4 4 ---R * ---R 2d x + %pi + 2c ---R sec(---------------) ---R 4 ---R * ---R 2d x + %pi + 2c ---R sin(---------------) ---R 4 ---R + ---R - ---R 2 2 +-+ 2d x + %pi + 2c 2 2d x + %pi + 2c %pi + 2c ---R 2a d x \|2 cos(---------------) sec(---------------)sin(--------) ---R 4 4 4 ---R * ---R d x ---R sin(---) ---R 2 ---R + ---R 2 2 +-+ 2d x + %pi + 2c 3 ---R (- 2a d x - 16a)\|2 cos(---------------) ---R 4 ---R + ---R 2 2 +-+ %pi + 2c d x 2d x + %pi + 2c 2 ---R 2a d x \|2 cos(--------)cos(---)cos(---------------) ---R 4 2 4 ---R * ---R 2d x + %pi + 2c ---R sec(---------------) ---R 4 ---R / ---R +-----------------------+ ---R 3 | 2d x + %pi + 2c 2 ---R 16x |a cos(---------------) ---R \| 4 ---R Type: Expression Integer +--d0053:= D(m0053,x) --E 288 --S 289 of 520 @@ -18121,17 +17425,18 @@ t0054:= 1/(a+b*sin(x)^2)^2 --R --R --R 1 ---R (194) ----------------------------- +--R (172) ----------------------------- --R 2 4 2 2 --R b sin(x) + 2a b sin(x) + a --R Type: Expression Integer --E 289 --S 290 of 520 -r0054:= 1/2*(2*a+b)*atan((a+b)^(1/2)*tan(x)/a^(1/2))/a^(3/2)/(a+b)^(3/2)+1/2*b*tan(x)/a/(a+b)/(a+(a+b)*tan(x)^2) +r0054:= 1/2*(2*a+b)*atan((a+b)^(1/2)*tan(x)/a^(1/2))/a^(3/2)/(a+b)^(3/2)+_ + 1/2*b*tan(x)/a/(a+b)/(a+(a+b)*tan(x)^2) --R --R ---R (195) +--R (173) --R +-----+ --R 2 2 2 2 tan(x)\|b + a --R ((b + 3a b + 2a )tan(x) + a b + 2a )atan(--------------) @@ -18150,7 +17455,7 @@ r0054:= 1/2*(2*a+b)*atan((a+b)^(1/2)*tan(x)/a^(1/2))/a^(3/2)/(a+b)^(3/2)+1/2*b*t a0054:= integrate(t0054,x) --R --R ---R (196) +--R (174) --R [ --R 2 2 2 2 --R ((b + 2a b)cos(x) - b - 3a b - 2a ) @@ -18205,7 +17510,7 @@ a0054:= integrate(t0054,x) m0054a:= a0054.1-r0054 --R --R ---R (197) +--R (175) --R 3 2 2 2 3 2 2 3 2 --R ((b + 3a b + 2a b)cos(x) - b - 4a b - 5a b - 2a )tan(x) --R + @@ -18259,7 +17564,7 @@ m0054a:= a0054.1-r0054 d0054a:= D(m0054a,x) --R --R ---R (198) +--R (176) --R 3 2 2 2 3 2 2 3 2 --R ((- b - 2a b - a b)cos(x) - b - 3a b - 3a b - a )sin(x) --R + @@ -18417,7 +17722,7 @@ d0054a:= D(m0054a,x) m0054b:= a0054.2-r0054 --R --R ---R (199) +--R (177) --R 3 2 2 2 3 2 2 3 2 --R ((b + 3a b + 2a b)cos(x) - b - 4a b - 5a b - 2a )tan(x) --R + @@ -18476,972 +17781,7 @@ m0054b:= a0054.2-r0054 --E 294 --S 295 of 520 -d0054b:= D(m0054b,x) ---R ---R ---R (200) ---R 6 2 5 3 4 4 3 5 2 4 ---R (- 4a b - 12a b - 13a b - 6a b - a b )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 3 ---R (- 8a b - 28a b - 36a b - 20a b - 4a b )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 2 ---R (- 8a b - 32a b - 49a b - 35a b - 11a b - a b)cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R (- 8a b - 36a b - 64a b - 56a b - 24a b - 4a b)cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R - 4a b - 20a b - 40a b - 40a b - 20a b - 4a b ---R * ---R 6 ---R sin(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 6 ---R (- 8b - 26a b - 38a b - 30a b - 12a b - 2a b )cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 5 ---R (- 48b - 188a b - 300a b - 244a b - 100a b - 16a b )cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R - 120b - 562a b - 1062a b - 1029a b - 532a b - 135a b ---R + ---R 6 ---R - 12a b ---R * ---R 4 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R - 160b - 848a b - 1836a b - 2076a b - 1292a b - 420a b ---R + ---R 6 ---R - 56a b ---R * ---R 3 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R - 120b - 662a b - 1514a b - 1831a b - 1225a b - 419a b ---R + ---R 6 7 ---R - 49a b + 4a ---R * ---R 2 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R - 48b - 244a b - 496a b - 488a b - 192a b + 44a b ---R + ---R 6 7 ---R 64a b + 16a ---R * ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 6 7 ---R - 8b - 30a b - 18a b + 82a b + 188a b + 174a b + 78a b + 14a ---R * ---R 4 ---R sin(x) ---R + ---R 6 2 5 3 4 4 3 5 2 8 ---R (- 12a b - 28a b - 21a b - 6a b - a b )cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 7 ---R (- 8b - 98a b - 238a b - 230a b - 98a b - 16a b )cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R - 40b - 310a b - 778a b - 910a b - 541a b - 154a b ---R + ---R 6 ---R - 15a b ---R * ---R 6 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R - 72b - 450a b - 1150a b - 1546a b - 1150a b - 444a b ---R + ---R 6 ---R - 68a b ---R * ---R 5 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R - 40b - 206a b - 530a b - 817a b - 721a b - 313a b ---R + ---R 6 7 ---R - 37a b + 8a ---R * ---R 4 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R 40b + 234a b + 558a b + 744a b + 660a b + 426a b ---R + ---R 6 7 ---R 182a b + 36a ---R * ---R 3 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R 72b + 366a b + 810a b + 1070a b + 976a b + 630a b ---R + ---R 6 7 ---R 254a b + 46a ---R * ---R 2 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R 40b + 186a b + 350a b + 352a b + 228a b + 122a b ---R + ---R 6 7 ---R 54a b + 12a ---R * ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 6 7 ---R 8b + 34a b + 46a b - 2a b - 68a b - 74a b - 34a b - 6a ---R * ---R 2 ---R sin(x) ---R + ---R 7 6 2 5 3 4 4 3 10 ---R (8b + 42a b + 78a b + 62a b + 18a b )cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 9 ---R (40b + 210a b + 386a b + 298a b + 78a b - 4a b )cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 6 8 ---R (64b + 312a b + 480a b + 204a b - 108a b - 84a b - 4a b)cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 7 ---R (- 120a b - 652a b - 1252a b - 1044a b - 340a b - 16a b)cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R - 112b - 804a b - 2188a b - 2834a b - 1730a b - 358a b ---R + ---R 6 7 ---R 38a b + 4a ---R * ---R 6 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R - 112b - 708a b - 1560a b - 1334a b - 22a b + 606a b ---R + ---R 6 7 ---R 278a b + 20a ---R * ---R 5 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R 120a b + 856a b + 2264a b + 2888a b + 1840a b + 512a b ---R + ---R 7 ---R 32a ---R * ---R 4 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 ---R 64b + 552a b + 1900a b + 3368a b + 3272a b + 1672a b ---R + ---R 6 7 ---R 364a b + 8a ---R * ---R 3 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 6 ---R 40b + 330a b + 1038a b + 1624a b + 1316a b + 474a b + 6a b ---R + ---R 7 ---R - 28a ---R * ---R 2 ---R cos(x) ---R + ---R 7 6 2 5 3 4 4 3 5 2 6 ---R 8b + 66a b + 182a b + 200a b + 20a b - 142a b - 114a b ---R + ---R 7 ---R - 28a ---R * ---R cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 ---R - 8a b - 40a b - 80a b - 80a b - 40a b - 8a ---R * ---R 4 ---R tan(x) ---R + ---R 2 5 3 4 4 3 5 2 4 ---R (- 8a b - 16a b - 10a b - 2a b )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 3 ---R (- 16a b - 40a b - 32a b - 8a b )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 2 ---R (- 16a b - 48a b - 50a b - 20a b - 2a b)cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 2 5 ---R (- 16a b - 56a b - 72a b - 40a b - 8a b)cos(x) - 8a b ---R + ---R 3 4 4 3 5 2 6 ---R - 32a b - 48a b - 32a b - 8a b ---R * ---R 6 ---R sin(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R (- 16a b - 52a b - 56a b - 24a b - 4a b )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 5 ---R (- 96a b - 312a b - 368a b - 184a b - 32a b )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R (- 240a b - 868a b - 1208a b - 794a b - 238a b - 24a b) ---R * ---R 4 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R (- 320a b - 1312a b - 2136a b - 1728a b - 696a b - 112a b) ---R * ---R 3 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R - 240a b - 1068a b - 1896a b - 1674a b - 724a b - 110a b ---R + ---R 7 ---R 8a ---R * ---R 2 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R - 96a b - 424a b - 712a b - 520a b - 88a b + 80a b ---R + ---R 7 ---R 32a ---R * ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 7 ---R - 16a b - 60a b - 56a b + 60a b + 156a b + 112a b + 28a ---R * ---R 4 ---R sin(x) ---R + ---R 6 2 5 3 4 4 3 5 2 8 ---R (- 64a b - 152a b - 116a b - 30a b - 2a b )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 7 ---R (- 272a b - 756a b - 728a b - 276a b - 32a b )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R (- 336a b - 1116a b - 1400a b - 828a b - 238a b - 30a b) ---R * ---R 6 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 5 ---R (112a b + 204a b - 184a b - 668a b - 528a b - 136a b)cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R 560a b + 1908a b + 2208a b + 790a b - 196a b - 110a b ---R + ---R 7 ---R 16a ---R * ---R 4 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R 336a b + 1220a b + 1608a b + 936a b + 320a b + 180a b ---R + ---R 7 ---R 72a ---R * ---R 3 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R - 112a b - 628a b - 1304a b - 1172a b - 292a b + 184a b ---R + ---R 7 ---R 92a ---R * ---R 2 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R - 176a b - 924a b - 1912a b - 1928a b - 912a b - 124a b ---R + ---R 7 ---R 24a ---R * ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 7 ---R - 48a b - 268a b - 604a b - 696a b - 424a b - 124a b - 12a ---R * ---R 2 ---R sin(x) ---R + ---R 6 2 5 3 4 4 3 10 ---R (16a b + 52a b + 56a b + 20a b )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 9 ---R (80a b + 244a b + 240a b + 68a b - 8a b )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 8 ---R (128a b + 288a b + 80a b - 200a b - 128a b - 8a b)cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 ---R (- 368a b - 1128a b - 1184a b - 456a b - 32a b)cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R - 224a b - 1160a b - 2096a b - 1572a b - 368a b + 52a b ---R + ---R 7 ---R 8a ---R * ---R 6 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 7 ---R (- 224a b - 744a b - 584a b + 508a b + 952a b + 420a b + 40a ) ---R * ---R 5 ---R cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 4 ---R (464a b + 1920a b + 3040a b + 2240a b + 720a b + 64a )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R 128a b + 848a b + 2120a b + 2568a b + 1544a b + 392a b ---R + ---R 7 ---R 16a ---R * ---R 3 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 7 ---R (80a b + 372a b + 632a b + 408a b - 48a b - 172a b - 56a ) ---R * ---R 2 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 7 ---R (16a b + 20a b - 136a b - 424a b - 496a b - 268a b - 56a )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 ---R - 16a b - 80a b - 160a b - 160a b - 80a b - 16a ---R * ---R 2 ---R tan(x) ---R + ---R 3 4 4 3 5 2 4 3 4 4 3 5 2 3 ---R (- 4a b - 4a b - a b )cos(x) + (- 8a b - 12a b - 4a b )cos(x) ---R + ---R 3 4 4 3 5 2 6 2 ---R (- 8a b - 16a b - 9a b - a b)cos(x) ---R + ---R 3 4 4 3 5 2 6 3 4 4 3 5 2 ---R (- 8a b - 20a b - 16a b - 4a b)cos(x) - 4a b - 12a b - 12a b ---R + ---R 6 ---R - 4a b ---R * ---R 6 ---R sin(x) ---R + ---R 2 5 3 4 4 3 5 2 6 ---R (- 16a b - 26a b - 12a b - 2a b )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 5 ---R (- 64a b - 132a b - 84a b - 16a b )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 4 ---R (- 112a b - 298a b - 278a b - 103a b - 12a b)cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 3 ---R (- 128a b - 416a b - 508a b - 276a b - 56a b)cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 2 ---R (- 112a b - 390a b - 512a b - 299a b - 61a b + 4a )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 ---R (- 64a b - 220a b - 264a b - 108a b + 16a b + 16a )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 ---R - 16a b - 54a b - 54a b + 4a b + 34a b + 14a ---R * ---R 4 ---R sin(x) ---R + ---R 6 2 5 3 4 4 3 5 2 8 ---R (- 32a b - 96a b - 86a b - 24a b - a b )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 7 ---R (- 128a b - 424a b - 458a b - 178a b - 16a b )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 6 ---R (- 128a b - 456a b - 582a b - 322a b - 84a b - 15a b)cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 5 ---R (128a b + 536a b + 726a b + 302a b - 84a b - 68a b)cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 7 ---R (320a b + 1400a b + 2142a b + 1278a b + 135a b - 73a b + 8a ) ---R * ---R 4 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 7 3 ---R (128a b + 584a b + 882a b + 450a b - 14a b - 2a b + 36a )cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R - 128a b - 664a b - 1426a b - 1534a b - 760a b - 70a b ---R + ---R 7 ---R 46a ---R * ---R 2 ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 ---R - 128a b - 696a b - 1534a b - 1694a b - 918a b - 178a b ---R + ---R 7 ---R 12a ---R * ---R cos(x) ---R + ---R 6 2 5 3 4 4 3 5 2 6 7 ---R - 32a b - 184a b - 432a b - 518a b - 322a b - 90a b - 6a ---R * ---R 2 ---R sin(x) ---R + ---R 3 4 4 3 10 2 5 3 4 4 3 5 2 9 ---R (2a b + 2a b )cos(x) + (- 8a b - 14a b - 10a b - 4a b )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 8 ---R (- 40a b - 112a b - 112a b - 44a b - 4a b)cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 ---R (- 64a b - 216a b - 252a b - 116a b - 16a b)cos(x) ---R + ---R 3 4 4 3 5 2 6 7 6 ---R (- 20a b - 28a b + 2a b + 14a b + 4a )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 5 ---R (112a b + 412a b + 592a b + 414a b + 142a b + 20a )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 4 ---R (112a b + 456a b + 720a b + 552a b + 208a b + 32a )cos(x) ---R + ---R 3 4 4 3 5 2 6 7 3 ---R (8a b + 28a b + 40a b + 28a b + 8a )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 2 ---R (- 64a b - 286a b - 502a b - 430a b - 178a b - 28a )cos(x) ---R + ---R 2 5 3 4 4 3 5 2 6 7 2 5 ---R (- 40a b - 190a b - 358a b - 334a b - 154a b - 28a )cos(x) - 8a b ---R + ---R 3 4 4 3 5 2 6 7 ---R - 40a b - 80a b - 80a b - 40a b - 8a ---R / ---R 2 7 3 6 4 5 5 4 6 3 7 2 6 ---R (8a b + 32a b + 50a b + 38a b + 14a b + 2a b )cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 5 ---R (16a b + 72a b + 128a b + 112a b + 48a b + 8a b )cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 8 ---R (- 8a b - 40a b - 84a b - 96a b - 64a b - 24a b - 4a b) ---R * ---R 4 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R - 32a b - 176a b - 400a b - 480a b - 320a b - 112a b ---R + ---R 8 ---R - 16a b ---R * ---R 3 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R - 8a b - 48a b - 118a b - 150a b - 100a b - 28a b ---R + ---R 8 9 ---R 2a b + 2a ---R * ---R 2 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R 16a b + 104a b + 288a b + 440a b + 400a b + 216a b ---R + ---R 8 9 ---R 64a b + 8a ---R * ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 8 ---R 8a b + 56a b + 168a b + 280a b + 280a b + 168a b + 56a b ---R + ---R 9 ---R 8a ---R * ---R 4 ---R sin(x) ---R + ---R 8 2 7 3 6 4 5 5 4 6 3 ---R 32a b + 160a b + 330a b + 360a b + 220a b + 72a b ---R + ---R 7 2 ---R 10a b ---R * ---R 8 ---R cos(x) ---R + ---R 8 2 7 3 6 4 5 5 4 6 3 ---R 128a b + 672a b + 1464a b + 1696a b + 1104a b + 384a b ---R + ---R 7 2 ---R 56a b ---R * ---R 7 ---R cos(x) ---R + ---R 8 2 7 3 6 4 5 5 4 6 3 ---R 128a b + 672a b + 1440a b + 1580a b + 880a b + 168a b ---R + ---R 7 2 8 ---R - 48a b - 20a b ---R * ---R 6 ---R cos(x) ---R + ---R 8 2 7 3 6 4 5 5 4 ---R - 128a b - 864a b - 2504a b - 4048a b - 3952a b ---R + ---R 6 3 7 2 8 ---R - 2336a b - 776a b - 112a b ---R * ---R 5 ---R cos(x) ---R + ---R 8 2 7 3 6 4 5 5 4 ---R - 320a b - 2080a b - 5788a b - 8932a b - 8238a b ---R + ---R 6 3 7 2 8 9 ---R - 4512a b - 1328a b - 140a b + 10a ---R * ---R 4 ---R cos(x) ---R + ---R 8 2 7 3 6 4 5 5 4 ---R - 128a b - 800a b - 2072a b - 2784a b - 1880a b ---R + ---R 6 3 7 2 8 9 ---R - 288a b + 440a b + 288a b + 56a ---R * ---R 3 ---R cos(x) ---R + ---R 8 2 7 3 6 4 5 5 4 6 3 ---R 128a b + 992a b + 3376a b + 6596a b + 8100a b + 6408a b ---R + ---R 7 2 8 9 ---R 3192a b + 916a b + 116a ---R * ---R 2 ---R cos(x) ---R + ---R 8 2 7 3 6 4 5 5 4 6 3 ---R 128a b + 992a b + 3368a b + 6544a b + 7960a b + 6208a b ---R + ---R 7 2 8 9 ---R 3032a b + 848a b + 104a ---R * ---R cos(x) ---R + ---R 8 2 7 3 6 4 5 5 4 6 3 ---R 32a b + 256a b + 898a b + 1804a b + 2270a b + 1832a b ---R + ---R 7 2 8 9 ---R 926a b + 268a b + 34a ---R * ---R 2 ---R sin(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 10 ---R (8a b + 40a b + 80a b + 80a b + 40a b + 8a b )cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 9 ---R (48a b + 240a b + 480a b + 480a b + 240a b + 48a b )cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 8 ---R (104a b + 504a b + 960a b + 880a b + 360a b + 24a b - 16a b) ---R * ---R 8 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 8 ---R (64a b + 224a b + 160a b - 320a b - 640a b - 416a b - 96a b) ---R * ---R 7 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R - 112a b - 784a b - 2232a b - 3320a b - 2720a b - 1152a b ---R + ---R 8 9 ---R - 184a b + 8a ---R * ---R 6 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R - 224a b - 1344a b - 3312a b - 4240a b - 2880a b - 864a b ---R + ---R 8 9 ---R 16a b + 48a ---R * ---R 5 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R - 112a b - 560a b - 1000a b - 520a b + 640a b + 1088a b ---R + ---R 8 9 ---R 600a b + 120a ---R * ---R 4 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R 64a b + 544a b + 1920a b + 3680a b + 4160a b + 2784a b ---R + ---R 8 9 ---R 1024a b + 160a ---R * ---R 3 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R 104a b + 744a b + 2280a b + 3880a b + 3960a b + 2424a b ---R + ---R 8 9 ---R 824a b + 120a ---R * ---R 2 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R 48a b + 336a b + 1008a b + 1680a b + 1680a b + 1008a b ---R + ---R 8 9 ---R 336a b + 48a ---R * ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 ---R 8a b + 56a b + 168a b + 280a b + 280a b + 168a b + 56a b + 8a ---R * ---R 4 ---R tan(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 6 ---R (16a b + 48a b + 52a b + 24a b + 4a b )cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 5 ---R (32a b + 112a b + 144a b + 80a b + 16a b )cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 4 ---R (- 16a b - 64a b - 104a b - 88a b - 40a b - 8a b)cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 3 ---R (- 64a b - 288a b - 512a b - 448a b - 192a b - 32a b)cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 9 2 ---R (- 16a b - 80a b - 156a b - 144a b - 56a b + 4a )cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 ---R 32a b + 176a b + 400a b + 480a b + 320a b + 112a b ---R + ---R 9 ---R 16a ---R * ---R cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 9 ---R 16a b + 96a b + 240a b + 320a b + 240a b + 96a b + 16a ---R * ---R 4 ---R sin(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 8 ---R (64a b + 256a b + 404a b + 316a b + 124a b + 20a b )cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R (256a b + 1088a b + 1840a b + 1552a b + 656a b + 112a b ) ---R * ---R 7 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R 256a b + 1088a b + 1792a b + 1368a b + 392a b - 56a b ---R + ---R 8 ---R - 40a b ---R * ---R 6 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 ---R - 256a b - 1472a b - 3536a b - 4560a b - 3344a b ---R + ---R 7 2 8 ---R - 1328a b - 224a b ---R * ---R 5 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 ---R - 640a b - 3520a b - 8056a b - 9808a b - 6668a b ---R + ---R 7 2 8 9 ---R - 2356a b - 300a b + 20a ---R * ---R 4 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 ---R - 256a b - 1344a b - 2800a b - 2768a b - 992a b ---R + ---R 7 2 8 9 ---R 416a b + 464a b + 112a ---R * ---R 3 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 ---R 256a b + 1728a b + 5024a b + 8168a b + 8032a b ---R + ---R 7 2 8 9 ---R 4784a b + 1600a b + 232a ---R * ---R 2 ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 ---R 256a b + 1728a b + 5008a b + 8080a b + 7840a b ---R + ---R 7 2 8 9 ---R 4576a b + 1488a b + 208a ---R * ---R cos(x) ---R + ---R 2 7 3 6 4 5 5 4 6 3 7 2 ---R 64a b + 448a b + 1348a b + 2260a b + 2280a b + 1384a b ---R + ---R 8 9 ---R 468a b + 68a ---R * ---R 2 ---R sin(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 10 ---R (16a b + 64a b + 96a b + 64a b + 16a b )cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 9 ---R (96a b + 384a b + 576a b + 384a b + 96a b )cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 8 ---R (208a b + 800a b + 1120a b + 640a b + 80a b - 32a b)cos(x) ---R + ---R 3 6 4 5 6 3 7 2 8 7 ---R (128a b + 320a b - 640a b - 640a b - 192a b)cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 ---R - 224a b - 1344a b - 3120a b - 3520a b - 1920a b - 384a b ---R + ---R 9 ---R 16a ---R * ---R 6 ---R cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 ---R - 448a b - 2240a b - 4384a b - 4096a b - 1664a b - 64a b ---R + ---R 9 ---R 96a ---R * ---R 5 ---R cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 ---R - 224a b - 896a b - 1104a b + 64a b + 1216a b + 960a b ---R + ---R 9 ---R 240a ---R * ---R 4 ---R cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 ---R 128a b + 960a b + 2880a b + 4480a b + 3840a b + 1728a b ---R + ---R 9 ---R 320a ---R * ---R 3 ---R cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 ---R 208a b + 1280a b + 3280a b + 4480a b + 3440a b + 1408a b ---R + ---R 9 ---R 240a ---R * ---R 2 ---R cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 9 ---R (96a b + 576a b + 1440a b + 1920a b + 1440a b + 576a b + 96a ) ---R * ---R cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 9 ---R 16a b + 96a b + 240a b + 320a b + 240a b + 96a b + 16a ---R * ---R 2 ---R tan(x) ---R + ---R 4 5 5 4 6 3 7 2 6 ---R (8a b + 16a b + 10a b + 2a b )cos(x) ---R + ---R 4 5 5 4 6 3 7 2 5 ---R (16a b + 40a b + 32a b + 8a b )cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 4 ---R (- 8a b - 24a b - 28a b - 16a b - 4a b)cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 3 ---R (- 32a b - 112a b - 144a b - 80a b - 16a b)cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 9 2 ---R (- 8a b - 32a b - 46a b - 26a b - 2a b + 2a )cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 9 4 5 ---R (16a b + 72a b + 128a b + 112a b + 48a b + 8a )cos(x) + 8a b ---R + ---R 5 4 6 3 7 2 8 9 ---R 40a b + 80a b + 80a b + 40a b + 8a ---R * ---R 4 ---R sin(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 ---R (32a b + 96a b + 106a b + 52a b + 10a b )cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 7 ---R (128a b + 416a b + 504a b + 272a b + 56a b )cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 6 ---R (128a b + 416a b + 480a b + 204a b - 8a b - 20a b)cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 5 ---R (- 128a b - 608a b - 1160a b - 1120a b - 552a b - 112a b)cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 ---R - 320a b - 1440a b - 2588a b - 2316a b - 1018a b - 160a b ---R + ---R 9 ---R 10a ---R * ---R 4 ---R cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 9 ---R (- 128a b - 544a b - 856a b - 528a b + 32a b + 176a b + 56a ) ---R * ---R 3 ---R cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 ---R 128a b + 736a b + 1776a b + 2308a b + 1708a b + 684a b ---R + ---R 9 ---R 116a ---R * ---R 2 ---R cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 ---R 128a b + 736a b + 1768a b + 2272a b + 1648a b + 640a b ---R + ---R 9 ---R 104a ---R * ---R cos(x) ---R + ---R 3 6 4 5 5 4 6 3 7 2 8 9 ---R 32a b + 192a b + 482a b + 648a b + 492a b + 200a b + 34a ---R * ---R 2 ---R sin(x) ---R + ---R 4 5 5 4 6 3 7 2 10 ---R (8a b + 24a b + 24a b + 8a b )cos(x) ---R + ---R 4 5 5 4 6 3 7 2 9 ---R (48a b + 144a b + 144a b + 48a b )cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 8 ---R (104a b + 296a b + 264a b + 56a b - 16a b)cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 7 ---R (64a b + 96a b - 96a b - 224a b - 96a b)cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 9 6 ---R (- 112a b - 560a b - 1000a b - 760a b - 200a b + 8a )cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 9 5 ---R (- 224a b - 896a b - 1296a b - 752a b - 80a b + 48a )cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 9 4 ---R (- 112a b - 336a b - 216a b + 248a b + 360a b + 120a )cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 9 3 ---R (64a b + 416a b + 1024a b + 1216a b + 704a b + 160a )cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 9 2 ---R (104a b + 536a b + 1104a b + 1136a b + 584a b + 120a )cos(x) ---R + ---R 4 5 5 4 6 3 7 2 8 9 4 5 ---R (48a b + 240a b + 480a b + 480a b + 240a b + 48a )cos(x) + 8a b ---R + ---R 5 4 6 3 7 2 8 9 ---R 40a b + 80a b + 80a b + 40a b + 8a ---R Type: Expression Integer +--d0054b:= D(m0054b,x) --E 295 --S 296 of 520 @@ -19450,7 +17790,7 @@ t0055:= (1+sin(x)^2)^(1/2) --R --R +-----------+ --R | 2 ---R (201) \|sin(x) + 1 +--R (178) \|sin(x) + 1 --R Type: Expression Integer --E 296 @@ -19458,7 +17798,7 @@ t0055:= (1+sin(x)^2)^(1/2) r0055:= x --R --R ---R (202) x +--R (179) x --R Type: Variable x --E 297 @@ -19468,30 +17808,17 @@ a0055:= integrate(t0055,x) --R --R x +------------+ --R ++ | 2 ---R (203) | \|sin(%R) + 1 d%R +--R (180) | \|sin(%R) + 1 d%R --R ++ --R Type: Union(Expression Integer,...) --E 298 --S 299 of 520 -m0055:= a0055-r0055 ---R ---R ---R x +------------+ ---R ++ | 2 ---R (204) | \|sin(%R) + 1 d%R - x ---R ++ ---R Type: Expression Integer +--m0055:= a0055-r0055 --E 299 --S 300 of 520 -d0055:= D(m0055,x) ---R ---R ---R +-----------+ ---R | 2 ---R (205) \|sin(x) + 1 - 1 ---R Type: Expression Integer +--d0055:= D(m0055,x) --E 300 --S 301 of 520 @@ -19500,7 +17827,7 @@ t0056:= (-1-sin(x)^2)^(1/2) --R --R +-------------+ --R | 2 ---R (206) \|- sin(x) - 1 +--R (181) \|- sin(x) - 1 --R Type: Expression Integer --E 301 @@ -19510,7 +17837,7 @@ r0056:= (-3+cos(2*x))^(1/2)*x/(3-cos(2*x))^(1/2) --R --R +-----------+ --R x\|cos(2x) - 3 ---R (207) ---------------- +--R (182) ---------------- --R +-------------+ --R \|- cos(2x) + 3 --R Type: Expression Integer @@ -19520,7 +17847,7 @@ r0056:= (-3+cos(2*x))^(1/2)*x/(3-cos(2*x))^(1/2) a0056:= integrate(t0056,x) --R --R ---R (208) +--R (183) --R +---+ 2 +---+ --R x\|- 1 x\|- 1 --R (2(%e ) - 2%e ) @@ -19559,7 +17886,7 @@ a0056:= integrate(t0056,x) m0056:= a0056-r0056 --R --R ---R (209) +--R (184) --R +---+ 2 +---+ --R x\|- 1 x\|- 1 +-------------+ --R (2(%e ) - 2%e )\|- cos(2x) + 3 @@ -19606,7 +17933,7 @@ m0056:= a0056-r0056 d0056:= D(m0056,x) --R --R ---R (210) +--R (185) --R +---+ 4 +---+ 3 --R x\|- 1 x\|- 1 --R (- 2cos(2x) + 6)(%e ) + (4cos(2x) - 12)(%e ) @@ -19651,7 +17978,7 @@ t0057:= 1/(1+sin(x)^2)^(1/2) --R --R --R 1 ---R (211) -------------- +--R (186) -------------- --R +-----------+ --R | 2 --R \|sin(x) + 1 @@ -19662,7 +17989,7 @@ t0057:= 1/(1+sin(x)^2)^(1/2) r0057:= atanh(x) --R --R ---R (212) atanh(x) +--R (187) atanh(x) --R Type: Expression Integer --E 307 @@ -19672,7 +17999,7 @@ a0057:= integrate(t0057,x) --R --R x --R ++ 1 ---R (213) | --------------- d%R +--R (188) | --------------- d%R --R ++ +------------+ --R | 2 --R \|sin(%R) + 1 @@ -19680,30 +18007,11 @@ a0057:= integrate(t0057,x) --E 308 --S 309 of 520 -m0057:= a0057-r0057 ---R ---R ---R x ---R ++ 1 ---R (214) | --------------- d%R - atanh(x) ---R ++ +------------+ ---R | 2 ---R \|sin(%R) + 1 ---R Type: Expression Integer +--m0057:= a0057-r0057 --E 309 --S 310 of 520 -d0057:= D(m0057,x) ---R ---R ---R +-----------+ ---R | 2 2 ---R \|sin(x) + 1 + x - 1 ---R (215) ----------------------- ---R +-----------+ ---R 2 | 2 ---R (x - 1)\|sin(x) + 1 ---R Type: Expression Integer +--d0057:= D(m0057,x) --E 310 --S 311 of 520 @@ -19711,7 +18019,7 @@ t0058:= 1/(-1-sin(x)^2)^(1/2) --R --R --R 1 ---R (216) ---------------- +--R (189) ---------------- --R +-------------+ --R | 2 --R \|- sin(x) - 1 @@ -19724,7 +18032,7 @@ r0058:= (3-cos(2*x))^(1/2)*atanh(x)/(-3+cos(2*x))^(1/2) --R --R +-------------+ --R atanh(x)\|- cos(2x) + 3 ---R (217) ------------------------ +--R (190) ------------------------ --R +-----------+ --R \|cos(2x) - 3 --R Type: Expression Integer @@ -19738,7 +18046,7 @@ a0058:= integrate(t0058,x) --R | +---+ 4 +---+ 2 --R x +---+ | %R\|- 1 %R\|- 1 --R ++ 2\|- 1 \|(%e ) - 6(%e ) + 1 ---R (218) | ---------------------------------------------- d%R +--R (191) | ---------------------------------------------- d%R --R ++ +---+ 6 +---+ 4 +---+ 2 --R %R\|- 1 %R\|- 1 %R\|- 1 --R (%e ) - 6(%e ) + (%e ) @@ -19746,55 +18054,11 @@ a0058:= integrate(t0058,x) --E 313 --S 314 of 520 -m0058:= a0058-r0058 ---R ---R ---R (219) ---R +----------------------------------+ ---R | +---+ 4 +---+ 2 ---R x +---+ | %R\|- 1 %R\|- 1 ---R +-----------+ ++ 2\|- 1 \|(%e ) - 6(%e ) + 1 ---R \|cos(2x) - 3 | ---------------------------------------------- d%R ---R ++ +---+ 6 +---+ 4 +---+ 2 ---R %R\|- 1 %R\|- 1 %R\|- 1 ---R (%e ) - 6(%e ) + (%e ) ---R + ---R +-------------+ ---R - atanh(x)\|- cos(2x) + 3 ---R / ---R +-----------+ ---R \|cos(2x) - 3 ---R Type: Expression Integer +--m0058:= a0058-r0058 --E 314 --S 315 of 520 -d0058:= D(m0058,x) ---R ---R ---R (220) ---R 2 +---+ +-------------+ +-----------+ ---R (2x - 2)\|- 1 \|- cos(2x) + 3 \|cos(2x) - 3 ---R * ---R +--------------------------------+ ---R | +---+ 4 +---+ 2 ---R | x\|- 1 x\|- 1 ---R \|(%e ) - 6(%e ) + 1 ---R + ---R +---+ 6 +---+ 4 ---R x\|- 1 x\|- 1 ---R (- cos(2x) + 3)(%e ) + (6cos(2x) - 18)(%e ) ---R + ---R +---+ 2 ---R x\|- 1 ---R (- cos(2x) + 3)(%e ) ---R / ---R +---+ 6 +---+ 4 +---+ 2 ---R 2 x\|- 1 2 x\|- 1 2 x\|- 1 ---R ((x - 1)(%e ) + (- 6x + 6)(%e ) + (x - 1)(%e ) ) ---R * ---R +-------------+ +-----------+ ---R \|- cos(2x) + 3 \|cos(2x) - 3 ---R Type: Expression Integer +--d0058:= D(m0058,x) --E 315 --S 316 of 520 @@ -19802,14 +18066,20 @@ t0059:= x/(a+b*sin(x)^2) --R --R --R x ---R (221) ------------- +--R (192) ------------- --R 2 --R b sin(x) + a --R Type: Expression Integer --E 316 --S 317 of 520 -r0059:= 1/4*(-2*%i*x*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+2*%i*x*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-polylog(2,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+polylog(2,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/a^(1/2)/(a+b)^(1/2) +r0059:= 1/4*(-2*%i*x*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)+_ + b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 2*%i*x*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)-_ + b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-_ + polylog(2,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + polylog(2,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/_ + a^(1/2)/(a+b)^(1/2) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -19832,7 +18102,7 @@ a0059:= integrate(t0059,x) --R --R x --R ++ %R ---R (222) | -------------- d%R +--R (193) | -------------- d%R --R ++ 2 --R b sin(%R) + a --R Type: Union(Expression Integer,...) @@ -19852,14 +18122,22 @@ t0060:= x^2/(a+b*sin(x)^2) --R --R 2 --R x ---R (223) ------------- +--R (194) ------------- --R 2 --R b sin(x) + a --R Type: Expression Integer --E 321 --S 322 of 520 -r0060:= -1/4*(2*%i*x^2*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*%i*x^2*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+2*x*polylog(2,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*x*polylog(2,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+%i*polylog(3,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-%i*polylog(3,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/a^(1/2)/(a+b)^(1/2) +r0060:= -1/4*(2*%i*x^2*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)+_ + b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 2*%i*x^2*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)-_ + b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + 2*x*polylog(2,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 2*x*polylog(2,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + %i*polylog(3,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + %i*polylog(3,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/_ + a^(1/2)/(a+b)^(1/2) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -19882,7 +18160,7 @@ a0060:= integrate(t0060,x) --R --R x 2 --R ++ %R ---R (224) | -------------- d%R +--R (195) | -------------- d%R --R ++ 2 --R b sin(%R) + a --R Type: Union(Expression Integer,...) @@ -19902,14 +18180,24 @@ t0061:= x^3/(a+b*sin(x)^2) --R --R 3 --R x ---R (225) ------------- +--R (196) ------------- --R 2 --R b sin(x) + a --R Type: Expression Integer --E 326 --S 327 of 520 -r0061:= -1/8*(4*%i*x^3*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-4*%i*x^3*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+6*x^2*polylog(2,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-6*x^2*polylog(2,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+6*%i*x*polylog(3,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-6*%i*x*polylog(3,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-3*polylog(4,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+3*polylog(4,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/a^(1/2)/(a+b)^(1/2) +r0061:= -1/8*(4*%i*x^3*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)+_ + b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 4*%i*x^3*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)-_ + b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + 6*x^2*polylog(2,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 6*x^2*polylog(2,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + 6*%i*x*polylog(3,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 6*%i*x*polylog(3,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-_ + 3*polylog(4,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 3*polylog(4,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/_ + a^(1/2)/(a+b)^(1/2) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -19932,7 +18220,7 @@ a0061:= integrate(t0061,x) --R --R x 3 --R ++ %R ---R (226) | -------------- d%R +--R (197) | -------------- d%R --R ++ 2 --R b sin(%R) + a --R Type: Union(Expression Integer,...) @@ -19952,7 +18240,7 @@ t0062:= x*(sin(x)^2)^(1/2) --R --R +-------+ --R | 2 ---R (227) x\|sin(x) +--R (198) x\|sin(x) --R Type: Expression Integer --E 331 @@ -19962,15 +18250,15 @@ r0062:= -csc(x)*(x*cos(x)-sin(x))*(sin(x)^2)^(1/2) --R --R +-------+ --R | 2 ---R (228) (csc(x)sin(x) - x cos(x)csc(x))\|sin(x) +--R (199) (csc(x)sin(x) - x cos(x)csc(x))\|sin(x) --R Type: Expression Integer --E 332 ---S 333 of 520 +--S 333 of 520 BUG? a0062:= integrate(t0062,x) --R --R ---R (229) sin(x) - x cos(x) +--R (200) sin(x) - x cos(x) --R Type: Union(Expression Integer,...) --E 333 @@ -19980,7 +18268,7 @@ m0062:= a0062-r0062 --R --R +-------+ --R | 2 ---R (230) (- csc(x)sin(x) + x cos(x)csc(x))\|sin(x) + sin(x) - x cos(x) +--R (201) (- csc(x)sin(x) + x cos(x)csc(x))\|sin(x) + sin(x) - x cos(x) --R Type: Expression Integer --E 334 @@ -19988,7 +18276,7 @@ m0062:= a0062-r0062 d0062:= D(m0062,x) --R --R ---R (231) +--R (202) --R +-------+ --R | 2 3 --R x sin(x)\|sin(x) + (cot(x) - x)csc(x)sin(x) @@ -20007,17 +18295,23 @@ t0063:= 1/(a+b*sin(x)^3) --R --R --R 1 ---R (232) ------------- +--R (203) ------------- --R 3 --R b sin(x) + a --R Type: Expression Integer --E 336 --S 337 of 520 -r0063:= -2/3*atan(((-1)^(1/3)*b^(1/3)-a^(1/3)*tan(1/2*x))/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2)+2/3*atan((b^(1/3)+a^(1/3)*tan(1/2*x))/(a^(2/3)-b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atan(((-1)^(2/3)*b^(1/3)+a^(1/3)*tan(1/2*x))/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2) +r0063:= -2/3*atan(((-1)^(1/3)*b^(1/3)-a^(1/3)*tan(1/2*x))/_ + (a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/_ + (a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2)+2/3*_ + atan((b^(1/3)+a^(1/3)*tan(1/2*x))/(a^(2/3)-b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atan(((-1)^(2/3)*b^(1/3)+_ + a^(1/3)*tan(1/2*x))/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2) --R --R ---R (233) +--R (204) --R - --R +---------------+ +-------------------+ --R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 @@ -20057,7 +18351,7 @@ r0063:= -2/3*atan(((-1)^(1/3)*b^(1/3)-a^(1/3)*tan(1/2*x))/(a^(2/3)-(-1)^(2/3)*b^ a0063:= integrate(t0063,x) --R --R ---R (234) +--R (205) --R ROOT --R 2 2 --R (6b - 6a ) @@ -20459,7 +18753,7 @@ a0063:= integrate(t0063,x) m0063:= a0063-r0063 --R --R ---R (235) +--R (206) --R +----------------------+ +---------------+ +-------------------+ --R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 --R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a @@ -20927,3776 +19221,7 @@ m0063:= a0063-r0063 --E 339 --S 340 of 520 -d0063:= D(m0063,x) ---R ---R ---R (236) ---R 3 3+---+2 3 3+---+ 3 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (12a \|- 1 - 12a \|- 1 + 12a )cos(x) + 3a \|- 1 ---R + ---R 3 3+---+ 3 ---R - 3a \|- 1 + 3a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) - 24a b \|- 1 ---R + ---R 2 3+---+ 2 ---R 24a b\|- 1 - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (24a \|- 1 - 24a \|- 1 + 24a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) - 3a \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a \|- 1 - 3a ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (12a \|- 1 - 12a \|- 1 + 12a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (15a \|- 1 - 15a \|- 1 + 15a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 15a \|- 1 + 15a \|- 1 - 15a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 12a \|- 1 + 12a \|- 1 - 12a )cos(x) - 3a \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a \|- 1 - 3a ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R - 36a b \|- 1 + 36a b\|- 1 - 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (96a b \|- 1 - 96a b \|- 1 + 96a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (288a b \|- 1 - 288a b \|- 1 + 288a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (288a b \|- 1 - 288a b \|- 1 + 288a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R 96a b \|- 1 - 96a b \|- 1 + 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 5 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R (- 180a b \|- 1 + 180a b\|- 1 - 180a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (- 120a b \|- 1 + 120a b\|- 1 - 120a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (36a b \|- 1 - 36a b\|- 1 + 36a b)cos(x) + 12a b \|- 1 ---R + ---R 2 3+---+ 2 ---R - 12a b\|- 1 + 12a b ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (20a b - 11a )\|- 1 + (- 20a b + 11a )\|- 1 + 20a b ---R + ---R 3 ---R - 11a ---R * ---R 6 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 33a )\|- 1 + (- 60a b + 33a )\|- 1 + 60a b ---R + ---R 3 ---R - 33a ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 60a )\|- 1 + (- 96a b + 60a )\|- 1 + 96a b ---R + ---R 3 ---R - 60a ---R * ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (36a b - 27a )\|- 1 + (- 36a b + 27a )\|- 1 + 36a b ---R + ---R 3 ---R - 27a ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (- 32b - 40a b)\|- 1 + (32b + 40a b)\|- 1 - 32b ---R + ---R 2 ---R - 40a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (- 96b - 120a b)\|- 1 + (96b + 120a b)\|- 1 - 96b ---R + ---R 2 ---R - 120a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (- 96b - 120a b)\|- 1 + (96b + 120a b)\|- 1 - 96b ---R + ---R 2 ---R - 120a b ---R * ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (- 32b - 40a b)\|- 1 + (32b + 40a b)\|- 1 - 32b - 40a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 33a )\|- 1 + (- 60a b + 33a )\|- 1 + 60a b ---R + ---R 3 ---R - 33a ---R * ---R 4 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (192a b - 120a )\|- 1 + (- 192a b + 120a )\|- 1 ---R + ---R 2 3 ---R 192a b - 120a ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (216a b - 162a )\|- 1 + (- 216a b + 162a )\|- 1 ---R + ---R 2 3 ---R 216a b - 162a ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 96a )\|- 1 + (- 96a b + 96a )\|- 1 + 96a b ---R + ---R 3 ---R - 96a ---R * ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (12a b - 21a )\|- 1 + (- 12a b + 21a )\|- 1 + 12a b ---R + ---R 3 ---R - 21a ---R * ---R 2 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (20a b - 11a )\|- 1 + (- 20a b + 11a )\|- 1 + 20a b ---R + ---R 3 ---R - 11a ---R * ---R 6 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 60a )\|- 1 + (- 96a b + 60a )\|- 1 + 96a b ---R + ---R 3 ---R - 60a ---R * ---R 5 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (180a b - 135a )\|- 1 + (- 180a b + 135a )\|- 1 ---R + ---R 2 3 ---R 180a b - 135a ---R * ---R 4 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (160a b - 160a )\|- 1 + (- 160a b + 160a )\|- 1 ---R + ---R 2 3 ---R 160a b - 160a ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 105a )\|- 1 + (- 60a b + 105a )\|- 1 + 60a b ---R + ---R 3 ---R - 105a ---R * ---R 2 ---R cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 36a \|- 1 + 36a \|- 1 - 36a )cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R (- 4a b - 5a )\|- 1 + (4a b + 5a )\|- 1 - 4a b - 5a ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)cos(x) + 24a b \|- 1 ---R + ---R 2 3+---+ 2 ---R - 24a b\|- 1 + 24a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (192a b \|- 1 - 192a b \|- 1 + 192a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (576a b \|- 1 - 576a b \|- 1 + 576a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (576a b \|- 1 - 576a b \|- 1 + 576a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R 192a b \|- 1 - 192a b \|- 1 + 192a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (48a b \|- 1 - 48a b\|- 1 + 48a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (144a b \|- 1 - 144a b\|- 1 + 144a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (144a b \|- 1 - 144a b\|- 1 + 144a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R 48a b \|- 1 - 48a b\|- 1 + 48a b ---R * ---R 2 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 5 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R (120a b \|- 1 - 120a b\|- 1 + 120a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (240a b \|- 1 - 240a b\|- 1 + 240a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (240a b \|- 1 - 240a b\|- 1 + 240a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (120a b \|- 1 - 120a b\|- 1 + 120a b)cos(x) + 24a b \|- 1 ---R + ---R 2 3+---+ 2 ---R - 24a b\|- 1 + 24a b ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (20a b - 11a )\|- 1 + (- 20a b + 11a )\|- 1 + 20a b ---R + ---R 3 ---R - 11a ---R * ---R 6 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 33a )\|- 1 + (- 60a b + 33a )\|- 1 + 60a b ---R + ---R 3 ---R - 33a ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 60a )\|- 1 + (- 96a b + 60a )\|- 1 + 96a b ---R + ---R 3 ---R - 60a ---R * ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (36a b - 27a )\|- 1 + (- 36a b + 27a )\|- 1 + 36a b ---R + ---R 3 ---R - 27a ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (- 32b - 40a b)\|- 1 + (32b + 40a b)\|- 1 - 32b ---R + ---R 2 ---R - 40a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (- 96b - 120a b)\|- 1 + (96b + 120a b)\|- 1 - 96b ---R + ---R 2 ---R - 120a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (- 96b - 120a b)\|- 1 + (96b + 120a b)\|- 1 - 96b ---R + ---R 2 ---R - 120a b ---R * ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (- 32b - 40a b)\|- 1 + (32b + 40a b)\|- 1 - 32b - 40a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 33a )\|- 1 + (- 60a b + 33a )\|- 1 + 60a b ---R + ---R 3 ---R - 33a ---R * ---R 4 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (192a b - 120a )\|- 1 + (- 192a b + 120a )\|- 1 ---R + ---R 2 3 ---R 192a b - 120a ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (216a b - 162a )\|- 1 + (- 216a b + 162a )\|- 1 ---R + ---R 2 3 ---R 216a b - 162a ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 96a )\|- 1 + (- 96a b + 96a )\|- 1 + 96a b ---R + ---R 3 ---R - 96a ---R * ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (12a b - 21a )\|- 1 + (- 12a b + 21a )\|- 1 + 12a b ---R + ---R 3 ---R - 21a ---R * ---R 2 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (20a b - 11a )\|- 1 + (- 20a b + 11a )\|- 1 + 20a b ---R + ---R 3 ---R - 11a ---R * ---R 6 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 60a )\|- 1 + (- 96a b + 60a )\|- 1 + 96a b ---R + ---R 3 ---R - 60a ---R * ---R 5 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (180a b - 135a )\|- 1 + (- 180a b + 135a )\|- 1 ---R + ---R 2 3 ---R 180a b - 135a ---R * ---R 4 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (160a b - 160a )\|- 1 + (- 160a b + 160a )\|- 1 ---R + ---R 2 3 ---R 160a b - 160a ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 105a )\|- 1 + (- 60a b + 105a )\|- 1 + 60a b ---R + ---R 3 ---R - 105a ---R * ---R 2 ---R cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 36a \|- 1 + 36a \|- 1 - 36a )cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R (- 4a b - 5a )\|- 1 + (4a b + 5a )\|- 1 - 4a b - 5a ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R - 36a b \|- 1 + 36a b\|- 1 - 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (96a b \|- 1 - 96a b \|- 1 + 96a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (288a b \|- 1 - 288a b \|- 1 + 288a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (288a b \|- 1 - 288a b \|- 1 + 288a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R 96a b \|- 1 - 96a b \|- 1 + 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 5 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R (- 180a b \|- 1 + 180a b\|- 1 - 180a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (- 120a b \|- 1 + 120a b\|- 1 - 120a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (36a b \|- 1 - 36a b\|- 1 + 36a b)cos(x) + 12a b \|- 1 ---R + ---R 2 3+---+ 2 ---R - 12a b\|- 1 + 12a b ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 3 3+---+ ---R (12a \|- 1 - 12a \|- 1 + 12a )cos(x) + 3a \|- 1 - 3a \|- 1 ---R + ---R 3 ---R 3a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) - 24a b \|- 1 ---R + ---R 2 3+---+ 2 ---R 24a b\|- 1 - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (24a \|- 1 - 24a \|- 1 + 24a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 3 3+---+ ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) - 3a \|- 1 + 3a \|- 1 ---R + ---R 3 ---R - 3a ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (12a \|- 1 - 12a \|- 1 + 12a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (15a \|- 1 - 15a \|- 1 + 15a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 15a \|- 1 + 15a \|- 1 - 15a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 3 3+---+ ---R (- 12a \|- 1 + 12a \|- 1 - 12a )cos(x) - 3a \|- 1 + 3a \|- 1 ---R + ---R 3 ---R - 3a ---R * ---R 3+-+2 3+-+2 ---R \|a \|b ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 12a b \|- 1 + 12a b\|- 1 - 12a b)cos(x) - 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a b\|- 1 - 3a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (24a b \|- 1 - 24a b \|- 1 + 24a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 3+---+2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) + 24a b \|- 1 ---R + ---R 2 2 3+---+ 2 2 ---R - 24a b \|- 1 + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) + 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 3a b\|- 1 + 3a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (- 12a b \|- 1 + 12a b\|- 1 - 12a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 15a b \|- 1 + 15a b\|- 1 - 15a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (15a b \|- 1 - 15a b\|- 1 + 15a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (12a b \|- 1 - 12a b\|- 1 + 12a b)cos(x) + 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 3a b\|- 1 + 3a b ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((8a b - 8a )\|- 1 + (- 8a b + 8a )\|- 1 + 8a b - 8a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (24a b - 24a )\|- 1 + (- 24a b + 24a )\|- 1 + 24a b ---R + ---R 4 ---R - 24a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 36a )\|- 1 + (- 36a b + 36a )\|- 1 + 36a b ---R + ---R 4 ---R - 36a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (12a b - 12a )\|- 1 + (- 12a b + 12a )\|- 1 + 12a b ---R + ---R 4 ---R - 12a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 32a b + 32a b)\|- 1 + (32a b - 32a b)\|- 1 ---R + ---R 3 3 ---R - 32a b + 32a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 96a b + 96a b)\|- 1 + (96a b - 96a b)\|- 1 ---R + ---R 3 3 ---R - 96a b + 96a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 96a b + 96a b)\|- 1 + (96a b - 96a b)\|- 1 ---R + ---R 3 3 ---R - 96a b + 96a b ---R * ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ 3 ---R (- 32a b + 32a b)\|- 1 + (32a b - 32a b)\|- 1 - 32a b ---R + ---R 3 ---R 32a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (24a b - 24a )\|- 1 + (- 24a b + 24a )\|- 1 + 24a b ---R + ---R 4 ---R - 24a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 72a )\|- 1 + (- 72a b + 72a )\|- 1 + 72a b ---R + ---R 4 ---R - 72a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 72a )\|- 1 + (- 72a b + 72a )\|- 1 + 72a b ---R + ---R 4 ---R - 72a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (24a b - 24a )\|- 1 + (- 24a b + 24a )\|- 1 + 24a b ---R + ---R 4 ---R - 24a ---R * ---R cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((8a b - 8a )\|- 1 + (- 8a b + 8a )\|- 1 + 8a b - 8a ) ---R * ---R 6 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 36a )\|- 1 + (- 36a b + 36a )\|- 1 + 36a b ---R + ---R 4 ---R - 36a ---R * ---R 5 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (60a b - 60a )\|- 1 + (- 60a b + 60a )\|- 1 + 60a b ---R + ---R 4 ---R - 60a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (40a b - 40a )\|- 1 + (- 40a b + 40a )\|- 1 + 40a b ---R + ---R 4 ---R - 40a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 12a b + 12a )\|- 1 + (12a b - 12a )\|- 1 - 12a b ---R + ---R 4 ---R 12a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (- 4a b + 4a )\|- 1 + (4a b - 4a )\|- 1 - 4a b + 4a ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (51a b \|- 1 - 51a b\|- 1 + 51a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (153a b \|- 1 - 153a b\|- 1 + 153a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (252a b \|- 1 - 252a b\|- 1 + 252a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 99a b \|- 1 - 99a b\|- 1 + 99a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 24a b \|- 1 + 24a b \|- 1 - 24a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 24a b \|- 1 + 24a b \|- 1 - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (153a b \|- 1 - 153a b\|- 1 + 153a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (504a b \|- 1 - 504a b\|- 1 + 504a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (594a b \|- 1 - 594a b\|- 1 + 594a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (288a b \|- 1 - 288a b\|- 1 + 288a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 45a b \|- 1 - 45a b\|- 1 + 45a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (51a b \|- 1 - 51a b\|- 1 + 51a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (252a b \|- 1 - 252a b\|- 1 + 252a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (495a b \|- 1 - 495a b\|- 1 + 495a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (480a b \|- 1 - 480a b\|- 1 + 480a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (225a b \|- 1 - 225a b\|- 1 + 225a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (36a b \|- 1 - 36a b\|- 1 + 36a b)cos(x) - 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a b\|- 1 - 3a b ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 32a b - 16a )\|- 1 + (32a b + 16a )\|- 1 - 32a b ---R + ---R 4 ---R - 16a ---R * ---R 6 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 96a b - 48a )\|- 1 + (96a b + 48a )\|- 1 - 96a b ---R + ---R 4 ---R - 48a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (- 168a b - 72a )\|- 1 + (168a b + 72a )\|- 1 ---R + ---R 2 2 4 ---R - 168a b - 72a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 72a b - 24a )\|- 1 + (72a b + 24a )\|- 1 - 72a b ---R + ---R 4 ---R - 24a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 64a b + 64a b)\|- 1 + (64a b - 64a b)\|- 1 ---R + ---R 3 3 ---R - 64a b + 64a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 192a b + 192a b)\|- 1 + (192a b - 192a b)\|- 1 ---R + ---R 3 3 ---R - 192a b + 192a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 192a b + 192a b)\|- 1 + (192a b - 192a b)\|- 1 ---R + ---R 3 3 ---R - 192a b + 192a b ---R * ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ 3 ---R (- 64a b + 64a b)\|- 1 + (64a b - 64a b)\|- 1 - 64a b ---R + ---R 3 ---R 64a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 96a b - 48a )\|- 1 + (96a b + 48a )\|- 1 - 96a b ---R + ---R 4 ---R - 48a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (- 336a b - 144a )\|- 1 + (336a b + 144a )\|- 1 ---R + ---R 2 2 4 ---R - 336a b - 144a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (- 432a b - 144a )\|- 1 + (432a b + 144a )\|- 1 ---R + ---R 2 2 4 ---R - 432a b - 144a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (- 240a b - 48a )\|- 1 + (240a b + 48a )\|- 1 ---R + ---R 2 2 4 ---R - 240a b - 48a ---R * ---R cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 48a b \|- 1 + 48a b \|- 1 - 48a b ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 32a b - 16a )\|- 1 + (32a b + 16a )\|- 1 - 32a b ---R + ---R 4 ---R - 16a ---R * ---R 6 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 168a b - 72a )\|- 1 + (168a b + 72a )\|- 1 - 168a b ---R + ---R 4 ---R - 72a ---R * ---R 5 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (- 360a b - 120a )\|- 1 + (360a b + 120a )\|- 1 ---R + ---R 2 2 4 ---R - 360a b - 120a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 400a b - 80a )\|- 1 + (400a b + 80a )\|- 1 - 400a b ---R + ---R 4 ---R - 80a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 240a b \|- 1 + 240a b \|- 1 - 240a b )cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 72a b + 24a )\|- 1 + (72a b - 24a )\|- 1 - 72a b ---R + ---R 4 ---R 24a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (- 8a b + 8a )\|- 1 + (8a b - 8a )\|- 1 - 8a b + 8a ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (51a b \|- 1 - 51a b\|- 1 + 51a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (153a b \|- 1 - 153a b\|- 1 + 153a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (252a b \|- 1 - 252a b\|- 1 + 252a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 99a b \|- 1 - 99a b\|- 1 + 99a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 24a b \|- 1 + 24a b \|- 1 - 24a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 24a b \|- 1 + 24a b \|- 1 - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (153a b \|- 1 - 153a b\|- 1 + 153a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (504a b \|- 1 - 504a b\|- 1 + 504a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (594a b \|- 1 - 594a b\|- 1 + 594a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (288a b \|- 1 - 288a b\|- 1 + 288a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 45a b \|- 1 - 45a b\|- 1 + 45a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (51a b \|- 1 - 51a b\|- 1 + 51a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (252a b \|- 1 - 252a b\|- 1 + 252a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (495a b \|- 1 - 495a b\|- 1 + 495a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (480a b \|- 1 - 480a b\|- 1 + 480a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (225a b \|- 1 - 225a b\|- 1 + 225a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (36a b \|- 1 - 36a b\|- 1 + 36a b)cos(x) - 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a b\|- 1 - 3a b ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((8a b - 8a )\|- 1 + (- 8a b + 8a )\|- 1 + 8a b - 8a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (24a b - 24a )\|- 1 + (- 24a b + 24a )\|- 1 + 24a b ---R + ---R 4 ---R - 24a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 36a )\|- 1 + (- 36a b + 36a )\|- 1 + 36a b ---R + ---R 4 ---R - 36a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (12a b - 12a )\|- 1 + (- 12a b + 12a )\|- 1 + 12a b ---R + ---R 4 ---R - 12a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 32a b + 32a b)\|- 1 + (32a b - 32a b)\|- 1 ---R + ---R 3 3 ---R - 32a b + 32a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 96a b + 96a b)\|- 1 + (96a b - 96a b)\|- 1 ---R + ---R 3 3 ---R - 96a b + 96a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 96a b + 96a b)\|- 1 + (96a b - 96a b)\|- 1 ---R + ---R 3 3 ---R - 96a b + 96a b ---R * ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ 3 ---R (- 32a b + 32a b)\|- 1 + (32a b - 32a b)\|- 1 - 32a b ---R + ---R 3 ---R 32a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (24a b - 24a )\|- 1 + (- 24a b + 24a )\|- 1 + 24a b ---R + ---R 4 ---R - 24a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 72a )\|- 1 + (- 72a b + 72a )\|- 1 + 72a b ---R + ---R 4 ---R - 72a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 72a )\|- 1 + (- 72a b + 72a )\|- 1 + 72a b ---R + ---R 4 ---R - 72a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (24a b - 24a )\|- 1 + (- 24a b + 24a )\|- 1 + 24a b ---R + ---R 4 ---R - 24a ---R * ---R cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((8a b - 8a )\|- 1 + (- 8a b + 8a )\|- 1 + 8a b - 8a ) ---R * ---R 6 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 36a )\|- 1 + (- 36a b + 36a )\|- 1 + 36a b ---R + ---R 4 ---R - 36a ---R * ---R 5 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (60a b - 60a )\|- 1 + (- 60a b + 60a )\|- 1 + 60a b ---R + ---R 4 ---R - 60a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (40a b - 40a )\|- 1 + (- 40a b + 40a )\|- 1 + 40a b ---R + ---R 4 ---R - 40a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 12a b + 12a )\|- 1 + (12a b - 12a )\|- 1 - 12a b ---R + ---R 4 ---R 12a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (- 4a b + 4a )\|- 1 + (4a b - 4a )\|- 1 - 4a b + 4a ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 12a b \|- 1 + 12a b\|- 1 - 12a b)cos(x) - 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a b\|- 1 - 3a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (24a b \|- 1 - 24a b \|- 1 + 24a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 3+---+2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) + 24a b \|- 1 ---R + ---R 2 2 3+---+ 2 2 ---R - 24a b \|- 1 + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) + 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 3a b\|- 1 + 3a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (- 12a b \|- 1 + 12a b\|- 1 - 12a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 15a b \|- 1 + 15a b\|- 1 - 15a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (15a b \|- 1 - 15a b\|- 1 + 15a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (12a b \|- 1 - 12a b\|- 1 + 12a b)cos(x) + 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 3a b\|- 1 + 3a b ---R * ---R 3+-+ ---R \|b ---R + ---R 2 2 4 6 ---R (3a b - 3a )sin(x) ---R + ---R 2 2 4 2 2 2 4 2 2 4 ---R ((9a b - 9a )cos(x) + (12a b - 12a )cos(x) + 3a b - 3a ) ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3 3 3 2 ---R (- 24a b + 24a b)cos(x) + (- 72a b + 72a b)cos(x) ---R + ---R 3 3 3 3 ---R (- 72a b + 72a b)cos(x) - 24a b + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 4 2 2 4 3 ---R (9a b - 9a )cos(x) + (24a b - 24a )cos(x) ---R + ---R 2 2 4 2 2 2 4 ---R (18a b - 18a )cos(x) - 3a b + 3a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 6 2 2 4 5 ---R (3a b - 3a )cos(x) + (12a b - 12a )cos(x) ---R + ---R 2 2 4 4 2 2 4 2 ---R (15a b - 15a )cos(x) + (- 15a b + 15a )cos(x) ---R + ---R 2 2 4 2 2 4 ---R (- 12a b + 12a )cos(x) - 3a b + 3a ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 36a b \|- 1 - 36a b\|- 1 + 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 96a b \|- 1 + 96a b \|- 1 - 96a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 96a b \|- 1 + 96a b \|- 1 - 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (180a b \|- 1 - 180a b\|- 1 + 180a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (120a b \|- 1 - 120a b\|- 1 + 120a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) - 12a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 12a b\|- 1 - 12a b ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 6 ---R (- 60a b \|- 1 + 60a b \|- 1 - 51a b - 9a )sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 180a b \|- 1 + 180a b \|- 1 - 153a b - 27a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R (- 288a b \|- 1 + 288a b \|- 1 - 252a b - 36a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R - 108a b \|- 1 + 108a b \|- 1 - 99a b - 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3 ---R (96a b \|- 1 - 96a b \|- 1 + 24a b + 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 2 ---R (288a b \|- 1 - 288a b \|- 1 + 72a b + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (288a b \|- 1 - 288a b \|- 1 + 72a b + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R 96a b \|- 1 - 96a b \|- 1 + 24a b + 72a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 4 ---R (- 180a b \|- 1 + 180a b \|- 1 - 153a b - 27a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 3 ---R (- 576a b \|- 1 + 576a b \|- 1 - 504a b - 72a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 594a b - 54a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R - 36a b \|- 1 + 36a b \|- 1 - 45a b + 9a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 6 ---R (- 60a b \|- 1 + 60a b \|- 1 - 51a b - 9a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 5 ---R (- 288a b \|- 1 + 288a b \|- 1 - 252a b - 36a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 4 ---R (- 540a b \|- 1 + 540a b \|- 1 - 495a b - 45a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 480a b \|- 1 + 480a b \|- 1 - 480a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 180a b \|- 1 + 180a b \|- 1 - 225a b + 45a )cos(x) ---R + ---R 2 2 4 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 36a b + 36a )cos(x) + 12a b \|- 1 - 12a b \|- 1 + 3a b ---R + ---R 4 ---R 9a ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (48a b \|- 1 - 48a b\|- 1 + 48a b )sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (144a b \|- 1 - 144a b\|- 1 + 144a b )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (216a b \|- 1 - 216a b\|- 1 + 240a b - 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R 72a b \|- 1 - 72a b\|- 1 + 96a b - 24a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 192a b \|- 1 + 192a b \|- 1 - 192a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 576a b \|- 1 + 576a b \|- 1 - 576a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 576a b \|- 1 + 576a b \|- 1 - 576a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 192a b \|- 1 + 192a b \|- 1 - 192a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (144a b \|- 1 - 144a b\|- 1 + 144a b )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3 ---R (432a b \|- 1 - 432a b\|- 1 + 480a b - 48a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 2 ---R (432a b \|- 1 - 432a b\|- 1 + 576a b - 144a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (144a b \|- 1 - 144a b\|- 1 + 288a b - 144a b)cos(x) ---R + ---R 3 3 ---R 48a b - 48a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (48a b \|- 1 - 48a b\|- 1 + 48a b )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 5 ---R (216a b \|- 1 - 216a b\|- 1 + 240a b - 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 4 ---R (360a b \|- 1 - 360a b\|- 1 + 480a b - 120a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3 ---R (240a b \|- 1 - 240a b\|- 1 + 480a b - 240a b)cos(x) ---R + ---R 3 3 2 ---R (240a b - 240a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 72a b \|- 1 + 72a b\|- 1 + 48a b - 120a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R - 24a b \|- 1 + 24a b\|- 1 - 24a b ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 6 ---R (- 60a b \|- 1 + 60a b \|- 1 - 51a b - 9a )sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 180a b \|- 1 + 180a b \|- 1 - 153a b - 27a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R (- 288a b \|- 1 + 288a b \|- 1 - 252a b - 36a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R - 108a b \|- 1 + 108a b \|- 1 - 99a b - 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3 ---R (96a b \|- 1 - 96a b \|- 1 + 24a b + 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 2 ---R (288a b \|- 1 - 288a b \|- 1 + 72a b + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (288a b \|- 1 - 288a b \|- 1 + 72a b + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R 96a b \|- 1 - 96a b \|- 1 + 24a b + 72a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 4 ---R (- 180a b \|- 1 + 180a b \|- 1 - 153a b - 27a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 3 ---R (- 576a b \|- 1 + 576a b \|- 1 - 504a b - 72a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 594a b - 54a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R - 36a b \|- 1 + 36a b \|- 1 - 45a b + 9a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 6 ---R (- 60a b \|- 1 + 60a b \|- 1 - 51a b - 9a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 5 ---R (- 288a b \|- 1 + 288a b \|- 1 - 252a b - 36a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 4 ---R (- 540a b \|- 1 + 540a b \|- 1 - 495a b - 45a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 480a b \|- 1 + 480a b \|- 1 - 480a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 180a b \|- 1 + 180a b \|- 1 - 225a b + 45a )cos(x) ---R + ---R 2 2 4 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 36a b + 36a )cos(x) + 12a b \|- 1 - 12a b \|- 1 + 3a b ---R + ---R 4 ---R 9a ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 36a b \|- 1 - 36a b\|- 1 + 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 96a b \|- 1 + 96a b \|- 1 - 96a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 96a b \|- 1 + 96a b \|- 1 - 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (180a b \|- 1 - 180a b\|- 1 + 180a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (120a b \|- 1 - 120a b\|- 1 + 120a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) - 12a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 12a b\|- 1 - 12a b ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 2 2 4 6 ---R (3a b - 3a )sin(x) ---R + ---R 2 2 4 2 2 2 4 2 2 4 4 ---R ((9a b - 9a )cos(x) + (12a b - 12a )cos(x) + 3a b - 3a )sin(x) ---R + ---R 3 3 3 3 3 2 ---R (- 24a b + 24a b)cos(x) + (- 72a b + 72a b)cos(x) ---R + ---R 3 3 3 3 ---R (- 72a b + 72a b)cos(x) - 24a b + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 4 2 2 4 3 ---R (9a b - 9a )cos(x) + (24a b - 24a )cos(x) ---R + ---R 2 2 4 2 2 2 4 ---R (18a b - 18a )cos(x) - 3a b + 3a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 6 2 2 4 5 ---R (3a b - 3a )cos(x) + (12a b - 12a )cos(x) ---R + ---R 2 2 4 4 2 2 4 2 ---R (15a b - 15a )cos(x) + (- 15a b + 15a )cos(x) ---R + ---R 2 2 4 2 2 4 ---R (- 12a b + 12a )cos(x) - 3a b + 3a ---R * ---R 3+-+ ---R \|a ---R / ---R 4 3+---+2 4 3+---+ 4 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) + 9a \|- 1 ---R + ---R 4 3+---+ 4 ---R - 9a \|- 1 + 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) + 24a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 24a b\|- 1 + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (36a \|- 1 - 36a \|- 1 + 36a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (36a \|- 1 - 36a \|- 1 + 36a )cos(x) + 9a \|- 1 ---R + ---R 4 3+---+ 4 ---R - 9a \|- 1 + 9a ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (45a \|- 1 - 45a \|- 1 + 45a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (60a \|- 1 - 60a \|- 1 + 60a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (45a \|- 1 - 45a \|- 1 + 45a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 4 3+---+ ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) + 3a \|- 1 - 3a \|- 1 ---R + ---R 4 ---R 3a ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R - 54a b \|- 1 + 54a b\|- 1 - 54a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 432a b \|- 1 + 432a b \|- 1 - 432a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 432a b \|- 1 + 432a b \|- 1 - 432a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 144a b \|- 1 + 144a b \|- 1 - 144a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 324a b \|- 1 + 324a b\|- 1 - 324a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R - 54a b \|- 1 + 54a b\|- 1 - 54a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 270a b \|- 1 + 270a b\|- 1 - 270a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 360a b \|- 1 + 360a b\|- 1 - 360a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 270a b \|- 1 + 270a b\|- 1 - 270a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) - 18a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 18a b\|- 1 - 18a b ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b ---R + ---R 4 ---R - 9a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b - 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (96a b - 24a b)\|- 1 + (- 96a b + 24a b)\|- 1 ---R + ---R 3 3 ---R 96a b - 24a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (288a b - 72a b)\|- 1 + (- 288a b + 72a b)\|- 1 ---R + ---R 3 3 ---R 288a b - 72a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (288a b - 72a b)\|- 1 + (- 288a b + 72a b)\|- 1 ---R + ---R 3 3 ---R 288a b - 72a b ---R * ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ 3 ---R (96a b - 24a b)\|- 1 + (- 96a b + 24a b)\|- 1 + 96a b ---R + ---R 3 ---R - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b ---R + ---R 4 ---R - 9a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (144a b - 36a )\|- 1 + (- 144a b + 36a )\|- 1 ---R + ---R 2 2 4 ---R 144a b - 36a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (216a b - 54a )\|- 1 + (- 216a b + 54a )\|- 1 ---R + ---R 2 2 4 ---R 216a b - 54a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (144a b - 36a )\|- 1 + (- 144a b + 36a )\|- 1 ---R + ---R 2 2 4 ---R 144a b - 36a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b - 9a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ) ---R * ---R 6 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R 5 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (180a b - 45a )\|- 1 + (- 180a b + 45a )\|- 1 + 180a b ---R + ---R 4 ---R - 45a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (240a b - 60a )\|- 1 + (- 240a b + 60a )\|- 1 + 240a b ---R + ---R 4 ---R - 60a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (180a b - 45a )\|- 1 + (- 180a b + 45a )\|- 1 + 180a b ---R + ---R 4 ---R - 45a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 12a b \|- 1 + 12a b\|- 1 - 12a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) - 36a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 36a b\|- 1 - 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 96a b \|- 1 + 96a b \|- 1 - 96a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 96a b \|- 1 + 96a b \|- 1 - 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R - 36a b \|- 1 + 36a b\|- 1 - 36a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 12a b \|- 1 + 12a b\|- 1 - 12a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 180a b \|- 1 + 180a b\|- 1 - 180a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 240a b \|- 1 + 240a b\|- 1 - 240a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 180a b \|- 1 + 180a b\|- 1 - 180a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) - 12a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 12a b\|- 1 - 12a b ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b ---R + ---R 4 ---R - 9a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b - 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (96a b - 24a b)\|- 1 + (- 96a b + 24a b)\|- 1 ---R + ---R 3 3 ---R 96a b - 24a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (288a b - 72a b)\|- 1 + (- 288a b + 72a b)\|- 1 ---R + ---R 3 3 ---R 288a b - 72a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (288a b - 72a b)\|- 1 + (- 288a b + 72a b)\|- 1 ---R + ---R 3 3 ---R 288a b - 72a b ---R * ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ 3 ---R (96a b - 24a b)\|- 1 + (- 96a b + 24a b)\|- 1 + 96a b ---R + ---R 3 ---R - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b ---R + ---R 4 ---R - 9a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (144a b - 36a )\|- 1 + (- 144a b + 36a )\|- 1 ---R + ---R 2 2 4 ---R 144a b - 36a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (216a b - 54a )\|- 1 + (- 216a b + 54a )\|- 1 ---R + ---R 2 2 4 ---R 216a b - 54a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (144a b - 36a )\|- 1 + (- 144a b + 36a )\|- 1 ---R + ---R 2 2 4 ---R 144a b - 36a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b - 9a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ) ---R * ---R 6 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R 5 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (180a b - 45a )\|- 1 + (- 180a b + 45a )\|- 1 + 180a b ---R + ---R 4 ---R - 45a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (240a b - 60a )\|- 1 + (- 240a b + 60a )\|- 1 + 240a b ---R + ---R 4 ---R - 60a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (180a b - 45a )\|- 1 + (- 180a b + 45a )\|- 1 + 180a b ---R + ---R 4 ---R - 45a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R - 54a b \|- 1 + 54a b\|- 1 - 54a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 432a b \|- 1 + 432a b \|- 1 - 432a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 432a b \|- 1 + 432a b \|- 1 - 432a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 144a b \|- 1 + 144a b \|- 1 - 144a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 324a b \|- 1 + 324a b\|- 1 - 324a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R - 54a b \|- 1 + 54a b\|- 1 - 54a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 270a b \|- 1 + 270a b\|- 1 - 270a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 360a b \|- 1 + 360a b\|- 1 - 360a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 270a b \|- 1 + 270a b\|- 1 - 270a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) - 18a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 18a b\|- 1 - 18a b ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 4 3+---+ ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) + 9a \|- 1 - 9a \|- 1 ---R + ---R 4 ---R 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) + 24a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 24a b\|- 1 + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (36a \|- 1 - 36a \|- 1 + 36a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 4 3+---+ ---R (36a \|- 1 - 36a \|- 1 + 36a )cos(x) + 9a \|- 1 - 9a \|- 1 ---R + ---R 4 ---R 9a ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (45a \|- 1 - 45a \|- 1 + 45a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (60a \|- 1 - 60a \|- 1 + 60a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (45a \|- 1 - 45a \|- 1 + 45a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 4 3+---+ 4 ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) + 3a \|- 1 - 3a \|- 1 + 3a ---R * ---R 3+-+2 3+-+2 ---R \|a \|b ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) - 9a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 9a b\|- 1 - 9a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (- 24a b \|- 1 + 24a b \|- 1 - 24a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R - 24a b \|- 1 + 24a b \|- 1 - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) - 9a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 9a b\|- 1 - 9a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 60a b \|- 1 + 60a b\|- 1 - 60a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) - 3a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 3a b\|- 1 - 3a b ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R ((6a b - 6a )\|- 1 + (- 6a b + 6a )\|- 1 + 6a b - 6a ) ---R * ---R 6 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (18a b - 18a )\|- 1 + (- 18a b + 18a )\|- 1 + 18a b ---R + ---R 5 ---R - 18a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (36a b - 36a )\|- 1 + (- 36a b + 36a )\|- 1 + 36a b ---R + ---R 5 ---R - 36a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (18a b - 18a )\|- 1 + (- 18a b + 18a )\|- 1 + 18a b ---R + ---R 5 ---R - 18a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (48a b - 48a b)\|- 1 + (- 48a b + 48a b)\|- 1 ---R + ---R 2 3 4 ---R 48a b - 48a b ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (144a b - 144a b)\|- 1 + (- 144a b + 144a b)\|- 1 ---R + ---R 2 3 4 ---R 144a b - 144a b ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (144a b - 144a b)\|- 1 + (- 144a b + 144a b)\|- 1 ---R + ---R 2 3 4 ---R 144a b - 144a b ---R * ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 ---R (48a b - 48a b)\|- 1 + (- 48a b + 48a b)\|- 1 + 48a b ---R + ---R 4 ---R - 48a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (18a b - 18a )\|- 1 + (- 18a b + 18a )\|- 1 + 18a b ---R + ---R 5 ---R - 18a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (72a b - 72a )\|- 1 + (- 72a b + 72a )\|- 1 + 72a b ---R + ---R 5 ---R - 72a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (108a b - 108a )\|- 1 + (- 108a b + 108a )\|- 1 ---R + ---R 3 2 5 ---R 108a b - 108a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (72a b - 72a )\|- 1 + (- 72a b + 72a )\|- 1 + 72a b ---R + ---R 5 ---R - 72a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (18a b - 18a )\|- 1 + (- 18a b + 18a )\|- 1 + 18a b ---R + ---R 5 ---R - 18a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R ((6a b - 6a )\|- 1 + (- 6a b + 6a )\|- 1 + 6a b - 6a ) ---R * ---R 6 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (36a b - 36a )\|- 1 + (- 36a b + 36a )\|- 1 + 36a b ---R + ---R 5 ---R - 36a ---R * ---R 5 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (90a b - 90a )\|- 1 + (- 90a b + 90a )\|- 1 + 90a b ---R + ---R 5 ---R - 90a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (120a b - 120a )\|- 1 + (- 120a b + 120a )\|- 1 ---R + ---R 3 2 5 ---R 120a b - 120a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (90a b - 90a )\|- 1 + (- 90a b + 90a )\|- 1 + 90a b ---R + ---R 5 ---R - 90a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (36a b - 36a )\|- 1 + (- 36a b + 36a )\|- 1 + 36a b ---R + ---R 5 ---R - 36a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R (6a b - 6a )\|- 1 + (- 6a b + 6a )\|- 1 + 6a b - 6a ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (27a b \|- 1 - 27a b\|- 1 + 27a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (81a b \|- 1 - 81a b\|- 1 + 81a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 81a b \|- 1 - 81a b\|- 1 + 81a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (216a b \|- 1 - 216a b \|- 1 + 216a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (648a b \|- 1 - 648a b \|- 1 + 648a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (648a b \|- 1 - 648a b \|- 1 + 648a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R 216a b \|- 1 - 216a b \|- 1 + 216a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (81a b \|- 1 - 81a b\|- 1 + 81a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (486a b \|- 1 - 486a b\|- 1 + 486a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 81a b \|- 1 - 81a b\|- 1 + 81a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (27a b \|- 1 - 27a b\|- 1 + 27a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (405a b \|- 1 - 405a b\|- 1 + 405a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (540a b \|- 1 - 540a b\|- 1 + 540a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (405a b \|- 1 - 405a b\|- 1 + 405a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) + 27a b \|- 1 ---R + ---R 4 3+---+ 4 ---R - 27a b\|- 1 + 27a b ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 12a b - 12a )\|- 1 + (12a b + 12a )\|- 1 - 12a b ---R + ---R 5 ---R - 12a ---R * ---R 6 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 36a b - 36a )\|- 1 + (36a b + 36a )\|- 1 - 36a b ---R + ---R 5 ---R - 36a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 72a b - 72a )\|- 1 + (72a b + 72a )\|- 1 - 72a b ---R + ---R 5 ---R - 72a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 36a b - 36a )\|- 1 + (36a b + 36a )\|- 1 - 36a b ---R + ---R 5 ---R - 36a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (- 96a b - 96a b)\|- 1 + (96a b + 96a b)\|- 1 ---R + ---R 2 3 4 ---R - 96a b - 96a b ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (- 288a b - 288a b)\|- 1 + (288a b + 288a b)\|- 1 ---R + ---R 2 3 4 ---R - 288a b - 288a b ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (- 288a b - 288a b)\|- 1 + (288a b + 288a b)\|- 1 ---R + ---R 2 3 4 ---R - 288a b - 288a b ---R * ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 ---R (- 96a b - 96a b)\|- 1 + (96a b + 96a b)\|- 1 - 96a b ---R + ---R 4 ---R - 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 36a b - 36a )\|- 1 + (36a b + 36a )\|- 1 - 36a b ---R + ---R 5 ---R - 36a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (- 144a b - 144a )\|- 1 + (144a b + 144a )\|- 1 ---R + ---R 3 2 5 ---R - 144a b - 144a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (- 216a b - 216a )\|- 1 + (216a b + 216a )\|- 1 ---R + ---R 3 2 5 ---R - 216a b - 216a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (- 144a b - 144a )\|- 1 + (144a b + 144a )\|- 1 ---R + ---R 3 2 5 ---R - 144a b - 144a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 36a b - 36a )\|- 1 + (36a b + 36a )\|- 1 - 36a b ---R + ---R 5 ---R - 36a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 12a b - 12a )\|- 1 + (12a b + 12a )\|- 1 - 12a b ---R + ---R 5 ---R - 12a ---R * ---R 6 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 72a b - 72a )\|- 1 + (72a b + 72a )\|- 1 - 72a b ---R + ---R 5 ---R - 72a ---R * ---R 5 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (- 180a b - 180a )\|- 1 + (180a b + 180a )\|- 1 ---R + ---R 3 2 5 ---R - 180a b - 180a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (- 240a b - 240a )\|- 1 + (240a b + 240a )\|- 1 ---R + ---R 3 2 5 ---R - 240a b - 240a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (- 180a b - 180a )\|- 1 + (180a b + 180a )\|- 1 ---R + ---R 3 2 5 ---R - 180a b - 180a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 72a b - 72a )\|- 1 + (72a b + 72a )\|- 1 - 72a b ---R + ---R 5 ---R - 72a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R (- 12a b - 12a )\|- 1 + (12a b + 12a )\|- 1 - 12a b - 12a ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (27a b \|- 1 - 27a b\|- 1 + 27a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (81a b \|- 1 - 81a b\|- 1 + 81a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 81a b \|- 1 - 81a b\|- 1 + 81a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (216a b \|- 1 - 216a b \|- 1 + 216a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (648a b \|- 1 - 648a b \|- 1 + 648a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (648a b \|- 1 - 648a b \|- 1 + 648a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R 216a b \|- 1 - 216a b \|- 1 + 216a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (81a b \|- 1 - 81a b\|- 1 + 81a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (486a b \|- 1 - 486a b\|- 1 + 486a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 81a b \|- 1 - 81a b\|- 1 + 81a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (27a b \|- 1 - 27a b\|- 1 + 27a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (405a b \|- 1 - 405a b\|- 1 + 405a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (540a b \|- 1 - 540a b\|- 1 + 540a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (405a b \|- 1 - 405a b\|- 1 + 405a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) + 27a b \|- 1 ---R + ---R 4 3+---+ 4 ---R - 27a b\|- 1 + 27a b ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R ((6a b - 6a )\|- 1 + (- 6a b + 6a )\|- 1 + 6a b - 6a ) ---R * ---R 6 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (18a b - 18a )\|- 1 + (- 18a b + 18a )\|- 1 + 18a b ---R + ---R 5 ---R - 18a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (36a b - 36a )\|- 1 + (- 36a b + 36a )\|- 1 + 36a b ---R + ---R 5 ---R - 36a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (18a b - 18a )\|- 1 + (- 18a b + 18a )\|- 1 + 18a b ---R + ---R 5 ---R - 18a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (48a b - 48a b)\|- 1 + (- 48a b + 48a b)\|- 1 ---R + ---R 2 3 4 ---R 48a b - 48a b ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (144a b - 144a b)\|- 1 + (- 144a b + 144a b)\|- 1 ---R + ---R 2 3 4 ---R 144a b - 144a b ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (144a b - 144a b)\|- 1 + (- 144a b + 144a b)\|- 1 ---R + ---R 2 3 4 ---R 144a b - 144a b ---R * ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 ---R (48a b - 48a b)\|- 1 + (- 48a b + 48a b)\|- 1 + 48a b ---R + ---R 4 ---R - 48a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (18a b - 18a )\|- 1 + (- 18a b + 18a )\|- 1 + 18a b ---R + ---R 5 ---R - 18a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (72a b - 72a )\|- 1 + (- 72a b + 72a )\|- 1 + 72a b ---R + ---R 5 ---R - 72a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (108a b - 108a )\|- 1 + (- 108a b + 108a )\|- 1 ---R + ---R 3 2 5 ---R 108a b - 108a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (72a b - 72a )\|- 1 + (- 72a b + 72a )\|- 1 + 72a b ---R + ---R 5 ---R - 72a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (18a b - 18a )\|- 1 + (- 18a b + 18a )\|- 1 + 18a b ---R + ---R 5 ---R - 18a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R ((6a b - 6a )\|- 1 + (- 6a b + 6a )\|- 1 + 6a b - 6a ) ---R * ---R 6 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (36a b - 36a )\|- 1 + (- 36a b + 36a )\|- 1 + 36a b ---R + ---R 5 ---R - 36a ---R * ---R 5 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (90a b - 90a )\|- 1 + (- 90a b + 90a )\|- 1 + 90a b ---R + ---R 5 ---R - 90a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (120a b - 120a )\|- 1 + (- 120a b + 120a )\|- 1 ---R + ---R 3 2 5 ---R 120a b - 120a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (90a b - 90a )\|- 1 + (- 90a b + 90a )\|- 1 + 90a b ---R + ---R 5 ---R - 90a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (36a b - 36a )\|- 1 + (- 36a b + 36a )\|- 1 + 36a b ---R + ---R 5 ---R - 36a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R (6a b - 6a )\|- 1 + (- 6a b + 6a )\|- 1 + 6a b - 6a ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) - 9a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 9a b\|- 1 - 9a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (- 24a b \|- 1 + 24a b \|- 1 - 24a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 2 3+---+2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) - 24a b \|- 1 ---R + ---R 3 2 3+---+ 3 2 ---R 24a b \|- 1 - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) - 9a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 9a b\|- 1 - 9a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 60a b \|- 1 + 60a b\|- 1 - 60a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) - 3a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 3a b\|- 1 - 3a b ---R * ---R 3+-+ ---R \|b ---R + ---R 3 2 5 6 ---R (3a b - 3a )sin(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 ---R ((9a b - 9a )cos(x) + (18a b - 18a )cos(x) + 9a b - 9a ) ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 4 3 2 3 4 2 ---R (24a b - 24a b)cos(x) + (72a b - 72a b)cos(x) ---R + ---R 2 3 4 2 3 4 ---R (72a b - 72a b)cos(x) + 24a b - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 5 4 3 2 5 3 ---R (9a b - 9a )cos(x) + (36a b - 36a )cos(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 ---R (54a b - 54a )cos(x) + (36a b - 36a )cos(x) + 9a b - 9a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 5 6 3 2 5 5 ---R (3a b - 3a )cos(x) + (18a b - 18a )cos(x) ---R + ---R 3 2 5 4 3 2 5 3 ---R (45a b - 45a )cos(x) + (60a b - 60a )cos(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 ---R (45a b - 45a )cos(x) + (18a b - 18a )cos(x) + 3a b - 3a ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (18a b \|- 1 - 18a b\|- 1 + 18a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (54a b \|- 1 - 54a b\|- 1 + 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 54a b \|- 1 - 54a b\|- 1 + 54a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (144a b \|- 1 - 144a b \|- 1 + 144a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (432a b \|- 1 - 432a b \|- 1 + 432a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (432a b \|- 1 - 432a b \|- 1 + 432a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R 144a b \|- 1 - 144a b \|- 1 + 144a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (54a b \|- 1 - 54a b\|- 1 + 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 54a b \|- 1 - 54a b\|- 1 + 54a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (18a b \|- 1 - 18a b\|- 1 + 18a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (270a b \|- 1 - 270a b\|- 1 + 270a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (360a b \|- 1 - 360a b\|- 1 + 360a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (270a b \|- 1 - 270a b\|- 1 + 270a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) + 18a b \|- 1 ---R + ---R 4 3+---+ 4 ---R - 18a b\|- 1 + 18a b ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 6 ---R (- 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a )sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 ---R (- 288a b \|- 1 + 288a b \|- 1 - 216a b - 72a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 ---R (- 864a b \|- 1 + 864a b \|- 1 - 648a b - 216a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 ---R (- 864a b \|- 1 + 864a b \|- 1 - 648a b - 216a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 ---R - 288a b \|- 1 + 288a b \|- 1 - 216a b - 72a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 4 ---R (- 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 ---R (- 432a b \|- 1 + 432a b \|- 1 - 324a b - 108a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 486a b - 162a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 432a b \|- 1 + 432a b \|- 1 - 324a b - 108a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 6 ---R (- 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 4 ---R (- 540a b \|- 1 + 540a b \|- 1 - 405a b - 135a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 ---R (- 720a b \|- 1 + 720a b \|- 1 - 540a b - 180a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 540a b \|- 1 + 540a b \|- 1 - 405a b - 135a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 6 ---R (36a b \|- 1 - 36a b\|- 1 + 24a b + 12a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 2 ---R (108a b \|- 1 - 108a b\|- 1 + 72a b + 36a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R (216a b \|- 1 - 216a b\|- 1 + 144a b + 72a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R 108a b \|- 1 - 108a b\|- 1 + 72a b + 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 4 3 2 3 ---R (288a b \|- 1 - 288a b \|- 1 + 192a b + 96a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 4 3 2 2 ---R (864a b \|- 1 - 864a b \|- 1 + 576a b + 288a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 4 3 2 ---R (864a b \|- 1 - 864a b \|- 1 + 576a b + 288a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 4 3 2 ---R 288a b \|- 1 - 288a b \|- 1 + 192a b + 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 4 ---R (108a b \|- 1 - 108a b\|- 1 + 72a b + 36a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 3 ---R (432a b \|- 1 - 432a b\|- 1 + 288a b + 144a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 2 ---R (648a b \|- 1 - 648a b\|- 1 + 432a b + 216a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R (432a b \|- 1 - 432a b\|- 1 + 288a b + 144a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R 108a b \|- 1 - 108a b\|- 1 + 72a b + 36a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 6 ---R (36a b \|- 1 - 36a b\|- 1 + 24a b + 12a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 5 ---R (216a b \|- 1 - 216a b\|- 1 + 144a b + 72a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 4 ---R (540a b \|- 1 - 540a b\|- 1 + 360a b + 180a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 3 ---R (720a b \|- 1 - 720a b\|- 1 + 480a b + 240a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 2 ---R (540a b \|- 1 - 540a b\|- 1 + 360a b + 180a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R (216a b \|- 1 - 216a b\|- 1 + 144a b + 72a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R 36a b \|- 1 - 36a b\|- 1 + 24a b + 12a b ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 6 ---R (- 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a )sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 ---R (- 288a b \|- 1 + 288a b \|- 1 - 216a b - 72a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 ---R (- 864a b \|- 1 + 864a b \|- 1 - 648a b - 216a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 ---R (- 864a b \|- 1 + 864a b \|- 1 - 648a b - 216a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 ---R - 288a b \|- 1 + 288a b \|- 1 - 216a b - 72a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 4 ---R (- 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 ---R (- 432a b \|- 1 + 432a b \|- 1 - 324a b - 108a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 486a b - 162a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 432a b \|- 1 + 432a b \|- 1 - 324a b - 108a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 6 ---R (- 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 4 ---R (- 540a b \|- 1 + 540a b \|- 1 - 405a b - 135a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 ---R (- 720a b \|- 1 + 720a b \|- 1 - 540a b - 180a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 540a b \|- 1 + 540a b \|- 1 - 405a b - 135a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (18a b \|- 1 - 18a b\|- 1 + 18a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (54a b \|- 1 - 54a b\|- 1 + 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 54a b \|- 1 - 54a b\|- 1 + 54a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (144a b \|- 1 - 144a b \|- 1 + 144a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (432a b \|- 1 - 432a b \|- 1 + 432a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (432a b \|- 1 - 432a b \|- 1 + 432a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R 144a b \|- 1 - 144a b \|- 1 + 144a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (54a b \|- 1 - 54a b\|- 1 + 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 54a b \|- 1 - 54a b\|- 1 + 54a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (18a b \|- 1 - 18a b\|- 1 + 18a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (270a b \|- 1 - 270a b\|- 1 + 270a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (360a b \|- 1 - 360a b\|- 1 + 360a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (270a b \|- 1 - 270a b\|- 1 + 270a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) + 18a b \|- 1 ---R + ---R 4 3+---+ 4 ---R - 18a b\|- 1 + 18a b ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 3 2 5 6 ---R (3a b - 3a )sin(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 4 ---R ((9a b - 9a )cos(x) + (18a b - 18a )cos(x) + 9a b - 9a )sin(x) ---R + ---R 2 3 4 3 2 3 4 2 ---R (24a b - 24a b)cos(x) + (72a b - 72a b)cos(x) ---R + ---R 2 3 4 2 3 4 ---R (72a b - 72a b)cos(x) + 24a b - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 5 4 3 2 5 3 ---R (9a b - 9a )cos(x) + (36a b - 36a )cos(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 ---R (54a b - 54a )cos(x) + (36a b - 36a )cos(x) + 9a b - 9a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 5 6 3 2 5 5 ---R (3a b - 3a )cos(x) + (18a b - 18a )cos(x) ---R + ---R 3 2 5 4 3 2 5 3 ---R (45a b - 45a )cos(x) + (60a b - 60a )cos(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 ---R (45a b - 45a )cos(x) + (18a b - 18a )cos(x) + 3a b - 3a ---R * ---R 3+-+ ---R \|a ---R Type: Expression Integer +--d0063:= D(m0063,x) --E 340 --S 341 of 520 @@ -24704,17 +19229,20 @@ t0064:= 1/(a+b*sin(x)^4) --R --R --R 1 ---R (237) ------------- +--R (207) ------------- --R 4 --R b sin(x) + a --R Type: Expression Integer --E 341 --S 342 of 520 -r0064:= 1/2*atan((a^(1/2)-(-b)^(1/2))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)-(-b)^(1/2))^(1/2)+1/2*atan((a^(1/2)+(-b)^(1/2))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)+(-b)^(1/2))^(1/2) +r0064:= 1/2*atan((a^(1/2)-(-b)^(1/2))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/_ + (a^(1/2)-(-b)^(1/2))^(1/2)+1/2*_ + atan((a^(1/2)+(-b)^(1/2))^(1/2)*_ + tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)+(-b)^(1/2))^(1/2) --R --R ---R (238) +--R (208) --R +-------------+ --R +-------------+ | +-+ +---+ --R | +-+ +---+ tan(x)\|\|a + \|- b @@ -24739,7 +19267,7 @@ r0064:= 1/2*atan((a^(1/2)-(-b)^(1/2))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)-(-b a0064:= integrate(t0064,x) --R --R ---R (239) +--R (209) --R +-------------------------------------------+ --R | +------------------------+ --R | 2 | b @@ -24880,7 +19408,7 @@ a0064:= integrate(t0064,x) m0064:= a0064-r0064 --R --R ---R (240) +--R (210) --R +-------------------------------------------+ --R | +------------------------+ --R | 2 | b @@ -25053,7 +19581,7 @@ m0064:= a0064-r0064 d0064:= D(m0064,x) --R --R ---R (241) +--R (211) --R 4 2 2 4 4 --R ((b + a)sin(x) + (2b + 2a)cos(x) sin(x) + (b + a)cos(x) )tan(x) --R + @@ -25097,17 +19625,21 @@ t0065:= 1/(a+b*sin(x)^6) --R --R --R 1 ---R (242) ------------- +--R (212) ------------- --R 6 --R b sin(x) + a --R Type: Expression Integer --E 346 --S 347 of 520 -r0065:= 1/3*atan((a^(1/3)+b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)+b^(1/3))^(1/2)+1/3*atan((a^(1/3)-(-1)^(1/3)*b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)-(-1)^(1/3)*b^(1/3))^(1/2)+1/3*atan((a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2) +r0065:= 1/3*atan((a^(1/3)+b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/_ + (a^(1/3)+b^(1/3))^(1/2)+1/3*atan((a^(1/3)-(-1)^(1/3)*b^(1/3))^(1/2)*_ + tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)-(-1)^(1/3)*b^(1/3))^(1/2)+_ + 1/3*atan((a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2)*_ + tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2) --R --R ---R (243) +--R (213) --R +------------------+ --R +-------------------+ +-----------+ |3+---+2 3+-+ 3+-+ --R | 3+---+3+-+ 3+-+ |3+-+ 3+-+ tan(x)\|\|- 1 \|b + \|a @@ -25139,7 +19671,7 @@ r0065:= 1/3*atan((a^(1/3)+b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)+b^(1/3 a0065:= integrate(t0065,x) --R --R ---R (244) +--R (214) --R - --R ROOT --R 2 @@ -25427,7 +19959,7 @@ a0065:= integrate(t0065,x) m0065:= a0065-r0065 --R --R ---R (245) +--R (215) --R - --R +-------------------+ +-----------+ +------------------+ --R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ @@ -25762,7 +20294,7 @@ m0065:= a0065-r0065 d0065:= D(m0065,x) --R --R ---R (246) +--R (216) --R 3+---+2 3+---+ 6 --R ((6b + 15a)\|- 1 + (- 6b - 15a)\|- 1 + 6b + 15a)sin(x) --R + @@ -26499,17 +21031,24 @@ t0066:= 1/(a+b*sin(x)^8) --R --R --R 1 ---R (247) ------------- +--R (217) ------------- --R 8 --R b sin(x) + a --R Type: Expression Integer --E 351 --S 352 of 520 -r0066:= 1/4*atan((a^(1/4)+(-b)^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/(a^(1/4)+(-b)^(1/4))^(1/2)+1/4*atan((a^(1/2)-a^(1/4)*(-b)^(1/4))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)-a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atan((a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atan((a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2) +r0066:= 1/4*atan((a^(1/4)+(-b)^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/_ + (a^(1/4)+(-b)^(1/4))^(1/2)+1/4*atan((a^(1/2)-_ + a^(1/4)*(-b)^(1/4))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/_ + (a^(1/2)-a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atan((a^(1/2)-_ + %i*a^(1/4)*(-b)^(1/4))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/_ + (a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2)+1/4*_ + atan((a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2)*_ + tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2) --R --R ---R (248) +--R (218) --R +-------------------+ +---------------------+ +-------------+ --R 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ --R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b @@ -26568,7 +21107,7 @@ r0066:= 1/4*atan((a^(1/4)+(-b)^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/(a^(1/4)+(-b a0066:= integrate(t0066,x) --R --R ---R (249) +--R (219) --R ROOT --R 2 --R (16a b + 16a ) @@ -27073,7 +21612,7 @@ a0066:= integrate(t0066,x) m0066:= a0066-r0066 --R --R ---R (250) +--R (220) --R +-------------------+ +---------------------+ --R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ --R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a @@ -27684,7 +22223,7 @@ m0066:= a0066-r0066 d0066:= D(m0066,x) --R --R ---R (251) +--R (221) --R 8 2 6 --R (- 4b - 36a)sin(x) + (32b - 144a)cos(x) sin(x) --R + @@ -29297,17 +23836,23 @@ t0067:= 1/(a-b*sin(x)^3) --R --R --R 1 ---R (252) - ------------- +--R (222) - ------------- --R 3 --R b sin(x) - a --R Type: Expression Integer --E 356 --S 357 of 520 -r0067:= -2/3*atan((b^(1/3)-a^(1/3)*tan(1/2*x))/(a^(2/3)-b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)-2/3*atan(((-1)^(2/3)*b^(1/3)-a^(1/3)*tan(1/2*x))/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+2/3*atan(((-1)^(1/3)*b^(1/3)+a^(1/3)*tan(1/2*x))/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) +r0067:= -2/3*atan((b^(1/3)-a^(1/3)*tan(1/2*x))/(a^(2/3)-b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)-2/3*atan(((-1)^(2/3)*b^(1/3)-_ + a^(1/3)*tan(1/2*x))/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+2/3*_ + atan(((-1)^(1/3)*b^(1/3)+a^(1/3)*tan(1/2*x))/_ + (a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/_ + (a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) --R --R ---R (253) +--R (223) --R 3+---+3+-+ x 3+-+ --R +---------------+ +-------------------+ \|- 1 \|b + tan(-)\|a --R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 2 @@ -29352,7 +23897,7 @@ r0067:= -2/3*atan((b^(1/3)-a^(1/3)*tan(1/2*x))/(a^(2/3)-b^(2/3))^(1/2))/a^(2/3)/ a0067:= integrate(t0067,x) --R --R ---R (254) +--R (224) --R ROOT --R 2 2 --R (6b - 6a ) @@ -29754,7 +24299,7 @@ a0067:= integrate(t0067,x) m0067:= a0067-r0067 --R --R ---R (255) +--R (225) --R +----------------------+ +---------------+ +-------------------+ --R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 --R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a @@ -30217,3776 +24762,7 @@ m0067:= a0067-r0067 --E 359 --S 360 of 520 -d0067:= D(m0067,x) ---R ---R ---R (256) ---R 3 3+---+2 3 3+---+ 3 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (12a \|- 1 - 12a \|- 1 + 12a )cos(x) + 3a \|- 1 ---R + ---R 3 3+---+ 3 ---R - 3a \|- 1 + 3a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) + 24a b \|- 1 ---R + ---R 2 3+---+ 2 ---R - 24a b\|- 1 + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (24a \|- 1 - 24a \|- 1 + 24a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) - 3a \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a \|- 1 - 3a ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (12a \|- 1 - 12a \|- 1 + 12a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (15a \|- 1 - 15a \|- 1 + 15a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 15a \|- 1 + 15a \|- 1 - 15a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 12a \|- 1 + 12a \|- 1 - 12a )cos(x) - 3a \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a \|- 1 - 3a ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R 36a b \|- 1 - 36a b\|- 1 + 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (96a b \|- 1 - 96a b \|- 1 + 96a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (288a b \|- 1 - 288a b \|- 1 + 288a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (288a b \|- 1 - 288a b \|- 1 + 288a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R 96a b \|- 1 - 96a b \|- 1 + 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 5 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R (180a b \|- 1 - 180a b\|- 1 + 180a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (120a b \|- 1 - 120a b\|- 1 + 120a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) - 12a b \|- 1 ---R + ---R 2 3+---+ 2 ---R 12a b\|- 1 - 12a b ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (20a b - 11a )\|- 1 + (- 20a b + 11a )\|- 1 + 20a b ---R + ---R 3 ---R - 11a ---R * ---R 6 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 33a )\|- 1 + (- 60a b + 33a )\|- 1 + 60a b ---R + ---R 3 ---R - 33a ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 60a )\|- 1 + (- 96a b + 60a )\|- 1 + 96a b ---R + ---R 3 ---R - 60a ---R * ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (36a b - 27a )\|- 1 + (- 36a b + 27a )\|- 1 + 36a b ---R + ---R 3 ---R - 27a ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (32b + 40a b)\|- 1 + (- 32b - 40a b)\|- 1 + 32b ---R + ---R 2 ---R 40a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (96b + 120a b)\|- 1 + (- 96b - 120a b)\|- 1 + 96b ---R + ---R 2 ---R 120a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (96b + 120a b)\|- 1 + (- 96b - 120a b)\|- 1 + 96b ---R + ---R 2 ---R 120a b ---R * ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (32b + 40a b)\|- 1 + (- 32b - 40a b)\|- 1 + 32b + 40a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 33a )\|- 1 + (- 60a b + 33a )\|- 1 + 60a b ---R + ---R 3 ---R - 33a ---R * ---R 4 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (192a b - 120a )\|- 1 + (- 192a b + 120a )\|- 1 ---R + ---R 2 3 ---R 192a b - 120a ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (216a b - 162a )\|- 1 + (- 216a b + 162a )\|- 1 ---R + ---R 2 3 ---R 216a b - 162a ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 96a )\|- 1 + (- 96a b + 96a )\|- 1 + 96a b ---R + ---R 3 ---R - 96a ---R * ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (12a b - 21a )\|- 1 + (- 12a b + 21a )\|- 1 + 12a b ---R + ---R 3 ---R - 21a ---R * ---R 2 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (20a b - 11a )\|- 1 + (- 20a b + 11a )\|- 1 + 20a b ---R + ---R 3 ---R - 11a ---R * ---R 6 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 60a )\|- 1 + (- 96a b + 60a )\|- 1 + 96a b ---R + ---R 3 ---R - 60a ---R * ---R 5 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (180a b - 135a )\|- 1 + (- 180a b + 135a )\|- 1 ---R + ---R 2 3 ---R 180a b - 135a ---R * ---R 4 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (160a b - 160a )\|- 1 + (- 160a b + 160a )\|- 1 ---R + ---R 2 3 ---R 160a b - 160a ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 105a )\|- 1 + (- 60a b + 105a )\|- 1 + 60a b ---R + ---R 3 ---R - 105a ---R * ---R 2 ---R cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 36a \|- 1 + 36a \|- 1 - 36a )cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R (- 4a b - 5a )\|- 1 + (4a b + 5a )\|- 1 - 4a b - 5a ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) - 24a b \|- 1 ---R + ---R 2 3+---+ 2 ---R 24a b\|- 1 - 24a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (192a b \|- 1 - 192a b \|- 1 + 192a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (576a b \|- 1 - 576a b \|- 1 + 576a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (576a b \|- 1 - 576a b \|- 1 + 576a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R 192a b \|- 1 - 192a b \|- 1 + 192a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (- 48a b \|- 1 + 48a b\|- 1 - 48a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R - 48a b \|- 1 + 48a b\|- 1 - 48a b ---R * ---R 2 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 5 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R (- 120a b \|- 1 + 120a b\|- 1 - 120a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (- 240a b \|- 1 + 240a b\|- 1 - 240a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (- 240a b \|- 1 + 240a b\|- 1 - 240a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (- 120a b \|- 1 + 120a b\|- 1 - 120a b)cos(x) - 24a b \|- 1 ---R + ---R 2 3+---+ 2 ---R 24a b\|- 1 - 24a b ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (20a b - 11a )\|- 1 + (- 20a b + 11a )\|- 1 + 20a b ---R + ---R 3 ---R - 11a ---R * ---R 6 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 33a )\|- 1 + (- 60a b + 33a )\|- 1 + 60a b ---R + ---R 3 ---R - 33a ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 60a )\|- 1 + (- 96a b + 60a )\|- 1 + 96a b ---R + ---R 3 ---R - 60a ---R * ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (36a b - 27a )\|- 1 + (- 36a b + 27a )\|- 1 + 36a b ---R + ---R 3 ---R - 27a ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (32b + 40a b)\|- 1 + (- 32b - 40a b)\|- 1 + 32b ---R + ---R 2 ---R 40a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (96b + 120a b)\|- 1 + (- 96b - 120a b)\|- 1 + 96b ---R + ---R 2 ---R 120a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 ---R (96b + 120a b)\|- 1 + (- 96b - 120a b)\|- 1 + 96b ---R + ---R 2 ---R 120a b ---R * ---R cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (32b + 40a b)\|- 1 + (- 32b - 40a b)\|- 1 + 32b + 40a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 33a )\|- 1 + (- 60a b + 33a )\|- 1 + 60a b ---R + ---R 3 ---R - 33a ---R * ---R 4 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (192a b - 120a )\|- 1 + (- 192a b + 120a )\|- 1 ---R + ---R 2 3 ---R 192a b - 120a ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (216a b - 162a )\|- 1 + (- 216a b + 162a )\|- 1 ---R + ---R 2 3 ---R 216a b - 162a ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 96a )\|- 1 + (- 96a b + 96a )\|- 1 + 96a b ---R + ---R 3 ---R - 96a ---R * ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (12a b - 21a )\|- 1 + (- 12a b + 21a )\|- 1 + 12a b ---R + ---R 3 ---R - 21a ---R * ---R 2 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (20a b - 11a )\|- 1 + (- 20a b + 11a )\|- 1 + 20a b ---R + ---R 3 ---R - 11a ---R * ---R 6 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (96a b - 60a )\|- 1 + (- 96a b + 60a )\|- 1 + 96a b ---R + ---R 3 ---R - 60a ---R * ---R 5 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (180a b - 135a )\|- 1 + (- 180a b + 135a )\|- 1 ---R + ---R 2 3 ---R 180a b - 135a ---R * ---R 4 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ ---R (160a b - 160a )\|- 1 + (- 160a b + 160a )\|- 1 ---R + ---R 2 3 ---R 160a b - 160a ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 ---R (60a b - 105a )\|- 1 + (- 60a b + 105a )\|- 1 + 60a b ---R + ---R 3 ---R - 105a ---R * ---R 2 ---R cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 36a \|- 1 + 36a \|- 1 - 36a )cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R (- 4a b - 5a )\|- 1 + (4a b + 5a )\|- 1 - 4a b - 5a ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R 36a b \|- 1 - 36a b\|- 1 + 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (96a b \|- 1 - 96a b \|- 1 + 96a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (288a b \|- 1 - 288a b \|- 1 + 288a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (288a b \|- 1 - 288a b \|- 1 + 288a b )cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R 96a b \|- 1 - 96a b \|- 1 + 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 5 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R (180a b \|- 1 - 180a b\|- 1 + 180a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (120a b \|- 1 - 120a b\|- 1 + 120a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) - 12a b \|- 1 ---R + ---R 2 3+---+ 2 ---R 12a b\|- 1 - 12a b ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 3 3+---+ ---R (12a \|- 1 - 12a \|- 1 + 12a )cos(x) + 3a \|- 1 - 3a \|- 1 ---R + ---R 3 ---R 3a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 ---R (24a b \|- 1 - 24a b\|- 1 + 24a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3+---+2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) + 24a b \|- 1 ---R + ---R 2 3+---+ 2 ---R - 24a b\|- 1 + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (24a \|- 1 - 24a \|- 1 + 24a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 3 3+---+ ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) - 3a \|- 1 + 3a \|- 1 ---R + ---R 3 ---R - 3a ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (12a \|- 1 - 12a \|- 1 + 12a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (15a \|- 1 - 15a \|- 1 + 15a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 15a \|- 1 + 15a \|- 1 - 15a )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 3 3+---+ ---R (- 12a \|- 1 + 12a \|- 1 - 12a )cos(x) - 3a \|- 1 + 3a \|- 1 ---R + ---R 3 ---R - 3a ---R * ---R 3+-+2 3+-+2 ---R \|a \|b ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 12a b \|- 1 + 12a b\|- 1 - 12a b)cos(x) - 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a b\|- 1 - 3a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 24a b \|- 1 + 24a b \|- 1 - 24a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 24a b \|- 1 + 24a b \|- 1 - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) + 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 3a b\|- 1 + 3a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (- 12a b \|- 1 + 12a b\|- 1 - 12a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 15a b \|- 1 + 15a b\|- 1 - 15a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (15a b \|- 1 - 15a b\|- 1 + 15a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (12a b \|- 1 - 12a b\|- 1 + 12a b)cos(x) + 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 3a b\|- 1 + 3a b ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((- 8a b + 8a )\|- 1 + (8a b - 8a )\|- 1 - 8a b + 8a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 24a b + 24a )\|- 1 + (24a b - 24a )\|- 1 - 24a b ---R + ---R 4 ---R 24a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 36a b + 36a )\|- 1 + (36a b - 36a )\|- 1 - 36a b ---R + ---R 4 ---R 36a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 12a b + 12a )\|- 1 + (12a b - 12a )\|- 1 - 12a b ---R + ---R 4 ---R 12a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 32a b + 32a b)\|- 1 + (32a b - 32a b)\|- 1 ---R + ---R 3 3 ---R - 32a b + 32a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 96a b + 96a b)\|- 1 + (96a b - 96a b)\|- 1 ---R + ---R 3 3 ---R - 96a b + 96a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 96a b + 96a b)\|- 1 + (96a b - 96a b)\|- 1 ---R + ---R 3 3 ---R - 96a b + 96a b ---R * ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ 3 ---R (- 32a b + 32a b)\|- 1 + (32a b - 32a b)\|- 1 - 32a b ---R + ---R 3 ---R 32a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 24a b + 24a )\|- 1 + (24a b - 24a )\|- 1 - 24a b ---R + ---R 4 ---R 24a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 72a b + 72a )\|- 1 + (72a b - 72a )\|- 1 - 72a b ---R + ---R 4 ---R 72a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 72a b + 72a )\|- 1 + (72a b - 72a )\|- 1 - 72a b ---R + ---R 4 ---R 72a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 24a b + 24a )\|- 1 + (24a b - 24a )\|- 1 - 24a b ---R + ---R 4 ---R 24a ---R * ---R cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((- 8a b + 8a )\|- 1 + (8a b - 8a )\|- 1 - 8a b + 8a ) ---R * ---R 6 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 36a b + 36a )\|- 1 + (36a b - 36a )\|- 1 - 36a b ---R + ---R 4 ---R 36a ---R * ---R 5 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 60a b + 60a )\|- 1 + (60a b - 60a )\|- 1 - 60a b ---R + ---R 4 ---R 60a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 40a b + 40a )\|- 1 + (40a b - 40a )\|- 1 - 40a b ---R + ---R 4 ---R 40a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (12a b - 12a )\|- 1 + (- 12a b + 12a )\|- 1 + 12a b ---R + ---R 4 ---R - 12a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (4a b - 4a )\|- 1 + (- 4a b + 4a )\|- 1 + 4a b - 4a ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (51a b \|- 1 - 51a b\|- 1 + 51a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (153a b \|- 1 - 153a b\|- 1 + 153a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (252a b \|- 1 - 252a b\|- 1 + 252a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 99a b \|- 1 - 99a b\|- 1 + 99a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (24a b \|- 1 - 24a b \|- 1 + 24a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 3+---+2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) + 24a b \|- 1 ---R + ---R 2 2 3+---+ 2 2 ---R - 24a b \|- 1 + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (153a b \|- 1 - 153a b\|- 1 + 153a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (504a b \|- 1 - 504a b\|- 1 + 504a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (594a b \|- 1 - 594a b\|- 1 + 594a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (288a b \|- 1 - 288a b\|- 1 + 288a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 45a b \|- 1 - 45a b\|- 1 + 45a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (51a b \|- 1 - 51a b\|- 1 + 51a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (252a b \|- 1 - 252a b\|- 1 + 252a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (495a b \|- 1 - 495a b\|- 1 + 495a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (480a b \|- 1 - 480a b\|- 1 + 480a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (225a b \|- 1 - 225a b\|- 1 + 225a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (36a b \|- 1 - 36a b\|- 1 + 36a b)cos(x) - 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a b\|- 1 - 3a b ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (32a b + 16a )\|- 1 + (- 32a b - 16a )\|- 1 + 32a b ---R + ---R 4 ---R 16a ---R * ---R 6 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (96a b + 48a )\|- 1 + (- 96a b - 48a )\|- 1 + 96a b ---R + ---R 4 ---R 48a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (168a b + 72a )\|- 1 + (- 168a b - 72a )\|- 1 ---R + ---R 2 2 4 ---R 168a b + 72a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b + 24a )\|- 1 + (- 72a b - 24a )\|- 1 + 72a b ---R + ---R 4 ---R 24a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 64a b + 64a b)\|- 1 + (64a b - 64a b)\|- 1 ---R + ---R 3 3 ---R - 64a b + 64a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 192a b + 192a b)\|- 1 + (192a b - 192a b)\|- 1 ---R + ---R 3 3 ---R - 192a b + 192a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 192a b + 192a b)\|- 1 + (192a b - 192a b)\|- 1 ---R + ---R 3 3 ---R - 192a b + 192a b ---R * ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ 3 ---R (- 64a b + 64a b)\|- 1 + (64a b - 64a b)\|- 1 - 64a b ---R + ---R 3 ---R 64a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (96a b + 48a )\|- 1 + (- 96a b - 48a )\|- 1 + 96a b ---R + ---R 4 ---R 48a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (336a b + 144a )\|- 1 + (- 336a b - 144a )\|- 1 ---R + ---R 2 2 4 ---R 336a b + 144a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (432a b + 144a )\|- 1 + (- 432a b - 144a )\|- 1 ---R + ---R 2 2 4 ---R 432a b + 144a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (240a b + 48a )\|- 1 + (- 240a b - 48a )\|- 1 ---R + ---R 2 2 4 ---R 240a b + 48a ---R * ---R cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R 48a b \|- 1 - 48a b \|- 1 + 48a b ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (32a b + 16a )\|- 1 + (- 32a b - 16a )\|- 1 + 32a b ---R + ---R 4 ---R 16a ---R * ---R 6 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (168a b + 72a )\|- 1 + (- 168a b - 72a )\|- 1 + 168a b ---R + ---R 4 ---R 72a ---R * ---R 5 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (360a b + 120a )\|- 1 + (- 360a b - 120a )\|- 1 ---R + ---R 2 2 4 ---R 360a b + 120a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (400a b + 80a )\|- 1 + (- 400a b - 80a )\|- 1 + 400a b ---R + ---R 4 ---R 80a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (240a b \|- 1 - 240a b \|- 1 + 240a b )cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 24a )\|- 1 + (- 72a b + 24a )\|- 1 + 72a b ---R + ---R 4 ---R - 24a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (8a b - 8a )\|- 1 + (- 8a b + 8a )\|- 1 + 8a b - 8a ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (51a b \|- 1 - 51a b\|- 1 + 51a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (153a b \|- 1 - 153a b\|- 1 + 153a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (252a b \|- 1 - 252a b\|- 1 + 252a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 99a b \|- 1 - 99a b\|- 1 + 99a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (24a b \|- 1 - 24a b \|- 1 + 24a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 3+---+2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) + 24a b \|- 1 ---R + ---R 2 2 3+---+ 2 2 ---R - 24a b \|- 1 + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (153a b \|- 1 - 153a b\|- 1 + 153a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (504a b \|- 1 - 504a b\|- 1 + 504a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (594a b \|- 1 - 594a b\|- 1 + 594a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (288a b \|- 1 - 288a b\|- 1 + 288a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 45a b \|- 1 - 45a b\|- 1 + 45a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (51a b \|- 1 - 51a b\|- 1 + 51a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (252a b \|- 1 - 252a b\|- 1 + 252a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (495a b \|- 1 - 495a b\|- 1 + 495a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (480a b \|- 1 - 480a b\|- 1 + 480a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (225a b \|- 1 - 225a b\|- 1 + 225a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (36a b \|- 1 - 36a b\|- 1 + 36a b)cos(x) - 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a b\|- 1 - 3a b ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((- 8a b + 8a )\|- 1 + (8a b - 8a )\|- 1 - 8a b + 8a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 24a b + 24a )\|- 1 + (24a b - 24a )\|- 1 - 24a b ---R + ---R 4 ---R 24a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 36a b + 36a )\|- 1 + (36a b - 36a )\|- 1 - 36a b ---R + ---R 4 ---R 36a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 12a b + 12a )\|- 1 + (12a b - 12a )\|- 1 - 12a b ---R + ---R 4 ---R 12a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 32a b + 32a b)\|- 1 + (32a b - 32a b)\|- 1 ---R + ---R 3 3 ---R - 32a b + 32a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 96a b + 96a b)\|- 1 + (96a b - 96a b)\|- 1 ---R + ---R 3 3 ---R - 96a b + 96a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 96a b + 96a b)\|- 1 + (96a b - 96a b)\|- 1 ---R + ---R 3 3 ---R - 96a b + 96a b ---R * ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ 3 ---R (- 32a b + 32a b)\|- 1 + (32a b - 32a b)\|- 1 - 32a b ---R + ---R 3 ---R 32a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 24a b + 24a )\|- 1 + (24a b - 24a )\|- 1 - 24a b ---R + ---R 4 ---R 24a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 72a b + 72a )\|- 1 + (72a b - 72a )\|- 1 - 72a b ---R + ---R 4 ---R 72a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 72a b + 72a )\|- 1 + (72a b - 72a )\|- 1 - 72a b ---R + ---R 4 ---R 72a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 24a b + 24a )\|- 1 + (24a b - 24a )\|- 1 - 24a b ---R + ---R 4 ---R 24a ---R * ---R cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((- 8a b + 8a )\|- 1 + (8a b - 8a )\|- 1 - 8a b + 8a ) ---R * ---R 6 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 36a b + 36a )\|- 1 + (36a b - 36a )\|- 1 - 36a b ---R + ---R 4 ---R 36a ---R * ---R 5 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 60a b + 60a )\|- 1 + (60a b - 60a )\|- 1 - 60a b ---R + ---R 4 ---R 60a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (- 40a b + 40a )\|- 1 + (40a b - 40a )\|- 1 - 40a b ---R + ---R 4 ---R 40a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (12a b - 12a )\|- 1 + (- 12a b + 12a )\|- 1 + 12a b ---R + ---R 4 ---R - 12a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (4a b - 4a )\|- 1 + (- 4a b + 4a )\|- 1 + 4a b - 4a ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 12a b \|- 1 + 12a b\|- 1 - 12a b)cos(x) - 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 3a b\|- 1 - 3a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 24a b \|- 1 + 24a b \|- 1 - 24a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 3+---+2 ---R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cos(x) - 24a b \|- 1 ---R + ---R 2 2 3+---+ 2 2 ---R 24a b \|- 1 - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) + 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 3a b\|- 1 + 3a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (- 12a b \|- 1 + 12a b\|- 1 - 12a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 15a b \|- 1 + 15a b\|- 1 - 15a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (15a b \|- 1 - 15a b\|- 1 + 15a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (12a b \|- 1 - 12a b\|- 1 + 12a b)cos(x) + 3a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 3a b\|- 1 + 3a b ---R * ---R 3+-+ ---R \|b ---R + ---R 2 2 4 6 ---R (3a b - 3a )sin(x) ---R + ---R 2 2 4 2 2 2 4 2 2 4 ---R ((9a b - 9a )cos(x) + (12a b - 12a )cos(x) + 3a b - 3a ) ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3 3 3 2 ---R (24a b - 24a b)cos(x) + (72a b - 72a b)cos(x) ---R + ---R 3 3 3 3 ---R (72a b - 72a b)cos(x) + 24a b - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 4 2 2 4 3 ---R (9a b - 9a )cos(x) + (24a b - 24a )cos(x) ---R + ---R 2 2 4 2 2 2 4 ---R (18a b - 18a )cos(x) - 3a b + 3a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 6 2 2 4 5 ---R (3a b - 3a )cos(x) + (12a b - 12a )cos(x) ---R + ---R 2 2 4 4 2 2 4 2 ---R (15a b - 15a )cos(x) + (- 15a b + 15a )cos(x) ---R + ---R 2 2 4 2 2 4 ---R (- 12a b + 12a )cos(x) - 3a b + 3a ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R - 36a b \|- 1 + 36a b\|- 1 - 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 96a b \|- 1 + 96a b \|- 1 - 96a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 96a b \|- 1 + 96a b \|- 1 - 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 180a b \|- 1 + 180a b\|- 1 - 180a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 120a b \|- 1 + 120a b\|- 1 - 120a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (36a b \|- 1 - 36a b\|- 1 + 36a b)cos(x) + 12a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 12a b\|- 1 + 12a b ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 6 ---R (- 60a b \|- 1 + 60a b \|- 1 - 51a b - 9a )sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 180a b \|- 1 + 180a b \|- 1 - 153a b - 27a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R (- 288a b \|- 1 + 288a b \|- 1 - 252a b - 36a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R - 108a b \|- 1 + 108a b \|- 1 - 99a b - 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3 ---R (- 96a b \|- 1 + 96a b \|- 1 - 24a b - 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 72a b - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 288a b \|- 1 + 288a b \|- 1 - 72a b - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R - 96a b \|- 1 + 96a b \|- 1 - 24a b - 72a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 4 ---R (- 180a b \|- 1 + 180a b \|- 1 - 153a b - 27a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 3 ---R (- 576a b \|- 1 + 576a b \|- 1 - 504a b - 72a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 594a b - 54a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R - 36a b \|- 1 + 36a b \|- 1 - 45a b + 9a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 6 ---R (- 60a b \|- 1 + 60a b \|- 1 - 51a b - 9a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 5 ---R (- 288a b \|- 1 + 288a b \|- 1 - 252a b - 36a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 4 ---R (- 540a b \|- 1 + 540a b \|- 1 - 495a b - 45a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 480a b \|- 1 + 480a b \|- 1 - 480a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 180a b \|- 1 + 180a b \|- 1 - 225a b + 45a )cos(x) ---R + ---R 2 2 4 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 36a b + 36a )cos(x) + 12a b \|- 1 - 12a b \|- 1 + 3a b ---R + ---R 4 ---R 9a ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 48a b \|- 1 + 48a b\|- 1 - 48a b )sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 144a b \|- 1 + 144a b\|- 1 - 144a b )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 216a b \|- 1 + 216a b\|- 1 - 240a b + 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R - 72a b \|- 1 + 72a b\|- 1 - 96a b + 24a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 192a b \|- 1 + 192a b \|- 1 - 192a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 576a b \|- 1 + 576a b \|- 1 - 576a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 576a b \|- 1 + 576a b \|- 1 - 576a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 192a b \|- 1 + 192a b \|- 1 - 192a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 144a b \|- 1 + 144a b\|- 1 - 144a b )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3 ---R (- 432a b \|- 1 + 432a b\|- 1 - 480a b + 48a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 2 ---R (- 432a b \|- 1 + 432a b\|- 1 - 576a b + 144a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 144a b \|- 1 + 144a b\|- 1 - 288a b + 144a b)cos(x) ---R + ---R 3 3 ---R - 48a b + 48a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 48a b \|- 1 + 48a b\|- 1 - 48a b )cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 5 ---R (- 216a b \|- 1 + 216a b\|- 1 - 240a b + 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 4 ---R (- 360a b \|- 1 + 360a b\|- 1 - 480a b + 120a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3 ---R (- 240a b \|- 1 + 240a b\|- 1 - 480a b + 240a b)cos(x) ---R + ---R 3 3 2 ---R (- 240a b + 240a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (72a b \|- 1 - 72a b\|- 1 - 48a b + 120a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 24a b \|- 1 - 24a b\|- 1 + 24a b ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 6 ---R (- 60a b \|- 1 + 60a b \|- 1 - 51a b - 9a )sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 180a b \|- 1 + 180a b \|- 1 - 153a b - 27a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R (- 288a b \|- 1 + 288a b \|- 1 - 252a b - 36a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R - 108a b \|- 1 + 108a b \|- 1 - 99a b - 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3 ---R (- 96a b \|- 1 + 96a b \|- 1 - 24a b - 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 72a b - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 288a b \|- 1 + 288a b \|- 1 - 72a b - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R - 96a b \|- 1 + 96a b \|- 1 - 24a b - 72a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 4 ---R (- 180a b \|- 1 + 180a b \|- 1 - 153a b - 27a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 3 ---R (- 576a b \|- 1 + 576a b \|- 1 - 504a b - 72a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 594a b - 54a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 ---R - 36a b \|- 1 + 36a b \|- 1 - 45a b + 9a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 6 ---R (- 60a b \|- 1 + 60a b \|- 1 - 51a b - 9a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 5 ---R (- 288a b \|- 1 + 288a b \|- 1 - 252a b - 36a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 4 ---R (- 540a b \|- 1 + 540a b \|- 1 - 495a b - 45a )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 480a b \|- 1 + 480a b \|- 1 - 480a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 4 2 ---R (- 180a b \|- 1 + 180a b \|- 1 - 225a b + 45a )cos(x) ---R + ---R 2 2 4 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 36a b + 36a )cos(x) + 12a b \|- 1 - 12a b \|- 1 + 3a b ---R + ---R 4 ---R 9a ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R - 36a b \|- 1 + 36a b\|- 1 - 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 96a b \|- 1 + 96a b \|- 1 - 96a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 96a b \|- 1 + 96a b \|- 1 - 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (- 180a b \|- 1 + 180a b\|- 1 - 180a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 120a b \|- 1 + 120a b\|- 1 - 120a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (36a b \|- 1 - 36a b\|- 1 + 36a b)cos(x) + 12a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 12a b\|- 1 + 12a b ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 2 2 4 6 ---R (3a b - 3a )sin(x) ---R + ---R 2 2 4 2 2 2 4 2 2 4 4 ---R ((9a b - 9a )cos(x) + (12a b - 12a )cos(x) + 3a b - 3a )sin(x) ---R + ---R 3 3 3 3 3 2 ---R (24a b - 24a b)cos(x) + (72a b - 72a b)cos(x) ---R + ---R 3 3 3 3 ---R (72a b - 72a b)cos(x) + 24a b - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 4 2 2 4 3 ---R (9a b - 9a )cos(x) + (24a b - 24a )cos(x) ---R + ---R 2 2 4 2 2 2 4 ---R (18a b - 18a )cos(x) - 3a b + 3a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 6 2 2 4 5 ---R (3a b - 3a )cos(x) + (12a b - 12a )cos(x) ---R + ---R 2 2 4 4 2 2 4 2 ---R (15a b - 15a )cos(x) + (- 15a b + 15a )cos(x) ---R + ---R 2 2 4 2 2 4 ---R (- 12a b + 12a )cos(x) - 3a b + 3a ---R * ---R 3+-+ ---R \|a ---R / ---R 4 3+---+2 4 3+---+ 4 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) + 9a \|- 1 ---R + ---R 4 3+---+ 4 ---R - 9a \|- 1 + 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) - 24a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 24a b\|- 1 - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (36a \|- 1 - 36a \|- 1 + 36a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (36a \|- 1 - 36a \|- 1 + 36a )cos(x) + 9a \|- 1 ---R + ---R 4 3+---+ 4 ---R - 9a \|- 1 + 9a ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (45a \|- 1 - 45a \|- 1 + 45a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (60a \|- 1 - 60a \|- 1 + 60a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (45a \|- 1 - 45a \|- 1 + 45a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 4 3+---+ ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) + 3a \|- 1 - 3a \|- 1 ---R + ---R 4 ---R 3a ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (18a b \|- 1 - 18a b\|- 1 + 18a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (54a b \|- 1 - 54a b\|- 1 + 54a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 54a b \|- 1 - 54a b\|- 1 + 54a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 432a b \|- 1 + 432a b \|- 1 - 432a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 432a b \|- 1 + 432a b \|- 1 - 432a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 144a b \|- 1 + 144a b \|- 1 - 144a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (54a b \|- 1 - 54a b\|- 1 + 54a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 54a b \|- 1 - 54a b\|- 1 + 54a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (18a b \|- 1 - 18a b\|- 1 + 18a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (270a b \|- 1 - 270a b\|- 1 + 270a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (360a b \|- 1 - 360a b\|- 1 + 360a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (270a b \|- 1 - 270a b\|- 1 + 270a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) + 18a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 18a b\|- 1 + 18a b ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b ---R + ---R 4 ---R - 9a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b - 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 96a b + 24a b)\|- 1 + (96a b - 24a b)\|- 1 ---R + ---R 3 3 ---R - 96a b + 24a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 288a b + 72a b)\|- 1 + (288a b - 72a b)\|- 1 ---R + ---R 3 3 ---R - 288a b + 72a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 288a b + 72a b)\|- 1 + (288a b - 72a b)\|- 1 ---R + ---R 3 3 ---R - 288a b + 72a b ---R * ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ 3 ---R (- 96a b + 24a b)\|- 1 + (96a b - 24a b)\|- 1 - 96a b ---R + ---R 3 ---R 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b ---R + ---R 4 ---R - 9a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (144a b - 36a )\|- 1 + (- 144a b + 36a )\|- 1 ---R + ---R 2 2 4 ---R 144a b - 36a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (216a b - 54a )\|- 1 + (- 216a b + 54a )\|- 1 ---R + ---R 2 2 4 ---R 216a b - 54a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (144a b - 36a )\|- 1 + (- 144a b + 36a )\|- 1 ---R + ---R 2 2 4 ---R 144a b - 36a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b - 9a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ) ---R * ---R 6 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R 5 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (180a b - 45a )\|- 1 + (- 180a b + 45a )\|- 1 + 180a b ---R + ---R 4 ---R - 45a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (240a b - 60a )\|- 1 + (- 240a b + 60a )\|- 1 + 240a b ---R + ---R 4 ---R - 60a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (180a b - 45a )\|- 1 + (- 180a b + 45a )\|- 1 + 180a b ---R + ---R 4 ---R - 45a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (12a b \|- 1 - 12a b\|- 1 + 12a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (36a b \|- 1 - 36a b\|- 1 + 36a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) + 36a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 36a b\|- 1 + 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 96a b \|- 1 + 96a b \|- 1 - 96a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 96a b \|- 1 + 96a b \|- 1 - 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (36a b \|- 1 - 36a b\|- 1 + 36a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (144a b \|- 1 - 144a b\|- 1 + 144a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (144a b \|- 1 - 144a b\|- 1 + 144a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 36a b \|- 1 - 36a b\|- 1 + 36a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (12a b \|- 1 - 12a b\|- 1 + 12a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (180a b \|- 1 - 180a b\|- 1 + 180a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (240a b \|- 1 - 240a b\|- 1 + 240a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (180a b \|- 1 - 180a b\|- 1 + 180a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (72a b \|- 1 - 72a b\|- 1 + 72a b)cos(x) + 12a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 12a b\|- 1 + 12a b ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b ---R + ---R 4 ---R - 9a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b - 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 96a b + 24a b)\|- 1 + (96a b - 24a b)\|- 1 ---R + ---R 3 3 ---R - 96a b + 24a b ---R * ---R 3 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 288a b + 72a b)\|- 1 + (288a b - 72a b)\|- 1 ---R + ---R 3 3 ---R - 288a b + 72a b ---R * ---R 2 ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ ---R (- 288a b + 72a b)\|- 1 + (288a b - 72a b)\|- 1 ---R + ---R 3 3 ---R - 288a b + 72a b ---R * ---R cos(x) ---R + ---R 3 3 3+---+2 3 3 3+---+ 3 ---R (- 96a b + 24a b)\|- 1 + (96a b - 24a b)\|- 1 - 96a b ---R + ---R 3 ---R 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b ---R + ---R 4 ---R - 9a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (144a b - 36a )\|- 1 + (- 144a b + 36a )\|- 1 ---R + ---R 2 2 4 ---R 144a b - 36a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (216a b - 54a )\|- 1 + (- 216a b + 54a )\|- 1 ---R + ---R 2 2 4 ---R 216a b - 54a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ ---R (144a b - 36a )\|- 1 + (- 144a b + 36a )\|- 1 ---R + ---R 2 2 4 ---R 144a b - 36a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (36a b - 9a )\|- 1 + (- 36a b + 9a )\|- 1 + 36a b - 9a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R ((12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ) ---R * ---R 6 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R 5 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (180a b - 45a )\|- 1 + (- 180a b + 45a )\|- 1 + 180a b ---R + ---R 4 ---R - 45a ---R * ---R 4 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (240a b - 60a )\|- 1 + (- 240a b + 60a )\|- 1 + 240a b ---R + ---R 4 ---R - 60a ---R * ---R 3 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (180a b - 45a )\|- 1 + (- 180a b + 45a )\|- 1 + 180a b ---R + ---R 4 ---R - 45a ---R * ---R 2 ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 ---R (72a b - 18a )\|- 1 + (- 72a b + 18a )\|- 1 + 72a b ---R + ---R 4 ---R - 18a ---R * ---R cos(x) ---R + ---R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 4 ---R (12a b - 3a )\|- 1 + (- 12a b + 3a )\|- 1 + 12a b - 3a ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (18a b \|- 1 - 18a b\|- 1 + 18a b)sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (54a b \|- 1 - 54a b\|- 1 + 54a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 54a b \|- 1 - 54a b\|- 1 + 54a b ---R * ---R 4 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 3 ---R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 2 ---R (- 432a b \|- 1 + 432a b \|- 1 - 432a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (- 432a b \|- 1 + 432a b \|- 1 - 432a b )cos(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R - 144a b \|- 1 + 144a b \|- 1 - 144a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (54a b \|- 1 - 54a b\|- 1 + 54a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R (216a b \|- 1 - 216a b\|- 1 + 216a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 ---R 54a b \|- 1 - 54a b\|- 1 + 54a b ---R * ---R 2 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 6 ---R (18a b \|- 1 - 18a b\|- 1 + 18a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 5 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 4 ---R (270a b \|- 1 - 270a b\|- 1 + 270a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (360a b \|- 1 - 360a b\|- 1 + 360a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (270a b \|- 1 - 270a b\|- 1 + 270a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (108a b \|- 1 - 108a b\|- 1 + 108a b)cos(x) + 18a b \|- 1 ---R + ---R 3 3+---+ 3 ---R - 18a b\|- 1 + 18a b ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 4 3+---+ ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) + 9a \|- 1 - 9a \|- 1 ---R + ---R 4 ---R 9a ---R * ---R 4 ---R sin(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 ---R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) ---R + ---R 3 3+---+2 3 3+---+ 3 3 3+---+2 ---R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cos(x) - 24a b \|- 1 ---R + ---R 3 3+---+ 3 ---R 24a b\|- 1 - 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (36a \|- 1 - 36a \|- 1 + 36a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 4 3+---+ ---R (36a \|- 1 - 36a \|- 1 + 36a )cos(x) + 9a \|- 1 - 9a \|- 1 ---R + ---R 4 ---R 9a ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (45a \|- 1 - 45a \|- 1 + 45a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (60a \|- 1 - 60a \|- 1 + 60a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (45a \|- 1 - 45a \|- 1 + 45a )cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 4 3+---+ 4 ---R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) + 3a \|- 1 - 3a \|- 1 + 3a ---R * ---R 3+-+2 3+-+2 ---R \|a \|b ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) - 9a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 9a b\|- 1 - 9a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (24a b \|- 1 - 24a b \|- 1 + 24a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 2 3+---+2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) + 24a b \|- 1 ---R + ---R 3 2 3+---+ 3 2 ---R - 24a b \|- 1 + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) - 9a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 9a b\|- 1 - 9a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 60a b \|- 1 + 60a b\|- 1 - 60a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) - 3a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 3a b\|- 1 - 3a b ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R ((- 6a b + 6a )\|- 1 + (6a b - 6a )\|- 1 - 6a b + 6a ) ---R * ---R 6 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 18a b + 18a )\|- 1 + (18a b - 18a )\|- 1 - 18a b ---R + ---R 5 ---R 18a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 36a b + 36a )\|- 1 + (36a b - 36a )\|- 1 - 36a b ---R + ---R 5 ---R 36a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 18a b + 18a )\|- 1 + (18a b - 18a )\|- 1 - 18a b ---R + ---R 5 ---R 18a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (48a b - 48a b)\|- 1 + (- 48a b + 48a b)\|- 1 ---R + ---R 2 3 4 ---R 48a b - 48a b ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (144a b - 144a b)\|- 1 + (- 144a b + 144a b)\|- 1 ---R + ---R 2 3 4 ---R 144a b - 144a b ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (144a b - 144a b)\|- 1 + (- 144a b + 144a b)\|- 1 ---R + ---R 2 3 4 ---R 144a b - 144a b ---R * ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 ---R (48a b - 48a b)\|- 1 + (- 48a b + 48a b)\|- 1 + 48a b ---R + ---R 4 ---R - 48a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 18a b + 18a )\|- 1 + (18a b - 18a )\|- 1 - 18a b ---R + ---R 5 ---R 18a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 72a b + 72a )\|- 1 + (72a b - 72a )\|- 1 - 72a b ---R + ---R 5 ---R 72a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (- 108a b + 108a )\|- 1 + (108a b - 108a )\|- 1 ---R + ---R 3 2 5 ---R - 108a b + 108a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 72a b + 72a )\|- 1 + (72a b - 72a )\|- 1 - 72a b ---R + ---R 5 ---R 72a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 18a b + 18a )\|- 1 + (18a b - 18a )\|- 1 - 18a b ---R + ---R 5 ---R 18a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R ((- 6a b + 6a )\|- 1 + (6a b - 6a )\|- 1 - 6a b + 6a ) ---R * ---R 6 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 36a b + 36a )\|- 1 + (36a b - 36a )\|- 1 - 36a b ---R + ---R 5 ---R 36a ---R * ---R 5 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 90a b + 90a )\|- 1 + (90a b - 90a )\|- 1 - 90a b ---R + ---R 5 ---R 90a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (- 120a b + 120a )\|- 1 + (120a b - 120a )\|- 1 ---R + ---R 3 2 5 ---R - 120a b + 120a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 90a b + 90a )\|- 1 + (90a b - 90a )\|- 1 - 90a b ---R + ---R 5 ---R 90a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 36a b + 36a )\|- 1 + (36a b - 36a )\|- 1 - 36a b ---R + ---R 5 ---R 36a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R (- 6a b + 6a )\|- 1 + (6a b - 6a )\|- 1 - 6a b + 6a ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (27a b \|- 1 - 27a b\|- 1 + 27a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (81a b \|- 1 - 81a b\|- 1 + 81a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 81a b \|- 1 - 81a b\|- 1 + 81a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 648a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 648a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R - 216a b \|- 1 + 216a b \|- 1 - 216a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (81a b \|- 1 - 81a b\|- 1 + 81a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (486a b \|- 1 - 486a b\|- 1 + 486a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 81a b \|- 1 - 81a b\|- 1 + 81a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (27a b \|- 1 - 27a b\|- 1 + 27a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (405a b \|- 1 - 405a b\|- 1 + 405a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (540a b \|- 1 - 540a b\|- 1 + 540a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (405a b \|- 1 - 405a b\|- 1 + 405a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) + 27a b \|- 1 ---R + ---R 4 3+---+ 4 ---R - 27a b\|- 1 + 27a b ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (12a b + 12a )\|- 1 + (- 12a b - 12a )\|- 1 + 12a b ---R + ---R 5 ---R 12a ---R * ---R 6 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (36a b + 36a )\|- 1 + (- 36a b - 36a )\|- 1 + 36a b ---R + ---R 5 ---R 36a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (72a b + 72a )\|- 1 + (- 72a b - 72a )\|- 1 + 72a b ---R + ---R 5 ---R 72a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (36a b + 36a )\|- 1 + (- 36a b - 36a )\|- 1 + 36a b ---R + ---R 5 ---R 36a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (- 96a b - 96a b)\|- 1 + (96a b + 96a b)\|- 1 ---R + ---R 2 3 4 ---R - 96a b - 96a b ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (- 288a b - 288a b)\|- 1 + (288a b + 288a b)\|- 1 ---R + ---R 2 3 4 ---R - 288a b - 288a b ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (- 288a b - 288a b)\|- 1 + (288a b + 288a b)\|- 1 ---R + ---R 2 3 4 ---R - 288a b - 288a b ---R * ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 ---R (- 96a b - 96a b)\|- 1 + (96a b + 96a b)\|- 1 - 96a b ---R + ---R 4 ---R - 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (36a b + 36a )\|- 1 + (- 36a b - 36a )\|- 1 + 36a b ---R + ---R 5 ---R 36a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (144a b + 144a )\|- 1 + (- 144a b - 144a )\|- 1 ---R + ---R 3 2 5 ---R 144a b + 144a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (216a b + 216a )\|- 1 + (- 216a b - 216a )\|- 1 ---R + ---R 3 2 5 ---R 216a b + 216a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (144a b + 144a )\|- 1 + (- 144a b - 144a )\|- 1 ---R + ---R 3 2 5 ---R 144a b + 144a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (36a b + 36a )\|- 1 + (- 36a b - 36a )\|- 1 + 36a b ---R + ---R 5 ---R 36a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (12a b + 12a )\|- 1 + (- 12a b - 12a )\|- 1 + 12a b ---R + ---R 5 ---R 12a ---R * ---R 6 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (72a b + 72a )\|- 1 + (- 72a b - 72a )\|- 1 + 72a b ---R + ---R 5 ---R 72a ---R * ---R 5 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (180a b + 180a )\|- 1 + (- 180a b - 180a )\|- 1 ---R + ---R 3 2 5 ---R 180a b + 180a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (240a b + 240a )\|- 1 + (- 240a b - 240a )\|- 1 ---R + ---R 3 2 5 ---R 240a b + 240a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (180a b + 180a )\|- 1 + (- 180a b - 180a )\|- 1 ---R + ---R 3 2 5 ---R 180a b + 180a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (72a b + 72a )\|- 1 + (- 72a b - 72a )\|- 1 + 72a b ---R + ---R 5 ---R 72a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R (12a b + 12a )\|- 1 + (- 12a b - 12a )\|- 1 + 12a b + 12a ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (27a b \|- 1 - 27a b\|- 1 + 27a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (81a b \|- 1 - 81a b\|- 1 + 81a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 81a b \|- 1 - 81a b\|- 1 + 81a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 648a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 648a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R - 216a b \|- 1 + 216a b \|- 1 - 216a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (81a b \|- 1 - 81a b\|- 1 + 81a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (486a b \|- 1 - 486a b\|- 1 + 486a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (324a b \|- 1 - 324a b\|- 1 + 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R 81a b \|- 1 - 81a b\|- 1 + 81a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (27a b \|- 1 - 27a b\|- 1 + 27a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (405a b \|- 1 - 405a b\|- 1 + 405a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (540a b \|- 1 - 540a b\|- 1 + 540a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (405a b \|- 1 - 405a b\|- 1 + 405a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (162a b \|- 1 - 162a b\|- 1 + 162a b)cos(x) + 27a b \|- 1 ---R + ---R 4 3+---+ 4 ---R - 27a b\|- 1 + 27a b ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R ((- 6a b + 6a )\|- 1 + (6a b - 6a )\|- 1 - 6a b + 6a ) ---R * ---R 6 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 18a b + 18a )\|- 1 + (18a b - 18a )\|- 1 - 18a b ---R + ---R 5 ---R 18a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 36a b + 36a )\|- 1 + (36a b - 36a )\|- 1 - 36a b ---R + ---R 5 ---R 36a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 18a b + 18a )\|- 1 + (18a b - 18a )\|- 1 - 18a b ---R + ---R 5 ---R 18a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (48a b - 48a b)\|- 1 + (- 48a b + 48a b)\|- 1 ---R + ---R 2 3 4 ---R 48a b - 48a b ---R * ---R 3 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (144a b - 144a b)\|- 1 + (- 144a b + 144a b)\|- 1 ---R + ---R 2 3 4 ---R 144a b - 144a b ---R * ---R 2 ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ ---R (144a b - 144a b)\|- 1 + (- 144a b + 144a b)\|- 1 ---R + ---R 2 3 4 ---R 144a b - 144a b ---R * ---R cos(x) ---R + ---R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 ---R (48a b - 48a b)\|- 1 + (- 48a b + 48a b)\|- 1 + 48a b ---R + ---R 4 ---R - 48a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 18a b + 18a )\|- 1 + (18a b - 18a )\|- 1 - 18a b ---R + ---R 5 ---R 18a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 72a b + 72a )\|- 1 + (72a b - 72a )\|- 1 - 72a b ---R + ---R 5 ---R 72a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (- 108a b + 108a )\|- 1 + (108a b - 108a )\|- 1 ---R + ---R 3 2 5 ---R - 108a b + 108a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 72a b + 72a )\|- 1 + (72a b - 72a )\|- 1 - 72a b ---R + ---R 5 ---R 72a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 18a b + 18a )\|- 1 + (18a b - 18a )\|- 1 - 18a b ---R + ---R 5 ---R 18a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R ((- 6a b + 6a )\|- 1 + (6a b - 6a )\|- 1 - 6a b + 6a ) ---R * ---R 6 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 36a b + 36a )\|- 1 + (36a b - 36a )\|- 1 - 36a b ---R + ---R 5 ---R 36a ---R * ---R 5 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 90a b + 90a )\|- 1 + (90a b - 90a )\|- 1 - 90a b ---R + ---R 5 ---R 90a ---R * ---R 4 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ ---R (- 120a b + 120a )\|- 1 + (120a b - 120a )\|- 1 ---R + ---R 3 2 5 ---R - 120a b + 120a ---R * ---R 3 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 90a b + 90a )\|- 1 + (90a b - 90a )\|- 1 - 90a b ---R + ---R 5 ---R 90a ---R * ---R 2 ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 ---R (- 36a b + 36a )\|- 1 + (36a b - 36a )\|- 1 - 36a b ---R + ---R 5 ---R 36a ---R * ---R cos(x) ---R + ---R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 5 ---R (- 6a b + 6a )\|- 1 + (6a b - 6a )\|- 1 - 6a b + 6a ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) - 9a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 9a b\|- 1 - 9a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (24a b \|- 1 - 24a b \|- 1 + 24a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 2 3+---+2 ---R (72a b \|- 1 - 72a b \|- 1 + 72a b )cos(x) + 24a b \|- 1 ---R + ---R 3 2 3+---+ 3 2 ---R - 24a b \|- 1 + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cos(x) - 9a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 9a b\|- 1 - 9a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 60a b \|- 1 + 60a b\|- 1 - 60a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) - 3a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 3a b\|- 1 - 3a b ---R * ---R 3+-+ ---R \|b ---R + ---R 3 2 5 6 ---R (3a b - 3a )sin(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 ---R ((9a b - 9a )cos(x) + (18a b - 18a )cos(x) + 9a b - 9a ) ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 4 3 2 3 4 2 ---R (- 24a b + 24a b)cos(x) + (- 72a b + 72a b)cos(x) ---R + ---R 2 3 4 2 3 4 ---R (- 72a b + 72a b)cos(x) - 24a b + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 5 4 3 2 5 3 ---R (9a b - 9a )cos(x) + (36a b - 36a )cos(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 ---R (54a b - 54a )cos(x) + (36a b - 36a )cos(x) + 9a b - 9a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 5 6 3 2 5 5 ---R (3a b - 3a )cos(x) + (18a b - 18a )cos(x) ---R + ---R 3 2 5 4 3 2 5 3 ---R (45a b - 45a )cos(x) + (60a b - 60a )cos(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 ---R (45a b - 45a )cos(x) + (18a b - 18a )cos(x) + 3a b - 3a ---R * ---R x 6 ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R - 54a b \|- 1 + 54a b\|- 1 - 54a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (144a b \|- 1 - 144a b \|- 1 + 144a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (432a b \|- 1 - 432a b \|- 1 + 432a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (432a b \|- 1 - 432a b \|- 1 + 432a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R 144a b \|- 1 - 144a b \|- 1 + 144a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 324a b \|- 1 + 324a b\|- 1 - 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R - 54a b \|- 1 + 54a b\|- 1 - 54a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 270a b \|- 1 + 270a b\|- 1 - 270a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 360a b \|- 1 + 360a b\|- 1 - 360a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 270a b \|- 1 + 270a b\|- 1 - 270a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) - 18a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 18a b\|- 1 - 18a b ---R * ---R x 5 ---R tan(-) ---R 2 ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 6 ---R (- 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a )sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 ---R (288a b \|- 1 - 288a b \|- 1 + 216a b + 72a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 ---R (864a b \|- 1 - 864a b \|- 1 + 648a b + 216a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 ---R (864a b \|- 1 - 864a b \|- 1 + 648a b + 216a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 ---R 288a b \|- 1 - 288a b \|- 1 + 216a b + 72a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 4 ---R (- 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 ---R (- 432a b \|- 1 + 432a b \|- 1 - 324a b - 108a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 486a b - 162a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 432a b \|- 1 + 432a b \|- 1 - 324a b - 108a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 6 ---R (- 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 4 ---R (- 540a b \|- 1 + 540a b \|- 1 - 405a b - 135a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 ---R (- 720a b \|- 1 + 720a b \|- 1 - 540a b - 180a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 540a b \|- 1 + 540a b \|- 1 - 405a b - 135a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 6 ---R (- 36a b \|- 1 + 36a b\|- 1 - 24a b - 12a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 2 ---R (- 108a b \|- 1 + 108a b\|- 1 - 72a b - 36a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R (- 216a b \|- 1 + 216a b\|- 1 - 144a b - 72a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R - 108a b \|- 1 + 108a b\|- 1 - 72a b - 36a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 4 3 2 3 ---R (288a b \|- 1 - 288a b \|- 1 + 192a b + 96a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 4 3 2 2 ---R (864a b \|- 1 - 864a b \|- 1 + 576a b + 288a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 4 3 2 ---R (864a b \|- 1 - 864a b \|- 1 + 576a b + 288a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 4 3 2 ---R 288a b \|- 1 - 288a b \|- 1 + 192a b + 96a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 4 ---R (- 108a b \|- 1 + 108a b\|- 1 - 72a b - 36a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 3 ---R (- 432a b \|- 1 + 432a b\|- 1 - 288a b - 144a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 2 ---R (- 648a b \|- 1 + 648a b\|- 1 - 432a b - 216a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R (- 432a b \|- 1 + 432a b\|- 1 - 288a b - 144a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R - 108a b \|- 1 + 108a b\|- 1 - 72a b - 36a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 6 ---R (- 36a b \|- 1 + 36a b\|- 1 - 24a b - 12a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 5 ---R (- 216a b \|- 1 + 216a b\|- 1 - 144a b - 72a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 4 ---R (- 540a b \|- 1 + 540a b\|- 1 - 360a b - 180a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 3 ---R (- 720a b \|- 1 + 720a b\|- 1 - 480a b - 240a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 2 ---R (- 540a b \|- 1 + 540a b\|- 1 - 360a b - 180a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R (- 216a b \|- 1 + 216a b\|- 1 - 144a b - 72a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 2 3 4 ---R - 36a b \|- 1 + 36a b\|- 1 - 24a b - 12a b ---R * ---R x 3 ---R tan(-) ---R 2 ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 6 ---R (- 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a )sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a ---R * ---R 4 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 ---R (288a b \|- 1 - 288a b \|- 1 + 216a b + 72a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 ---R (864a b \|- 1 - 864a b \|- 1 + 648a b + 216a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 ---R (864a b \|- 1 - 864a b \|- 1 + 648a b + 216a b)cos(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 4 ---R 288a b \|- 1 - 288a b \|- 1 + 216a b + 72a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 4 ---R (- 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 ---R (- 432a b \|- 1 + 432a b \|- 1 - 324a b - 108a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 648a b \|- 1 + 648a b \|- 1 - 486a b - 162a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 432a b \|- 1 + 432a b \|- 1 - 324a b - 108a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 108a b \|- 1 + 108a b \|- 1 - 81a b - 27a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 6 ---R (- 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 4 ---R (- 540a b \|- 1 + 540a b \|- 1 - 405a b - 135a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 ---R (- 720a b \|- 1 + 720a b \|- 1 - 540a b - 180a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 ---R (- 540a b \|- 1 + 540a b \|- 1 - 405a b - 135a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R (- 216a b \|- 1 + 216a b \|- 1 - 162a b - 54a )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 5 ---R - 36a b \|- 1 + 36a b \|- 1 - 27a b - 9a ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R - 54a b \|- 1 + 54a b\|- 1 - 54a b ---R * ---R 4 ---R sin(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 3 ---R (144a b \|- 1 - 144a b \|- 1 + 144a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 2 ---R (432a b \|- 1 - 432a b \|- 1 + 432a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R (432a b \|- 1 - 432a b \|- 1 + 432a b )cos(x) ---R + ---R 3 2 3+---+2 3 2 3+---+ 3 2 ---R 144a b \|- 1 - 144a b \|- 1 + 144a b ---R * ---R 3 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 324a b \|- 1 + 324a b\|- 1 - 324a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 ---R - 54a b \|- 1 + 54a b\|- 1 - 54a b ---R * ---R 2 ---R sin(x) ---R + ---R 4 3+---+2 4 3+---+ 4 6 ---R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 5 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 ---R (- 270a b \|- 1 + 270a b\|- 1 - 270a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 3 ---R (- 360a b \|- 1 + 360a b\|- 1 - 360a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 2 ---R (- 270a b \|- 1 + 270a b\|- 1 - 270a b)cos(x) ---R + ---R 4 3+---+2 4 3+---+ 4 4 3+---+2 ---R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cos(x) - 18a b \|- 1 ---R + ---R 4 3+---+ 4 ---R 18a b\|- 1 - 18a b ---R * ---R x ---R tan(-) ---R 2 ---R + ---R 3 2 5 6 ---R (3a b - 3a )sin(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 4 ---R ((9a b - 9a )cos(x) + (18a b - 18a )cos(x) + 9a b - 9a )sin(x) ---R + ---R 2 3 4 3 2 3 4 2 ---R (- 24a b + 24a b)cos(x) + (- 72a b + 72a b)cos(x) ---R + ---R 2 3 4 2 3 4 ---R (- 72a b + 72a b)cos(x) - 24a b + 24a b ---R * ---R 3 ---R sin(x) ---R + ---R 3 2 5 4 3 2 5 3 ---R (9a b - 9a )cos(x) + (36a b - 36a )cos(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 ---R (54a b - 54a )cos(x) + (36a b - 36a )cos(x) + 9a b - 9a ---R * ---R 2 ---R sin(x) ---R + ---R 3 2 5 6 3 2 5 5 ---R (3a b - 3a )cos(x) + (18a b - 18a )cos(x) ---R + ---R 3 2 5 4 3 2 5 3 ---R (45a b - 45a )cos(x) + (60a b - 60a )cos(x) ---R + ---R 3 2 5 2 3 2 5 3 2 5 ---R (45a b - 45a )cos(x) + (18a b - 18a )cos(x) + 3a b - 3a ---R * ---R 3+-+ ---R \|a ---R Type: Expression Integer +--d0067:= D(m0067,x) --E 360 --S 361 of 520 @@ -33994,17 +24770,19 @@ t0068:= 1/(a-b*sin(x)^4) --R --R --R 1 ---R (257) - ------------- +--R (226) - ------------- --R 4 --R b sin(x) - a --R Type: Expression Integer --E 361 --S 362 of 520 -r0068:= 1/2*atan((a^(1/2)-b^(1/2))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)-b^(1/2))^(1/2)+1/2*atan((a^(1/2)+b^(1/2))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)+b^(1/2))^(1/2) +r0068:= 1/2*atan((a^(1/2)-b^(1/2))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/_ + (a^(1/2)-b^(1/2))^(1/2)+1/2*atan((a^(1/2)+b^(1/2))^(1/2)*_ + tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)+b^(1/2))^(1/2) --R --R ---R (258) +--R (227) --R +-----------+ --R +-------------+ | +-+ +-+ --R | +-+ +-+ tan(x)\|\|b + \|a @@ -34029,7 +24807,7 @@ r0068:= 1/2*atan((a^(1/2)-b^(1/2))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)-b^(1/2 a0068:= integrate(t0068,x) --R --R ---R (259) +--R (228) --R - --R +-----------------------------------------+ --R | +----------------------+ @@ -34166,7 +24944,7 @@ a0068:= integrate(t0068,x) m0068:= a0068-r0068 --R --R ---R (260) +--R (229) --R - --R +-----------------------------------------+ --R | +----------------------+ @@ -34335,7 +25113,7 @@ m0068:= a0068-r0068 d0068:= D(m0068,x) --R --R ---R (261) +--R (230) --R 4 2 2 4 --R ((- b + a)sin(x) + (- 2b + 2a)cos(x) sin(x) + (- b + a)cos(x) ) --R * @@ -34382,17 +25160,21 @@ t0069:= 1/(a-b*sin(x)^6) --R --R --R 1 ---R (262) - ------------- +--R (231) - ------------- --R 6 --R b sin(x) - a --R Type: Expression Integer --E 366 --S 367 of 520 -r0069:= 1/3*atan((a^(1/3)-b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)-b^(1/3))^(1/2)+1/3*atan((a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2)+1/3*atan((a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2) +r0069:= 1/3*atan((a^(1/3)-b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/_ + (a^(1/3)-b^(1/3))^(1/2)+1/3*atan((a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2)_ + *tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2)+_ + 1/3*atan((a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2)*tan(x)/a^(1/6))/_ + a^(5/6)/(a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2) --R --R ---R (263) +--R (232) --R +-----------------+ --R +--------------------+ +-------------+ |3+---+3+-+ 3+-+ --R | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ tan(x)\|\|- 1 \|b + \|a @@ -34424,7 +25206,7 @@ r0069:= 1/3*atan((a^(1/3)-b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)-b^(1/3 a0069:= integrate(t0069,x) --R --R ---R (264) +--R (233) --R ROOT --R 2 --R (12a b - 12a ) @@ -34712,7 +25494,7 @@ a0069:= integrate(t0069,x) m0069:= a0069-r0069 --R --R ---R (265) +--R (234) --R +--------------------+ +-------------+ +-----------------+ --R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ --R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a @@ -35057,7 +25839,7 @@ m0069:= a0069-r0069 d0069:= D(m0069,x) --R --R ---R (266) +--R (235) --R 3+---+2 3+---+ 6 --R ((- 6b + 15a)\|- 1 + (6b - 15a)\|- 1 - 6b + 15a)sin(x) --R + @@ -35800,17 +26582,22 @@ t0070:= 1/(a-b*sin(x)^8) --R --R --R 1 ---R (267) - ------------- +--R (236) - ------------- --R 8 --R b sin(x) - a --R Type: Expression Integer --E 371 --S 372 of 520 -r0070:= 1/4*atan((a^(1/4)-b^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/(a^(1/4)-b^(1/4))^(1/2)+1/4*atan((a^(1/4)-%i*b^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/(a^(1/4)-%i*b^(1/4))^(1/2)+1/4*atan((a^(1/4)+%i*b^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/(a^(1/4)+%i*b^(1/4))^(1/2)+1/4*atan((a^(1/4)+b^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/(a^(1/4)+b^(1/4))^(1/2) +r0070:= 1/4*atan((a^(1/4)-b^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/_ + (a^(1/4)-b^(1/4))^(1/2)+1/4*atan((a^(1/4)-%i*b^(1/4))^(1/2)*_ + tan(x)/a^(1/8))/a^(7/8)/(a^(1/4)-%i*b^(1/4))^(1/2)+_ + 1/4*atan((a^(1/4)+%i*b^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/_ + (a^(1/4)+%i*b^(1/4))^(1/2)+1/4*atan((a^(1/4)+b^(1/4))^(1/2)*_ + tan(x)/a^(1/8))/a^(7/8)/(a^(1/4)+b^(1/4))^(1/2) --R --R ---R (268) +--R (237) --R +-------------+ +---------------+ +-------------+ --R | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ --R \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a @@ -35865,7 +26652,7 @@ r0070:= 1/4*atan((a^(1/4)-b^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/(a^(1/4)-b^(1/4 a0070:= integrate(t0070,x) --R --R ---R (269) +--R (238) --R - --R ROOT --R 2 @@ -36370,7 +27157,7 @@ a0070:= integrate(t0070,x) m0070:= a0070-r0070 --R --R ---R (270) +--R (239) --R - --R +-------------+ +---------------+ +-------------+ --R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ @@ -36967,7 +27754,7 @@ m0070:= a0070-r0070 d0070:= D(m0070,x) --R --R ---R (271) +--R (240) --R 8 2 6 --R (- b + a)sin(x) + (- 4b + 4a)cos(x) sin(x) --R + @@ -37113,17 +27900,19 @@ t0071:= 1/(1+sin(x)^3) --R --R --R 1 ---R (272) ----------- +--R (241) ----------- --R 3 --R sin(x) + 1 --R Type: Expression Integer --E 376 --S 377 of 520 -r0071:= -2/3*atan(((-1)^(1/3)-tan(1/2*x))/(1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^(1/2)+2/3*atan(((-1)^(2/3)+tan(1/2*x))/(1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)-cos(x)/(3+3*sin(x)) +r0071:= -2/3*atan(((-1)^(1/3)-tan(1/2*x))/(1-(-1)^(2/3))^(1/2))/_ + (1-(-1)^(2/3))^(1/2)+2/3*atan(((-1)^(2/3)+tan(1/2*x))/_ + (1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)-cos(x)/(3+3*sin(x)) --R --R ---R (273) +--R (242) --R x 3+---+ --R +----------+ tan(-) - \|- 1 --R |3+---+ 2 @@ -37154,7 +27943,7 @@ r0071:= -2/3*atan(((-1)^(1/3)-tan(1/2*x))/(1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^( a0071:= integrate(t0071,x) --R --R ---R (274) +--R (243) --R %pi x 4 %pi x 2 x 2 %pi x x --R - cos(---)sin(-) - 2cos(---)cos(-) sin(-) - 4cos(---)cos(-)sin(-) --R 12 2 12 2 2 12 2 2 @@ -37786,7 +28575,7 @@ a0071:= integrate(t0071,x) m0071:= a0071-r0071 --R --R ---R (275) +--R (244) --R %pi x 4 %pi x 2 x 2 --R - cos(---)sin(-) - 2cos(---)cos(-) sin(-) --R 12 2 12 2 2 @@ -38623,19 +29412,20 @@ t0072:= 1/(1+sin(x)^4) --R --R --R 1 ---R (276) ----------- +--R (245) ----------- --R 4 --R sin(x) + 1 --R Type: Expression Integer --E 381 --S 382 of 520 -r0072:= 1/2*atan((1-%i)^(1/2)*tan(x))/(1-%i)^(1/2)+1/2*atan((1+%i)^(1/2)*tan(x))/(1+%i)^(1/2) +r0072:= 1/2*atan((1-%i)^(1/2)*tan(x))/(1-%i)^(1/2)+_ + 1/2*atan((1+%i)^(1/2)*tan(x))/(1+%i)^(1/2) --R --R --R +------+ +------+ +------+ +------+ --R \|1 - %i atan(\|1 + %i tan(x)) + \|1 + %i atan(\|1 - %i tan(x)) ---R (277) --------------------------------------------------------------- +--R (246) --------------------------------------------------------------- --R +------+ +------+ --R 2\|1 - %i \|1 + %i --R Type: Expression Complex Integer @@ -38645,7 +29435,7 @@ r0072:= 1/2*atan((1-%i)^(1/2)*tan(x))/(1-%i)^(1/2)+1/2*atan((1+%i)^(1/2)*tan(x)) a0072:= integrate(t0072,x) --R --R ---R (278) +--R (247) --R 4+-+ %pi --R \|2 cos(---) --R 8 @@ -38758,7 +29548,7 @@ a0072:= integrate(t0072,x) m0072:= a0072-r0072 --R --R ---R (279) +--R (248) --R +------+ +------+4+-+ %pi --R \|1 - %i \|1 + %i \|2 cos(---) --R 8 @@ -38877,7 +29667,7 @@ m0072:= a0072-r0072 d0072:= D(m0072,x) --R --R ---R (280) +--R (249) --R 4+-+2 %pi 2 4+-+2 %pi %pi 4+-+2 %pi 2 --R (2\|2 sin(---) - 4\|2 cos(---)sin(---) - 2\|2 cos(---) - 2) --R 8 8 8 8 @@ -39944,17 +30734,20 @@ t0073:= 1/(1+sin(x)^8) --R --R --R 1 ---R (281) ----------- +--R (250) ----------- --R 8 --R sin(x) + 1 --R Type: Expression Integer --E 386 --S 387 of 520 -r0073:= 1/4*atan((1-(-1)^(1/4))^(1/2)*tan(x))/(1-(-1)^(1/4))^(1/2)+1/4*atan((1+(-1)^(1/4))^(1/2)*tan(x))/(1+(-1)^(1/4))^(1/2)+1/4*atan((1-(-1)^(3/4))^(1/2)*tan(x))/(1-(-1)^(3/4))^(1/2)+1/4*atan((1+(-1)^(3/4))^(1/2)*tan(x))/(1+(-1)^(3/4))^(1/2) +r0073:= 1/4*atan((1-(-1)^(1/4))^(1/2)*tan(x))/(1-(-1)^(1/4))^(1/2)+_ + 1/4*atan((1+(-1)^(1/4))^(1/2)*tan(x))/(1+(-1)^(1/4))^(1/2)+_ + 1/4*atan((1-(-1)^(3/4))^(1/2)*tan(x))/(1-(-1)^(3/4))^(1/2)+_ + 1/4*atan((1+(-1)^(3/4))^(1/2)*tan(x))/(1+(-1)^(3/4))^(1/2) --R --R ---R (282) +--R (251) --R +-----------------+ +-----------------+ +-----------------+ --R | +-+ +---+ | +-+ +---+ | +-+ +---+ --R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 @@ -40031,7 +30824,7 @@ r0073:= 1/4*atan((1-(-1)^(1/4))^(1/2)*tan(x))/(1-(-1)^(1/4))^(1/2)+1/4*atan((1+( a0073:= integrate(t0073,x) --R --R ---R (283) +--R (252) --R +---------+ --R | +-+ --R |3\|2 - 4 @@ -43844,17 +34637,19 @@ t0074:= 1/(1-sin(x)^3) --R --R --R 1 ---R (284) - ----------- +--R (253) - ----------- --R 3 --R sin(x) - 1 --R Type: Expression Integer --E 391 --S 392 of 520 -r0074:= -2/3*atan(((-1)^(2/3)-tan(1/2*x))/(1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)+2/3*atan(((-1)^(1/3)+tan(1/2*x))/(1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^(1/2)+cos(x)/(3-3*sin(x)) +r0074:= -2/3*atan(((-1)^(2/3)-tan(1/2*x))/(1+(-1)^(1/3))^(1/2))/_ + (1+(-1)^(1/3))^(1/2)+2/3*atan(((-1)^(1/3)+tan(1/2*x))/_ + (1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^(1/2)+cos(x)/(3-3*sin(x)) --R --R ---R (285) +--R (254) --R x 3+---+ --R +----------+ tan(-) + \|- 1 --R |3+---+ 2 @@ -43885,7 +34680,7 @@ r0074:= -2/3*atan(((-1)^(2/3)-tan(1/2*x))/(1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^( a0074:= integrate(t0074,x) --R --R ---R (286) +--R (255) --R %pi x 4 %pi x 2 x 2 %pi x x --R cos(---)sin(-) + 2cos(---)cos(-) sin(-) - 4cos(---)cos(-)sin(-) --R 12 2 12 2 2 12 2 2 @@ -44526,17 +35321,18 @@ t0075:= 1/(1-sin(x)^6) --R --R --R 1 ---R (287) - ----------- +--R (256) - ----------- --R 6 --R sin(x) - 1 --R Type: Expression Integer --E 396 --S 397 of 520 -r0075:= 1/3*atan((1+(-1)^(1/3))^(1/2)*tan(x))/(1+(-1)^(1/3))^(1/2)+1/3*atan((1-(-1)^(2/3))^(1/2)*tan(x))/(1-(-1)^(2/3))^(1/2)+1/3*tan(x) +r0075:= 1/3*atan((1+(-1)^(1/3))^(1/2)*tan(x))/(1+(-1)^(1/3))^(1/2)+_ + 1/3*atan((1-(-1)^(2/3))^(1/2)*tan(x))/(1-(-1)^(2/3))^(1/2)+1/3*tan(x) --R --R ---R (288) +--R (257) --R +-------------+ +----------+ --R | 3+---+2 |3+---+ --R \|- \|- 1 + 1 atan(tan(x)\|\|- 1 + 1 ) @@ -44559,7 +35355,7 @@ r0075:= 1/3*atan((1+(-1)^(1/3))^(1/2)*tan(x))/(1+(-1)^(1/3))^(1/2)+1/3*atan((1-( a0075:= integrate(t0075,x) --R --R ---R (289) +--R (258) --R %pi x 8 %pi x 2 x 6 --R cos(---)sin(-) + 4cos(---)cos(-) sin(-) --R 12 2 12 2 2 @@ -45822,17 +36618,19 @@ t0076:= 1/(1-sin(x)^8) --R --R --R 1 ---R (290) - ----------- +--R (259) - ----------- --R 8 --R sin(x) - 1 --R Type: Expression Integer --E 401 --S 402 of 520 -r0076:= 1/4*atan((1-%i)^(1/2)*tan(x))/(1-%i)^(1/2)+1/4*atan((1+%i)^(1/2)*tan(x))/(1+%i)^(1/2)+1/8*atan(2^(1/2)*tan(x))*2^(1/2)+1/4*tan(x) +r0076:= 1/4*atan((1-%i)^(1/2)*tan(x))/(1-%i)^(1/2)+_ + 1/4*atan((1+%i)^(1/2)*tan(x))/(1+%i)^(1/2)+_ + 1/8*atan(2^(1/2)*tan(x))*2^(1/2)+1/4*tan(x) --R --R ---R (291) +--R (260) --R +------+ +------+ +-+ +-+ +------+ +------+ --R \|1 - %i \|1 + %i \|2 atan(\|2 tan(x)) + 2\|1 - %i atan(\|1 + %i tan(x)) --R + @@ -45848,7 +36646,7 @@ r0076:= 1/4*atan((1-%i)^(1/2)*tan(x))/(1-%i)^(1/2)+1/4*atan((1+%i)^(1/2)*tan(x)) a0076:= integrate(t0076,x) --R --R ---R (292) +--R (261) --R +-+4+-+ %pi x 8 +-+4+-+ %pi x 2 x 6 --R \|2 \|2 cos(---)sin(-) + 4\|2 \|2 cos(---)cos(-) sin(-) --R 8 2 8 2 2 @@ -46068,14 +36866,18 @@ t0077:= sin(a+b*x+c*x^2)/x^2-b*cos(a+b*x+c*x^2)/x --R --R 2 2 --R sin(c x + b x + a) - b x cos(c x + b x + a) ---R (293) --------------------------------------------- +--R (262) --------------------------------------------- --R 2 --R x --R Type: Expression Integer --E 406 --S 407 of 520 -r0077:= c^(1/2)*2^(1/2)*%pi^(1/2)*cos(1/4*(b^2-4*a*c)/c)*FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))+c^(1/2)*2^(1/2)*%pi^(1/2)*FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*sin(1/4*(b^2-4*a*c)/c)-sin(a+b*x+c*x^2)/x +r0077:= c^(1/2)*2^(1/2)*%pi^(1/2)*cos(1/4*(b^2-4*a*c)/c)*_ + FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))+_ + c^(1/2)*2^(1/2)*%pi^(1/2)*_ + FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + sin(1/4*(b^2-4*a*c)/c)-sin(a+b*x+c*x^2)/x --R --R There are no library operations named FresnelC --R Use HyperDoc Browse or issue @@ -46097,7 +36899,7 @@ a0077:= integrate(t0077,x) --R --R x 2 2 --R ++ sin(%R c + %R b + a) - %R b cos(%R c + %R b + a) ---R (294) | ------------------------------------------------ d%R +--R (263) | ------------------------------------------------ d%R --R ++ 2 --R %R --R Type: Union(Expression Integer,...) @@ -46117,14 +36919,18 @@ t0078:= sin(a+b*x-c*x^2)/x^2-b*cos(a+b*x-c*x^2)/x --R --R 2 2 --R - sin(c x - b x - a) - b x cos(c x - b x - a) ---R (295) ----------------------------------------------- +--R (264) ----------------------------------------------- --R 2 --R x --R Type: Expression Integer --E 411 --S 412 of 520 -r0078:= c^(1/2)*2^(1/2)*%pi^(1/2)*cos(1/4*(b^2+4*a*c)/c)*FresnelC(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))+c^(1/2)*2^(1/2)*%pi^(1/2)*FresnelS(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*sin(1/4*(b^2+4*a*c)/c)-sin(a+b*x-c*x^2)/x +r0078:= c^(1/2)*2^(1/2)*%pi^(1/2)*cos(1/4*(b^2+4*a*c)/c)*_ + FresnelC(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))+_ + c^(1/2)*2^(1/2)*%pi^(1/2)*_ + FresnelS(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + sin(1/4*(b^2+4*a*c)/c)-sin(a+b*x-c*x^2)/x --R --R There are no library operations named FresnelC --R Use HyperDoc Browse or issue @@ -46146,7 +36952,7 @@ a0078:= integrate(t0078,x) --R --R x 2 2 --R ++ - sin(%R c - %R b - a) - %R b cos(%R c - %R b - a) ---R (296) | -------------------------------------------------- d%R +--R (265) | -------------------------------------------------- d%R --R ++ 2 --R %R --R Type: Union(Expression Integer,...) @@ -46165,12 +36971,18 @@ t0079:= (d+e*x)^2*sin(a+b*x+c*x^2) --R --R --R 2 2 2 2 ---R (297) (e x + 2d e x + d )sin(c x + b x + a) +--R (266) (e x + 2d e x + d )sin(c x + b x + a) --R Type: Expression Integer --E 416 --S 417 of 520 -r0079:= -1/4*e*(4*c*d-b*e)*cos(a+b*x+c*x^2)/c^2-1/2*e^2*x*cos(a+b*x+c*x^2)/c+1/8*2^(1/2)*%pi^(1/2)*FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*((2*c*d-b*e)^2*cos(a-1/4*b^2/c)-2*c*e^2*sin(a-1/4*b^2/c))/c^(5/2)+1/8*2^(1/2)*%pi^(1/2)*FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*(2*c*e^2*cos(a-1/4*b^2/c)+(2*c*d-b*e)^2*sin(a-1/4*b^2/c))/c^(5/2) +r0079:= -1/4*e*(4*c*d-b*e)*cos(a+b*x+c*x^2)/c^2-_ + 1/2*e^2*x*cos(a+b*x+c*x^2)/c+1/8*2^(1/2)*%pi^(1/2)*_ + FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*((2*c*d-b*e)^2*_ + cos(a-1/4*b^2/c)-2*c*e^2*sin(a-1/4*b^2/c))/c^(5/2)+_ + 1/8*2^(1/2)*%pi^(1/2)*_ + FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + (2*c*e^2*cos(a-1/4*b^2/c)+(2*c*d-b*e)^2*sin(a-1/4*b^2/c))/c^(5/2) --R --R There are no library operations named FresnelS --R Use HyperDoc Browse or issue @@ -46192,7 +37004,7 @@ a0079:= integrate(t0079,x) --R --R x --R ++ 2 2 2 2 ---R (298) | (%R e + 2%R d e + d )sin(%R c + %R b + a)d%R +--R (267) | (%R e + 2%R d e + d )sin(%R c + %R b + a)d%R --R ++ --R Type: Union(Expression Integer,...) --E 418 @@ -46210,16 +37022,18 @@ t0080:= sin((a+b*x)/(c+d*x))^2 --R --R --R b x + a 2 ---R (299) sin(-------) +--R (268) sin(-------) --R d x + c --R Type: Expression Integer --E 421 --S 422 of 520 -r0080:= 1/2*x-1/2*(c+d*x)*cos(2*(a+b*x)/(c+d*x))/d+(b*c-a*d)*Ci(-2*(b*c-a*d)/d/(c+d*x))*sin(2*b/d)/d^2+(b*c-a*d)*cos(2*b/d)*Si(2*a/(c+d*x)-2*b*c/d/(c+d*x))/d^2 +r0080:= 1/2*x-1/2*(c+d*x)*cos(2*(a+b*x)/(c+d*x))/d+_ + (b*c-a*d)*Ci(-2*(b*c-a*d)/d/(c+d*x))*sin(2*b/d)/d^2+_ + (b*c-a*d)*cos(2*b/d)*Si(2*a/(c+d*x)-2*b*c/d/(c+d*x))/d^2 --R --R ---R (300) +--R (269) --R 2a d - 2b c 2b 2 2b x + 2a --R (- 2a d + 2b c)Ci(-----------)sin(--) + (- d x - c d)cos(---------) --R 2 d d x + c @@ -46241,54 +37055,17 @@ a0080:= integrate(t0080,x) --R --R x --R ++ %R b + a 2 ---R (301) | sin(--------) d%R +--R (270) | sin(--------) d%R --R ++ %R d + c --R Type: Union(Expression Integer,...) --E 423 --S 424 of 520 -m0080:= a0080-r0080 ---R ---R ---R (302) ---R x ---R 2 ++ %R b + a 2 2a d - 2b c 2b ---R 2d | sin(--------) d%R + (2a d - 2b c)Ci(-----------)sin(--) ---R ++ %R d + c 2 d ---R d x + c d ---R + ---R 2 2b x + 2a 2a d - 2b c 2b 2 ---R (d x + c d)cos(---------) + (2a d - 2b c)Si(-----------)cos(--) - d x ---R d x + c 2 d ---R d x + c d ---R / ---R 2 ---R 2d ---R Type: Expression Integer +--m0080:= a0080-r0080 --E 424 --S 425 of 520 -d0080:= D(m0080,x) ---R ---R ---R (303) ---R 2b x + 2a 2a d - 2b c 2b ---R (2a d - 2b c)sin(---------) + (- 2a d + 2b c)cos(-----------)sin(--) ---R d x + c 2 d ---R d x + c d ---R + ---R 2 b x + a 2 2b 2a d - 2b c ---R (2d x + 2c d)sin(-------) + (- 2a d + 2b c)cos(--)sin(-----------) ---R d x + c d 2 ---R d x + c d ---R + ---R 2 2b x + 2a 2 ---R (d x + c d)cos(---------) - d x - c d ---R d x + c ---R / ---R 2 ---R 2d x + 2c d ---R Type: Expression Integer +--d0080:= D(m0080,x) --E 425 --S 426 of 520 @@ -46297,19 +37074,20 @@ t0081:= sin(a+b*x^2)^2/x^3 --R --R 2 2 --R sin(b x + a) ---R (304) -------------- +--R (271) -------------- --R 3 --R x --R Type: Expression Integer --E 426 --S 427 of 520 -r0081:= 1/4*(-1+cos(2*a+2*b*x^2)+2*b*Ci(2*b*x^2)*sin(2*a)*x^2+2*b*cos(2*a)*Si(2*b*x^2)*x^2)/x^2 +r0081:= 1/4*(-1+cos(2*a+2*b*x^2)+2*b*Ci(2*b*x^2)*sin(2*a)*x^2+_ + 2*b*cos(2*a)*Si(2*b*x^2)*x^2)/x^2 --R --R --R 2 2 2 2 2 --R 2b x Ci(2b x )sin(2a) + cos(2b x + 2a) + 2b x Si(2b x )cos(2a) - 1 ---R (305) ------------------------------------------------------------------- +--R (272) ------------------------------------------------------------------- --R 2 --R 4x --R Type: Expression Integer @@ -46321,45 +37099,18 @@ a0081:= integrate(t0081,x) --R --R x 2 2 --R ++ sin(%R b + a) ---R (306) | -------------- d%R +--R (273) | -------------- d%R --R ++ 3 --R %R --R Type: Union(Expression Integer,...) --E 428 --S 429 of 520 -m0081:= a0081-r0081 ---R ---R ---R (307) ---R x 2 2 ---R 2 ++ sin(%R b + a) 2 2 2 ---R 4x | -------------- d%R - 2b x Ci(2b x )sin(2a) - cos(2b x + 2a) ---R ++ 3 ---R %R ---R + ---R 2 2 ---R - 2b x Si(2b x )cos(2a) + 1 ---R / ---R 2 ---R 4x ---R Type: Expression Integer +--m0081:= a0081-r0081 --E 429 --S 430 of 520 -d0081:= D(m0081,x) ---R ---R ---R (308) ---R 2 2 2 2 2 2 ---R 2b x sin(2b x + 2a) - 2b x cos(2a)sin(2b x ) + 2sin(b x + a) ---R + ---R 2 2 2 ---R - 2b x cos(2b x )sin(2a) + cos(2b x + 2a) - 1 ---R / ---R 3 ---R 2x ---R Type: Expression Integer +--d0081:= D(m0081,x) --E 430 --S 431 of 520 @@ -46368,17 +37119,19 @@ t0082:= sin(a+b*x^2)^3/x^3 --R --R 2 3 --R sin(b x + a) ---R (309) -------------- +--R (274) -------------- --R 3 --R x --R Type: Expression Integer --E 431 --S 432 of 520 -r0082:= 3/8*b*cos(a)*Ci(b*x^2)-3/8*b*cos(3*a)*Ci(3*b*x^2)-3/8*sin(a+b*x^2)/x^2+1/8*sin(3*a+3*b*x^2)/x^2-3/8*b*sin(a)*Si(b*x^2)+3/8*b*sin(3*a)*Si(3*b*x^2) +r0082:= 3/8*b*cos(a)*Ci(b*x^2)-3/8*b*cos(3*a)*Ci(3*b*x^2)-_ + 3/8*sin(a+b*x^2)/x^2+1/8*sin(3*a+3*b*x^2)/x^2-_ + 3/8*b*sin(a)*Si(b*x^2)+3/8*b*sin(3*a)*Si(3*b*x^2) --R --R ---R (310) +--R (275) --R 2 2 2 2 --R sin(3b x + 3a) - 3sin(b x + a) + 3b x Si(3b x )sin(3a) --R + @@ -46396,51 +37149,18 @@ a0082:= integrate(t0082,x) --R --R x 2 3 --R ++ sin(%R b + a) ---R (311) | -------------- d%R +--R (276) | -------------- d%R --R ++ 3 --R %R --R Type: Union(Expression Integer,...) --E 433 --S 434 of 520 -m0082:= a0082-r0082 ---R ---R ---R (312) ---R x 2 3 ---R 2 ++ sin(%R b + a) 2 2 ---R 8x | -------------- d%R - sin(3b x + 3a) + 3sin(b x + a) ---R ++ 3 ---R %R ---R + ---R 2 2 2 2 2 2 ---R - 3b x Si(3b x )sin(3a) + 3b x Si(b x )sin(a) + 3b x Ci(3b x )cos(3a) ---R + ---R 2 2 ---R - 3b x Ci(b x )cos(a) ---R / ---R 2 ---R 8x ---R Type: Expression Integer +--m0082:= a0082-r0082 --E 434 --S 435 of 520 -d0082:= D(m0082,x) ---R ---R ---R (313) ---R 2 2 2 2 3 ---R sin(3b x + 3a) - 3b x sin(3a)sin(3b x ) + 4sin(b x + a) ---R + ---R 2 2 2 2 2 ---R - 3sin(b x + a) + 3b x sin(a)sin(b x ) - 3b x cos(3b x + 3a) ---R + ---R 2 2 2 2 2 2 ---R 3b x cos(3a)cos(3b x ) + 3b x cos(b x + a) - 3b x cos(a)cos(b x ) ---R / ---R 3 ---R 4x ---R Type: Expression Integer +--d0082:= D(m0082,x) --E 435 --S 436 of 520 @@ -46448,15 +37168,16 @@ t0083:= sin(a+b*x^n) --R --R --R n ---R (314) sin(b x + a) +--R (277) sin(b x + a) --R Type: Expression Integer --E 436 --S 437 of 520 -r0083:= -1/2*%i*x/n*(-exp(%i*a)*(-%i*b*x^n)^(-1/n)*Gamma(1/n,-%i*b*x^n)+(%i*b*x^n)^(-1/n)*exp(-%i*a)*Gamma(1/n,%i*b*x^n)) +r0083:= -1/2*%i*x/n*(-exp(%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-%i*b*x^n)+(%i*b*x^n)^(-1/n)*exp(-%i*a)*Gamma(1/n,%i*b*x^n)) --R --R ---R (315) +--R (278) --R 1 --R - - --R - %i a n n _ 1 n @@ -46479,70 +37200,17 @@ a0083:= integrate(t0083,x) --R --R x --R ++ n ---R (316) | sin(b %R + a)d%R +--R (279) | sin(b %R + a)d%R --R ++ --R Type: Union(Expression Integer,...) --E 438 --S 439 of 520 -m0083:= a0083-r0083 ---R ---R ---R (317) ---R 1 ---R x - - ---R ++ n - %i a n n _ 1 n ---R 2n | sin(b %R + a)d%R + %i x %e (%i b x ) | (-,%i b x ) ---R ++ n ---R + ---R 1 ---R - - ---R %i a n n _ 1 n ---R - %i x %e (- %i b x ) | (-,- %i b x ) ---R n ---R / ---R 2n ---R Type: Expression Complex Integer +--m0083:= a0083-r0083 --E 439 --S 440 of 520 -d0083:= D(m0083,x) ---R ---R ---R (318) ---R 1 - n - 1 ---R - - ------- ---R - %i a n n - %i a n - 1 n n ---R (%i %e (%i b x ) + b x %e x (%i b x ) ) ---R * ---R _ 1 n ---R | (-,%i b x ) ---R n ---R + ---R 1 - n - 1 ---R - - ------- ---R %i a n n %i a n - 1 n n ---R (- %i %e (- %i b x ) + b x %e x (- %i b x ) ) ---R * ---R _ 1 n ---R | (-,- %i b x ) ---R n ---R + ---R - n + 1 1 ---R n ------- - - ---R - %i a n - 1 - %i b x n n n n ---R b n x %e x %e (%i b x ) (%i b x ) ---R + ---R - n + 1 1 ---R n ------- - - ---R %i a n - 1 %i b x n n n n ---R b n x %e x %e (- %i b x ) (- %i b x ) ---R + ---R n ---R 2n sin(b x + a) ---R / ---R 2n ---R Type: Expression Complex Integer +--d0083:= D(m0083,x) --E 440 --S 441 of 520 @@ -46550,15 +37218,17 @@ t0084:= sin(a+b*x^n)^2 --R --R --R n 2 ---R (319) sin(b x + a) +--R (280) sin(b x + a) --R Type: Expression Integer --E 441 --S 442 of 520 -r0084:= 1/2*x/n*(2^(-(1+n)/n)*exp(2*%i*a)*(-%i*b*x^n)^(-1/n)*Gamma(1/n,-2*%i*b*x^n)+2^(-(1+n)/n)*exp(-2*%i*a)*(%i*b*x^n)^(-1/n)*Gamma(1/n,2*%i*b*x^n)+n) +r0084:= 1/2*x/n*(2^(-(1+n)/n)*exp(2*%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-2*%i*b*x^n)+2^(-(1+n)/n)*exp(-2*%i*a)*(%i*b*x^n)^(-1/n)*_ + Gamma(1/n,2*%i*b*x^n)+n) --R --R ---R (320) +--R (281) --R - n - 1 1 --R ------- - - --R - 2%i a n n n _ 1 n @@ -46581,96 +37251,17 @@ a0084:= integrate(t0084,x) --R --R x --R ++ n 2 ---R (321) | sin(b %R + a) d%R +--R (282) | sin(b %R + a) d%R --R ++ --R Type: Union(Expression Integer,...) --E 443 --S 444 of 520 -m0084:= a0084-r0084 ---R ---R ---R (322) ---R x ---R ++ n 2 ---R 2n | sin(b %R + a) d%R ---R ++ ---R + ---R - n - 1 1 ---R ------- - - ---R - 2%i a n n n _ 1 n ---R - x %e 2 (%i b x ) | (-,2%i b x ) ---R n ---R + ---R - n - 1 1 ---R ------- - - ---R 2%i a n n n _ 1 n ---R - x %e 2 (- %i b x ) | (-,- 2%i b x ) - n x ---R n ---R / ---R 2n ---R Type: Expression Complex Integer +--m0084:= a0084-r0084 --E 444 --S 445 of 520 -d0084:= D(m0084,x) ---R ---R ---R (323) ---R - n - 1 1 ---R ------- - - ---R - 2%i a n n n ---R - %e 2 (%i b x ) ---R + ---R - n - 1 - n - 1 ---R ------- ------- ---R - 2%i a n n - 1 n n ---R %i b x %e 2 x (%i b x ) ---R * ---R _ 1 n ---R | (-,2%i b x ) ---R n ---R + ---R - n - 1 1 ---R ------- - - ---R 2%i a n n n ---R - %e 2 (- %i b x ) ---R + ---R - n - 1 - n - 1 ---R ------- ------- ---R 2%i a n n - 1 n n ---R - %i b x %e 2 x (- %i b x ) ---R * ---R _ 1 n ---R | (-,- 2%i b x ) ---R n ---R + ---R - n - 1 1 ---R ------- n - - ---R - 2%i a n n - 1 - 2%i b x n n ---R 2%i b n x %e 2 x %e (%i b x ) ---R * ---R - n + 1 ---R ------- ---R n n ---R (2%i b x ) ---R + ---R - ---R - n - 1 - n + 1 ---R ------- n ------- ---R 2%i a n n - 1 2%i b x n n ---R 2%i b n x %e 2 x %e (- 2%i b x ) ---R * ---R 1 ---R - - ---R n n ---R (- %i b x ) ---R + ---R n 2 ---R 2n sin(b x + a) - n ---R / ---R 2n ---R Type: Expression Complex Integer +--d0084:= D(m0084,x) --E 445 --S 446 of 520 @@ -46678,15 +37269,19 @@ t0085:= sin(a+b*x^n)^3 --R --R --R n 3 ---R (324) sin(b x + a) +--R (283) sin(b x + a) --R Type: Expression Integer --E 446 --S 447 of 520 -r0085:= 1/8*%i/n*x*(3*exp(%i*a)*(-%i*b*x^n)^(-1/n)*Gamma(1/n,-%i*b*x^n)-3*(%i*b*x^n)^(-1/n)*exp(-%i*a)*Gamma(1/n,%i*b*x^n)-exp(3*%i*a)*(-%i*b*x^n)^(-1/n)*3^(-1/n)*Gamma(1/n,-3*%i*b*x^n)+(%i*b*x^n)^(-1/n)*3^(-1/n)*exp(-3*%i*a)*Gamma(1/n,3*%i*b*x^n)) +r0085:= 1/8*%i/n*x*(3*exp(%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-%i*b*x^n)-3*(%i*b*x^n)^(-1/n)*exp(-%i*a)*_ + Gamma(1/n,%i*b*x^n)-exp(3*%i*a)*(-%i*b*x^n)^(-1/n)*3^(-1/n)*_ + Gamma(1/n,-3*%i*b*x^n)+(%i*b*x^n)^(-1/n)*3^(-1/n)*exp(-3*%i*a)*_ + Gamma(1/n,3*%i*b*x^n)) --R --R ---R (325) +--R (284) --R 1 1 --R - - - - --R - 3%i a n n n _ 1 n @@ -46721,125 +37316,17 @@ a0085:= integrate(t0085,x) --R --R x --R ++ n 3 ---R (326) | sin(b %R + a) d%R +--R (285) | sin(b %R + a) d%R --R ++ --R Type: Union(Expression Integer,...) --E 448 --S 449 of 520 -m0085:= a0085-r0085 ---R ---R ---R (327) ---R 1 1 ---R x - - - - ---R ++ n 3 - 3%i a n n n _ 1 n ---R 8n | sin(b %R + a) d%R - %i x %e 3 (%i b x ) | (-,3%i b x ) ---R ++ n ---R + ---R 1 ---R - - ---R - %i a n n _ 1 n ---R 3%i x %e (%i b x ) | (-,%i b x ) ---R n ---R + ---R 1 ---R - - ---R %i a n n _ 1 n ---R - 3%i x %e (- %i b x ) | (-,- %i b x ) ---R n ---R + ---R 1 1 ---R - - - - ---R 3%i a n n n _ 1 n ---R %i x %e 3 (- %i b x ) | (-,- 3%i b x ) ---R n ---R / ---R 8n ---R Type: Expression Complex Integer +--m0085:= a0085-r0085 --E 449 --S 450 of 520 -d0085:= D(m0085,x) ---R ---R ---R (328) ---R 1 1 ---R - - - - ---R - 3%i a n n n ---R - %i %e 3 (%i b x ) ---R + ---R 1 - n - 1 ---R - - ------- ---R - 3%i a n n - 1 n n ---R - b x %e 3 x (%i b x ) ---R * ---R _ 1 n ---R | (-,3%i b x ) ---R n ---R + ---R 1 - n - 1 ---R - - ------- ---R - %i a n n - %i a n - 1 n n ---R (3%i %e (%i b x ) + 3b x %e x (%i b x ) ) ---R * ---R _ 1 n ---R | (-,%i b x ) ---R n ---R + ---R 1 - n - 1 ---R - - ------- ---R %i a n n %i a n - 1 n n ---R (- 3%i %e (- %i b x ) + 3b x %e x (- %i b x ) ) ---R * ---R _ 1 n ---R | (-,- %i b x ) ---R n ---R + ---R 1 1 ---R - - - - ---R 3%i a n n n ---R %i %e 3 (- %i b x ) ---R + ---R 1 - n - 1 ---R - - ------- ---R 3%i a n n - 1 n n ---R - b x %e 3 x (- %i b x ) ---R * ---R _ 1 n ---R | (-,- 3%i b x ) ---R n ---R + ---R 1 1 - n + 1 ---R - - n - - ------- ---R - 3%i a n n - 1 - 3%i b x n n n n ---R - 3b n x %e 3 x %e (%i b x ) (3%i b x ) ---R + ---R - n + 1 1 ---R n ------- - - ---R - %i a n - 1 - %i b x n n n n ---R 3b n x %e x %e (%i b x ) (%i b x ) ---R + ---R - n + 1 ---R n ------- ---R %i a n - 1 %i b x n n ---R 3b n x %e x %e (- %i b x ) ---R + ---R 1 - n + 1 ---R - - n ------- ---R 3%i a n n - 1 3%i b x n n ---R - 3b n x %e 3 x %e (- 3%i b x ) ---R * ---R 1 ---R - - ---R n n ---R (- %i b x ) ---R + ---R n 3 ---R 8n sin(b x + a) ---R / ---R 8n ---R Type: Expression Complex Integer +--d0085:= D(m0085,x) --E 450 --S 451 of 520 @@ -46847,15 +37334,17 @@ t0086:= x^m*sin(a+b*x^n) --R --R --R m n ---R (329) x sin(b x + a) +--R (286) x sin(b x + a) --R Type: Expression Integer --E 451 --S 452 of 520 -r0086:= 1/2*%i*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)-exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,%i*b*x^n))/n +r0086:= 1/2*%i*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)-exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,%i*b*x^n))/n --R --R ---R (330) +--R (287) --R - m - 1 --R ------- --R - %i a m n n _ m + 1 n @@ -46880,100 +37369,17 @@ a0086:= integrate(t0086,x) --R --R x --R ++ m n ---R (331) | %R sin(b %R + a)d%R +--R (288) | %R sin(b %R + a)d%R --R ++ --R Type: Union(Expression Integer,...) --E 453 --S 454 of 520 -m0086:= a0086-r0086 ---R ---R ---R (332) ---R - m - 1 ---R ------- ---R - %i a m n n _ m + 1 n ---R %i %e x (%i b x ) | (-----,%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R %i a m n n _ m + 1 n ---R - %i %e x (- %i b x ) | (-----,- %i b x ) ---R n ---R / ---R 2n ---R * ---R x ---R + ---R x ---R ++ m n ---R | %R sin(b %R + a)d%R ---R ++ ---R Type: UnivariatePolynomial(x,Expression Complex Integer) +--m0086:= a0086-r0086 --E 454 --S 455 of 520 -d0086:= D(m0086,x) ---R ---R ---R (333) ---R - m - 1 ---R ------- ---R - %i a m - 1 n n ---R %i m %e x (%i b x ) ---R + ---R - n - m - 1 ---R ----------- ---R - %i a m n - 1 n n ---R (b m + b)%e x x (%i b x ) ---R * ---R _ m + 1 n ---R | (-----,%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R %i a m - 1 n n ---R - %i m %e x (- %i b x ) ---R + ---R - n - m - 1 ---R ----------- ---R %i a m n - 1 n n ---R (b m + b)%e x x (- %i b x ) ---R * ---R _ m + 1 n ---R | (-----,- %i b x ) ---R n ---R + ---R - n + m + 1 - m - 1 ---R n ----------- ------- ---R - %i a m n - 1 - %i b x n n n n ---R b n %e x x %e (%i b x ) (%i b x ) ---R + ---R - n + m + 1 - m - 1 ---R n ----------- ------- ---R %i a m n - 1 %i b x n n n n ---R b n %e x x %e (- %i b x ) (- %i b x ) ---R / ---R 2n ---R * ---R x ---R + ---R - m - 1 ---R ------- ---R - %i a m n n _ m + 1 n ---R %i %e x (%i b x ) | (-----,%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R %i a m n n _ m + 1 n m n ---R - %i %e x (- %i b x ) | (-----,- %i b x ) + 2n x sin(b x + a) ---R n ---R / ---R 2n ---R Type: UnivariatePolynomial(x,Expression Complex Integer) +--d0086:= D(m0086,x) --E 455 --S 456 of 520 @@ -46981,15 +37387,18 @@ t0087:= x^m*sin(a+b*x^n)^2 --R --R --R m n 2 ---R (334) x sin(b x + a) +--R (289) x sin(b x + a) --R Type: Expression Integer --E 456 --S 457 of 520 -r0087:= x^(1+m)/(2+2*m)+2^(-2-(1+m)/n)*exp(1)^(2*%i*a)*x^(1+m)*Gamma((1+m)/n,-2*%i*b*x^n)/((-%i*b*x^n)^((1+m)/n))/n+2^(-2-(1+m)/n)*x^(1+m)*Gamma((1+m)/n,2*%i*b*x^n)/(exp(1)^(2*%i*a))/((%i*b*x^n)^((1+m)/n))/n +r0087:= x^(1+m)/(2+2*m)+2^(-2-(1+m)/n)*exp(1)^(2*%i*a)*x^(1+m)*_ + Gamma((1+m)/n,-2*%i*b*x^n)/((-%i*b*x^n)^((1+m)/n))/n+_ + 2^(-2-(1+m)/n)*x^(1+m)*_ + Gamma((1+m)/n,2*%i*b*x^n)/(exp(1)^(2*%i*a))/((%i*b*x^n)^((1+m)/n))/n --R --R ---R (335) +--R (290) --R - 2n - m - 1 m + 1 --R ------------ ----- --R n m + 1 n n _ m + 1 n @@ -47020,131 +37429,17 @@ a0087:= integrate(t0087,x) --R --R x --R ++ m n 2 ---R (336) | %R sin(b %R + a) d%R +--R (291) | %R sin(b %R + a) d%R --R ++ --R Type: Union(Expression Integer,...) --E 458 --S 459 of 520 -m0087:= a0087-r0087 ---R ---R ---R (337) ---R m + 1 m + 1 ---R ----- ----- ---R 2%i a n n n n ---R (2m + 2)n %e (- %i b x ) (%i b x ) ---R * ---R x ---R ++ m n 2 ---R | %R sin(b %R + a) d%R ---R ++ ---R + ---R - 2n - m - 1 m + 1 ---R ------------ ----- ---R n m + 1 n n _ m + 1 n ---R (- 2m - 2)2 x (- %i b x ) | (-----,2%i b x ) ---R n ---R + ---R - 2n - m - 1 m + 1 ---R ------------ ----- ---R 2%i a 2 n m + 1 n n _ m + 1 n ---R (- 2m - 2)(%e ) 2 x (%i b x ) | (-----,- 2%i b x ) ---R n ---R + ---R m + 1 m + 1 ---R ----- ----- ---R 2%i a m + 1 n n n n ---R - n %e x (- %i b x ) (%i b x ) ---R / ---R m + 1 m + 1 ---R ----- ----- ---R 2%i a n n n n ---R (2m + 2)n %e (- %i b x ) (%i b x ) ---R Type: Expression Complex Integer +--m0087:= a0087-r0087 --E 459 --S 460 of 520 -d0087:= D(m0087,x) ---R ---R ---R (338) ---R - 2n - m - 1 m + 1 2 m + 1 ---R ------------ ----- ----- ---R n m n n n n ---R (- 2m - 2)2 x ((- %i b x ) ) (%i b x ) ---R + ---R - 2n - m - 1 m + 1 2 ---R ------------ ----- ---R n m + 1 n - 1 n n ---R (2%i b m + 2%i b)2 x x ((- %i b x ) ) ---R * ---R - n + m + 1 ---R ----------- ---R n n ---R (%i b x ) ---R * ---R _ m + 1 n ---R | (-----,2%i b x ) ---R n ---R + ---R - 2n - m - 1 m + 1 ---R ------------ ----- ---R 2%i a 2 n m n n ---R (- 2m - 2)(%e ) 2 x (- %i b x ) ---R + ---R - 2n - m - 1 ---R ------------ ---R 2%i a 2 n m + 1 n - 1 ---R (- 2%i b m - 2%i b)(%e ) 2 x x ---R * ---R - n + m + 1 ---R ----------- ---R n n ---R (- %i b x ) ---R * ---R m + 1 2 ---R ----- ---R n n _ m + 1 n ---R ((%i b x ) ) | (-----,- 2%i b x ) ---R n ---R + ---R - 2n - m - 1 m + 1 2 ---R ------------ n ----- ---R n m + 1 n - 1 - 2%i b x n n ---R 4%i b n 2 x x %e ((- %i b x ) ) ---R * ---R m + 1 - n + m + 1 ---R ----- ----------- ---R n n n n ---R (%i b x ) (2%i b x ) ---R + ---R m + 1 2 ---R ----- ---R 2%i a m n 2 2%i a m n n ---R (2n %e x sin(b x + a) - n %e x )((- %i b x ) ) ---R + ---R - ---R - 2n - m - 1 ---R ------------ n ---R 2%i a 2 n m + 1 n - 1 2%i b x ---R 4%i b n (%e ) 2 x x %e ---R * ---R - n + m + 1 m + 1 ---R ----------- ----- ---R n n n n ---R (- 2%i b x ) (- %i b x ) ---R * ---R m + 1 2 ---R ----- ---R n n ---R ((%i b x ) ) ---R / ---R m + 1 2 m + 1 2 ---R ----- ----- ---R 2%i a n n n n ---R 2n %e ((- %i b x ) ) ((%i b x ) ) ---R Type: Expression Complex Integer +--d0087:= D(m0087,x) --E 460 --S 461 of 520 @@ -47152,15 +37447,20 @@ t0088:= x^m*sin(a+b*x^n)^3 --R --R --R m n 3 ---R (339) x sin(b x + a) +--R (292) x sin(b x + a) --R Type: Expression Integer --E 461 --S 462 of 520 -r0088:= -1/8*%i/n*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*Gamma((1+m)/n,-3*%i*b*x^n)*exp(3*%i*a)-3*(-%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)+3*exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,%i*b*x^n)-(%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*Gamma((1+m)/n,3*%i*b*x^n)*exp(-3*%i*a)) +r0088:= -1/8*%i/n*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*_ + Gamma((1+m)/n,-3*%i*b*x^n)*exp(3*%i*a)-3*(-%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)+_ + 3*exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,%i*b*x^n)-(%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*_ + Gamma((1+m)/n,3*%i*b*x^n)*exp(-3*%i*a)) --R --R ---R (340) +--R (293) --R - m - 1 - m - 1 --R ------- ------- --R - 3%i a n m n n _ m + 1 n @@ -47195,156 +37495,17 @@ a0088:= integrate(t0088,x) --R --R x --R ++ m n 3 ---R (341) | %R sin(b %R + a) d%R +--R (294) | %R sin(b %R + a) d%R --R ++ --R Type: Union(Expression Integer,...) --E 463 --S 464 of 520 -m0088:= a0088-r0088 ---R ---R ---R (342) ---R x ---R ++ m n 3 ---R 8n | %R sin(b %R + a) d%R ---R ++ ---R + ---R - m - 1 - m - 1 ---R ------- ------- ---R - 3%i a n m n n _ m + 1 n ---R - %i x %e 3 x (%i b x ) | (-----,3%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R - %i a m n n _ m + 1 n ---R 3%i x %e x (%i b x ) | (-----,%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R %i a m n n _ m + 1 n ---R - 3%i x %e x (- %i b x ) | (-----,- %i b x ) ---R n ---R + ---R - m - 1 - m - 1 ---R ------- ------- ---R 3%i a n m n n _ m + 1 n ---R %i x %e 3 x (- %i b x ) | (-----,- 3%i b x ) ---R n ---R / ---R 8n ---R Type: Expression Complex Integer +--m0088:= a0088-r0088 --E 464 --S 465 of 520 -d0088:= D(m0088,x) ---R ---R ---R (343) ---R - m - 1 - m - 1 ---R ------- ------- ---R - 3%i a n m - 3%i a n m - 1 ---R (- %i %e 3 x - %i m x %e 3 x ) ---R * ---R - m - 1 ---R ------- ---R n n ---R (%i b x ) ---R + ---R - m - 1 - n - m - 1 ---R ------- ----------- ---R - 3%i a n m n - 1 n n ---R (- b m - b)x %e 3 x x (%i b x ) ---R * ---R _ m + 1 n ---R | (-----,3%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R - %i a m - %i a m - 1 n n ---R (3%i %e x + 3%i m x %e x )(%i b x ) ---R + ---R - n - m - 1 ---R ----------- ---R - %i a m n - 1 n n ---R (3b m + 3b)x %e x x (%i b x ) ---R * ---R _ m + 1 n ---R | (-----,%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R %i a m %i a m - 1 n n ---R (- 3%i %e x - 3%i m x %e x )(- %i b x ) ---R + ---R - n - m - 1 ---R ----------- ---R %i a m n - 1 n n ---R (3b m + 3b)x %e x x (- %i b x ) ---R * ---R _ m + 1 n ---R | (-----,- %i b x ) ---R n ---R + ---R - m - 1 - m - 1 ---R ------- ------- ---R 3%i a n m 3%i a n m - 1 ---R (%i %e 3 x + %i m x %e 3 x ) ---R * ---R - m - 1 ---R ------- ---R n n ---R (- %i b x ) ---R + ---R - m - 1 - n - m - 1 ---R ------- ----------- ---R 3%i a n m n - 1 n n ---R (- b m - b)x %e 3 x x (- %i b x ) ---R * ---R _ m + 1 n ---R | (-----,- 3%i b x ) ---R n ---R + ---R - ---R - m - 1 - m - 1 ---R ------- n ------- ---R - 3%i a n m n - 1 - 3%i b x n n ---R 3b n x %e 3 x x %e (%i b x ) ---R * ---R - n + m + 1 ---R ----------- ---R n n ---R (3%i b x ) ---R + ---R - n + m + 1 - m - 1 ---R n ----------- ------- ---R - %i a m n - 1 - %i b x n n n n ---R 3b n x %e x x %e (%i b x ) (%i b x ) ---R + ---R - n + m + 1 ---R n ----------- ---R %i a m n - 1 %i b x n n ---R 3b n x %e x x %e (- %i b x ) ---R + ---R - m - 1 - n + m + 1 ---R ------- n ----------- ---R 3%i a n m n - 1 3%i b x n n ---R - 3b n x %e 3 x x %e (- 3%i b x ) ---R * ---R - m - 1 ---R ------- ---R n n ---R (- %i b x ) ---R + ---R m n 3 ---R 8n x sin(b x + a) ---R / ---R 8n ---R Type: Expression Complex Integer +--d0088:= D(m0088,x) --E 465 --S 466 of 520 @@ -47353,7 +37514,7 @@ t0089:= x/sin(x)^(3/2)+x*sin(x)^(1/2) --R --R 2 --R x sin(x) + x ---R (344) --------------- +--R (295) --------------- --R +------+ --R sin(x)\|sin(x) --R Type: Expression Integer @@ -47364,7 +37525,7 @@ r0089:= -2*(x*cos(x)-2*sin(x))/sin(x)^(1/2) --R --R --R 4sin(x) - 2x cos(x) ---R (345) ------------------- +--R (296) ------------------- --R +------+ --R \|sin(x) --R Type: Expression Integer @@ -47382,27 +37543,11 @@ a0089:= integrate(t0089,x) --E 468 --S 469 of 520 -m0089:= a0089-r0089 ---R ---R ---R +------+ ---R a0089\|sin(x) - 4sin(x) + 2x cos(x) ---R (346) ------------------------------------ ---R +------+ ---R \|sin(x) ---R Type: Expression Integer +--m0089:= a0089-r0089 --E 469 --S 470 of 520 -d0089:= D(m0089,x) ---R ---R ---R 2 2 ---R - 2x sin(x) - x cos(x) ---R (347) ------------------------ ---R +------+ ---R sin(x)\|sin(x) ---R Type: Expression Integer +--d0089:= D(m0089,x) --E 470 --S 471 of 520 @@ -47411,7 +37556,7 @@ t0090:= x/sin(x)^(5/2)-1/3*x/sin(x)^(1/2) --R --R 2 --R - x sin(x) + 3x ---R (348) ----------------- +--R (297) ----------------- --R 2 +------+ --R 3sin(x) \|sin(x) --R Type: Expression Integer @@ -47422,7 +37567,7 @@ r0090:= -2/3*(x*cos(x)+2*sin(x))/sin(x)^(3/2) --R --R --R - 4sin(x) - 2x cos(x) ---R (349) --------------------- +--R (298) --------------------- --R +------+ --R 3sin(x)\|sin(x) --R Type: Expression Integer @@ -47434,7 +37579,7 @@ a0090:= integrate(t0090,x) --R --R +------+ --R (4sin(x) + 2x cos(x))\|sin(x) ---R (350) ------------------------------ +--R (299) ------------------------------ --R 2 --R 3cos(x) - 3 --R Type: Union(Expression Integer,...) @@ -47444,7 +37589,7 @@ a0090:= integrate(t0090,x) m0090:= a0090-r0090 --R --R ---R (351) +--R (300) --R 3 2 2 3 --R 4sin(x) + 2x cos(x)sin(x) + (4cos(x) - 4)sin(x) + 2x cos(x) - 2x cos(x) --R --------------------------------------------------------------------------- @@ -47457,7 +37602,7 @@ m0090:= a0090-r0090 d0090:= D(m0090,x) --R --R ---R (352) +--R (301) --R 5 2 4 3 3 --R 8cos(x)sin(x) + (2x cos(x) + 2x)sin(x) + (8cos(x) - 8cos(x))sin(x) --R + @@ -47478,19 +37623,20 @@ t0091:= x/sin(x)^(7/2)+3/5*x*sin(x)^(1/2) --R --R 4 --R 3x sin(x) + 5x ---R (353) ----------------- +--R (302) ----------------- --R 3 +------+ --R 5sin(x) \|sin(x) --R Type: Expression Integer --E 476 --S 477 of 520 -r0091:= 2/15*(16*sin(x)-18*sin(x)*cos(x)^2-12*x*cos(x)+9*x*cos(x)^3)/sin(x)^(5/2) +r0091:= 2/15*(16*sin(x)-18*sin(x)*cos(x)^2-12*x*cos(x)+_ + 9*x*cos(x)^3)/sin(x)^(5/2) --R --R --R 2 3 --R (- 36cos(x) + 32)sin(x) + 18x cos(x) - 24x cos(x) ---R (354) --------------------------------------------------- +--R (303) --------------------------------------------------- --R 2 +------+ --R 15sin(x) \|sin(x) --R Type: Expression Integer @@ -47508,32 +37654,11 @@ a0091:= integrate(t0091,x) --E 478 --S 479 of 520 -m0091:= a0091-r0091 ---R ---R ---R (355) ---R 2 +------+ 2 3 ---R 15a0091 sin(x) \|sin(x) + (36cos(x) - 32)sin(x) - 18x cos(x) + 24x cos(x) ---R ---------------------------------------------------------------------------- ---R 2 +------+ ---R 15sin(x) \|sin(x) ---R Type: Expression Integer +--m0091:= a0091-r0091 --E 479 --S 480 of 520 -d0091:= D(m0091,x) ---R ---R ---R (356) ---R 3 2 2 ---R - 24cos(x)sin(x) + (18x cos(x) - 8x)sin(x) ---R + ---R 3 4 2 ---R (- 24cos(x) + 24cos(x))sin(x) + 15x cos(x) - 20x cos(x) ---R / ---R 3 +------+ ---R 5sin(x) \|sin(x) ---R Type: Expression Integer +--d0091:= D(m0091,x) --E 480 --S 481 of 520 @@ -47542,14 +37667,15 @@ t0092:= x^2/sin(x)^(3/2)+x^2*sin(x)^(1/2) --R --R 2 2 2 --R x sin(x) + x ---R (357) --------------- +--R (304) --------------- --R +------+ --R sin(x)\|sin(x) --R Type: Expression Integer --E 481 --S 482 of 520 -r0092:= -16*EllipticE(-1/4*%pi+1/2*x,2)-2*x^2*cos(x)/sin(x)^(1/2)+8*x*sin(x)^(1/2) +r0092:= -16*EllipticE(-1/4*%pi+1/2*x,2)-2*x^2*cos(x)/sin(x)^(1/2)+_ + 8*x*sin(x)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -47595,7 +37721,7 @@ t0093:= sin(x)*(b-a/x^2)^(1/2)/(a-b*x^2)^(1/2) --R sin(x) |-------- --R | 2 --R \| x ---R (358) ----------------- +--R (305) ----------------- --R +----------+ --R | 2 --R \|- b x + a @@ -47612,7 +37738,7 @@ r0093:= (b-a/x^2)^(1/2)*x*Si(x)/(a-b*x^2)^(1/2) --R x Si(x) |-------- --R | 2 --R \| x ---R (359) ------------------ +--R (306) ------------------ --R +----------+ --R | 2 --R \|- b x + a @@ -47631,36 +37757,11 @@ a0093:= integrate(t0093,x) --E 488 --S 489 of 520 -m0093:= a0093-r0093 ---R ---R ---R +--------+ ---R | 2 +----------+ ---R |b x - a | 2 ---R - x Si(x) |-------- + a0093\|- b x + a ---R | 2 ---R \| x ---R (360) ----------------------------------------- ---R +----------+ ---R | 2 ---R \|- b x + a ---R Type: Expression Integer +--m0093:= a0093-r0093 --E 489 --S 490 of 520 -d0093:= D(m0093,x) ---R ---R ---R 2 ---R (- b x + a)sin(x) ---R (361) -------------------------- ---R +--------+ ---R +----------+ | 2 ---R 2 | 2 |b x - a ---R x \|- b x + a |-------- ---R | 2 ---R \| x ---R Type: Expression Integer +--d0093:= D(m0093,x) --E 490 --S 491 of 520 @@ -47668,7 +37769,7 @@ t0094:= sin(a+b*log(c*x^n)) --R --R --R n ---R (362) sin(b log(c x ) + a) +--R (307) sin(b log(c x ) + a) --R Type: Expression Integer --E 491 @@ -47678,7 +37779,7 @@ r0094:= x*(-b*n*cos(a+b*log(c*x^n))+sin(a+b*log(c*x^n)))/(1+b^2*n^2) --R --R n n --R x sin(b log(c x ) + a) - b n x cos(b log(c x ) + a) ---R (363) --------------------------------------------------- +--R (308) --------------------------------------------------- --R 2 2 --R b n + 1 --R Type: Expression Integer @@ -47688,7 +37789,7 @@ r0094:= x*(-b*n*cos(a+b*log(c*x^n))+sin(a+b*log(c*x^n)))/(1+b^2*n^2) a0094:= integrate(t0094,x) --R --R ---R (364) +--R (309) --R x sin(b n log(x) + b log(c) + a) - b n x cos(b n log(x) + b log(c) + a) --R ----------------------------------------------------------------------- --R 2 2 @@ -47700,7 +37801,7 @@ a0094:= integrate(t0094,x) m0094:= a0094-r0094 --R --R ---R (365) +--R (310) --R n n --R - x sin(b log(c x ) + a) + b n x cos(b log(c x ) + a) --R + @@ -47715,7 +37816,7 @@ m0094:= a0094-r0094 d0094:= D(m0094,x) --R --R ---R (366) +--R (311) --R n 2 2 n - 1 n --R (- x - b n x x )sin(b log(c x ) + a) --R + @@ -47735,7 +37836,7 @@ t0095:= x*sin(a+b*log(c*x^n)) --R --R --R n ---R (367) x sin(b log(c x ) + a) +--R (312) x sin(b log(c x ) + a) --R Type: Expression Integer --E 496 @@ -47745,7 +37846,7 @@ r0095:= x^2*(-b*n*cos(a+b*log(c*x^n))+2*sin(a+b*log(c*x^n)))/(4+b^2*n^2) --R --R 2 n 2 n --R 2x sin(b log(c x ) + a) - b n x cos(b log(c x ) + a) ---R (368) ---------------------------------------------------- +--R (313) ---------------------------------------------------- --R 2 2 --R b n + 4 --R Type: Expression Integer @@ -47755,7 +37856,7 @@ r0095:= x^2*(-b*n*cos(a+b*log(c*x^n))+2*sin(a+b*log(c*x^n)))/(4+b^2*n^2) a0095:= integrate(t0095,x) --R --R ---R (369) +--R (314) --R 2 2 --R 2x sin(b n log(x) + b log(c) + a) - b n x cos(b n log(x) + b log(c) + a) --R ------------------------------------------------------------------------ @@ -47768,7 +37869,7 @@ a0095:= integrate(t0095,x) m0095:= a0095-r0095 --R --R ---R (370) +--R (315) --R 2 n 2 n --R - 2x sin(b log(c x ) + a) + b n x cos(b log(c x ) + a) --R + @@ -47784,7 +37885,7 @@ m0095:= a0095-r0095 d0095:= D(m0095,x) --R --R ---R (371) +--R (316) --R n 2 2 2 n - 1 n --R (- 4x x - b n x x )sin(b log(c x ) + a) --R + @@ -47804,7 +37905,7 @@ t0096:= x^2*sin(a+b*log(c*x^n)) --R --R --R 2 n ---R (372) x sin(b log(c x ) + a) +--R (317) x sin(b log(c x ) + a) --R Type: Expression Integer --E 501 @@ -47814,7 +37915,7 @@ r0096:= x^3*(-b*n*cos(a+b*log(c*x^n))+3*sin(a+b*log(c*x^n)))/(9+b^2*n^2) --R --R 3 n 3 n --R 3x sin(b log(c x ) + a) - b n x cos(b log(c x ) + a) ---R (373) ---------------------------------------------------- +--R (318) ---------------------------------------------------- --R 2 2 --R b n + 9 --R Type: Expression Integer @@ -47824,7 +37925,7 @@ r0096:= x^3*(-b*n*cos(a+b*log(c*x^n))+3*sin(a+b*log(c*x^n)))/(9+b^2*n^2) a0096:= integrate(t0096,x) --R --R ---R (374) +--R (319) --R 3 3 --R 3x sin(b n log(x) + b log(c) + a) - b n x cos(b n log(x) + b log(c) + a) --R ------------------------------------------------------------------------ @@ -47837,7 +37938,7 @@ a0096:= integrate(t0096,x) m0096:= a0096-r0096 --R --R ---R (375) +--R (320) --R 3 n 3 n --R - 3x sin(b log(c x ) + a) + b n x cos(b log(c x ) + a) --R + @@ -47853,7 +37954,7 @@ m0096:= a0096-r0096 d0096:= D(m0096,x) --R --R ---R (376) +--R (321) --R 2 n 2 2 3 n - 1 n --R (- 9x x - b n x x )sin(b log(c x ) + a) --R + @@ -47874,7 +37975,7 @@ t0097:= sin(a+b*log(c*x^n))/x^2 --R --R n --R sin(b log(c x ) + a) ---R (377) -------------------- +--R (322) -------------------- --R 2 --R x --R Type: Expression Integer @@ -47886,7 +37987,7 @@ r0097:= -1/(1+b^2*n^2)/x*(sin(a+b*log(c*x^n))+b*n*cos(a+b*log(c*x^n))) --R --R n n --R - sin(b log(c x ) + a) - b n cos(b log(c x ) + a) ---R (378) ------------------------------------------------- +--R (323) ------------------------------------------------- --R 2 2 --R (b n + 1)x --R Type: Expression Integer @@ -47896,7 +37997,7 @@ r0097:= -1/(1+b^2*n^2)/x*(sin(a+b*log(c*x^n))+b*n*cos(a+b*log(c*x^n))) a0097:= integrate(t0097,x) --R --R ---R (379) +--R (324) --R - sin(b n log(x) + b log(c) + a) - b n cos(b n log(x) + b log(c) + a) --R --------------------------------------------------------------------- --R 2 2 @@ -47908,7 +38009,7 @@ a0097:= integrate(t0097,x) m0097:= a0097-r0097 --R --R ---R (380) +--R (325) --R n n --R sin(b log(c x ) + a) + b n cos(b log(c x ) + a) --R + @@ -47923,7 +38024,7 @@ m0097:= a0097-r0097 d0097:= D(m0097,x) --R --R ---R (381) +--R (326) --R n 2 2 n - 1 n --R (- x - b n x x )sin(b log(c x ) + a) --R + @@ -47943,17 +38044,18 @@ t0098:= x^m*sin(a+b*log(c*x^n)) --R --R --R m n ---R (382) x sin(b log(c x ) + a) +--R (327) x sin(b log(c x ) + a) --R Type: Expression Integer --E 511 --S 512 of 520 -r0098:= -b*n*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)+(1+m)*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+b^2*n^2) +r0098:= -b*n*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)+_ + (1+m)*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+b^2*n^2) --R --R --R m + 1 n m + 1 n --R (m + 1)x sin(b log(c x ) + a) - b n x cos(b log(c x ) + a) ---R (383) ------------------------------------------------------------------ +--R (328) ------------------------------------------------------------------ --R 2 2 2 --R b n + m + 2m + 1 --R Type: Expression Integer @@ -47963,7 +38065,7 @@ r0098:= -b*n*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)+(1+m)*x^(1+m)*sin(a+b a0098:= integrate(t0098,x) --R --R ---R (384) +--R (329) --R m log(x) --R (m + 1)x %e sin(b n log(x) + b log(c) + a) --R + @@ -47979,7 +38081,7 @@ a0098:= integrate(t0098,x) m0098:= a0098-r0098 --R --R ---R (385) +--R (330) --R m + 1 n m + 1 n --R (- m - 1)x sin(b log(c x ) + a) + b n x cos(b log(c x ) + a) --R + @@ -47998,7 +38100,7 @@ m0098:= a0098-r0098 d0098:= D(m0098,x) --R --R ---R (386) +--R (331) --R 2 m n 2 2 m + 1 n - 1 n --R ((- m - 2m - 1)x x - b n x x )sin(b log(c x ) + a) --R + @@ -48018,15 +38120,16 @@ t0099:= sin(a+b*log(c*x^n))^2 --R --R --R n 2 ---R (387) sin(b log(c x ) + a) +--R (332) sin(b log(c x ) + a) --R Type: Expression Integer --E 516 --S 517 of 520 -r0099:= -x*(-2*b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-1+cos(a+b*log(c*x^n))^2)/(1+4*b^2*n^2) +r0099:= -x*(-2*b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-_ + 1+cos(a+b*log(c*x^n))^2)/(1+4*b^2*n^2) --R --R ---R (388) +--R (333) --R n n --R - 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) --R + @@ -48042,7 +38145,7 @@ r0099:= -x*(-2*b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-1+cos(a+b*l a0099:= integrate(t0099,x) --R --R ---R (389) +--R (334) --R - 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) --R + --R 2 2 2 @@ -48057,7 +38160,7 @@ a0099:= integrate(t0099,x) m0099:= a0099-r0099 --R --R ---R (390) +--R (335) --R n n n 2 --R 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) + x cos(b log(c x ) + a) --R + @@ -48075,7 +38178,7 @@ m0099:= a0099-r0099 d0099:= D(m0099,x) --R --R ---R (391) +--R (336) --R 2 2 n - 1 n 2 --R - 2b n x x sin(b log(c x ) + a) --R + diff --git a/src/input/richtrig100-199.input.pamphlet b/src/input/richtrig100-199.input.pamphlet index 7e563eb..dbb7a83 100644 --- a/src/input/richtrig100-199.input.pamphlet +++ b/src/input/richtrig100-199.input.pamphlet @@ -27,7 +27,8 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --E 1 --S 2 of 504 ---Rr0100:= -1/4*x^2*(-b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-2+2*cos(a+b*log(c*x^n))^2)/(1+b^2*n^2) +r0100:= -1/4*x^2*(-b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-_ + 2+2*cos(a+b*log(c*x^n))^2)/(1+b^2*n^2) --R --R --R (2) @@ -40,11 +41,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 4b n + 4 --R Type: Expression Integer ---R --E 2 --S 3 of 504 ---Ra0100:= integrate(t0100,x) +a0100:= integrate(t0100,x) --R --R --R (3) @@ -57,11 +57,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 4b n + 4 --R Type: Union(Expression Integer,...) ---R --E 3 --S 4 of 504 ---Rm0100:= a0100-r0100 +m0100:= a0100-r0100 --R --R --R (4) @@ -77,11 +76,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 2b n + 2 --R Type: Expression Integer ---R --E 4 --S 5 of 504 ---Rd0100:= D(m0100,x) +d0100:= D(m0100,x) --R --R --R (5) @@ -103,21 +101,20 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 n --R (2b n + 2)x --R Type: Expression Integer ---R --E 5 --S 6 of 504 ---Rt0101:= x^2*sin(a+b*log(c*x^n))^2 +t0101:= x^2*sin(a+b*log(c*x^n))^2 --R --R --R 2 n 2 --R (6) x sin(b log(c x ) + a) --R Type: Expression Integer ---R --E 6 --S 7 of 504 ---Rr0101:= -1/3*x^3*(-2*b^2*n^2+6*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-9+9*cos(a+b*log(c*x^n))^2)/(9+4*b^2*n^2) +r0101:= -1/3*x^3*(-2*b^2*n^2+6*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-_ + 9+9*cos(a+b*log(c*x^n))^2)/(9+4*b^2*n^2) --R --R --R (7) @@ -130,11 +127,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 12b n + 27 --R Type: Expression Integer ---R --E 7 --S 8 of 504 ---Ra0101:= integrate(t0101,x) +a0101:= integrate(t0101,x) --R --R --R (8) @@ -147,11 +143,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 12b n + 27 --R Type: Union(Expression Integer,...) ---R --E 8 --S 9 of 504 ---Rm0101:= a0101-r0101 +m0101:= a0101-r0101 --R --R --R (9) @@ -170,11 +165,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 4b n + 9 --R Type: Expression Integer ---R --E 9 --S 10 of 504 ---Rd0101:= D(m0101,x) +d0101:= D(m0101,x) --R --R --R (10) @@ -196,11 +190,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 n --R (4b n + 9)x --R Type: Expression Integer ---R --E 10 --S 11 of 504 ---Rt0102:= sin(a+b*log(c*x^n))^2/x^2 +t0102:= sin(a+b*log(c*x^n))^2/x^2 --R --R --R n 2 @@ -209,11 +202,11 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 --R x --R Type: Expression Integer ---R --E 11 --S 12 of 504 ---Rr0102:= -1/(1+4*b^2*n^2)/x*(2*b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))+1-cos(a+b*log(c*x^n))^2) +r0102:= -1/(1+4*b^2*n^2)/x*(2*b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*_ + sin(a+b*log(c*x^n))+1-cos(a+b*log(c*x^n))^2) --R --R --R (12) @@ -226,11 +219,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R (4b n + 1)x --R Type: Expression Integer ---R --E 12 --S 13 of 504 ---Ra0102:= integrate(t0102,x) +a0102:= integrate(t0102,x) --R --R --R (13) @@ -242,11 +234,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R (4b n + 1)x --R Type: Union(Expression Integer,...) ---R --E 13 --S 14 of 504 ---Rm0102:= a0102-r0102 +m0102:= a0102-r0102 --R --R --R (14) @@ -261,11 +252,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R (4b n + 1)x --R Type: Expression Integer ---R --E 14 --S 15 of 504 ---Rd0102:= D(m0102,x) +d0102:= D(m0102,x) --R --R --R (15) @@ -287,21 +277,21 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 2 n --R (4b n + 1)x x --R Type: Expression Integer ---R --E 15 --S 16 of 504 ---Rt0103:= x^m*sin(a+b*log(c*x^n))^2 +t0103:= x^m*sin(a+b*log(c*x^n))^2 --R --R --R m n 2 --R (16) x sin(b log(c x ) + a) --R Type: Expression Integer ---R --E 16 --S 17 of 504 ---Rr0103:= 2*b^2*n^2*x^(1+m)/(1+m)/((1+m)^2+4*b^2*n^2)-2*b*n*x^(1+m)*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))/((1+m)^2+4*b^2*n^2)+(1+m)*x^(1+m)*sin(a+b*log(c*x^n))^2/((1+m)^2+4*b^2*n^2) +r0103:= 2*b^2*n^2*x^(1+m)/(1+m)/((1+m)^2+4*b^2*n^2)-_ + 2*b*n*x^(1+m)*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))/((1+m)^2+_ + 4*b^2*n^2)+(1+m)*x^(1+m)*sin(a+b*log(c*x^n))^2/((1+m)^2+4*b^2*n^2) --R --R --R (17) @@ -314,11 +304,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 2 3 2 --R (4b m + 4b )n + m + 3m + 3m + 1 --R Type: Expression Integer ---R --E 17 --S 18 of 504 ---Ra0103:= integrate(t0103,x) +a0103:= integrate(t0103,x) --R --R --R (18) @@ -339,11 +328,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 2 3 2 --R (4b m + 4b )n + m + 3m + 3m + 1 --R Type: Union(Expression Integer,...) ---R --E 18 --S 19 of 504 ---Rm0103:= a0103-r0103 +m0103:= a0103-r0103 --R --R --R (19) @@ -373,11 +361,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 2 3 2 --R (4b m + 4b )n + m + 3m + 3m + 1 --R Type: Expression Integer ---R --E 19 --S 20 of 504 ---Rd0103:= D(m0103,x) +d0103:= D(m0103,x) --R --R --R (20) @@ -411,21 +398,22 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 2 n --R (4b n + m + 2m + 1)x --R Type: Expression Integer ---R --E 20 --S 21 of 504 ---Rt0104:= sin(a+b*log(c*x^n))^3 +t0104:= sin(a+b*log(c*x^n))^3 --R --R --R n 3 --R (21) sin(b log(c x ) + a) --R Type: Expression Integer ---R --E 21 --S 22 of 504 ---Rr0104:= -6*b^3*n^3*x*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)+6*b^2*n^2*x*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)-3*b*n*x*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(1+9*b^2*n^2)+x*sin(a+b*log(c*x^n))^3/(1+9*b^2*n^2) +r0104:= -6*b^3*n^3*x*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)+_ + 6*b^2*n^2*x*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)-_ + 3*b*n*x*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(1+9*b^2*n^2)+_ + x*sin(a+b*log(c*x^n))^3/(1+9*b^2*n^2) --R --R --R (22) @@ -441,11 +429,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R 9b n + 10b n + 1 --R Type: Expression Integer ---R --E 22 --S 23 of 504 ---Ra0104:= integrate(t0104,x) +a0104:= integrate(t0104,x) --R --R --R (23) @@ -463,11 +450,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R 9b n + 10b n + 1 --R Type: Union(Expression Integer,...) ---R --E 23 --S 24 of 504 ---Rm0104:= a0104-r0104 +m0104:= a0104-r0104 --R --R --R (24) @@ -494,11 +480,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R 9b n + 10b n + 1 --R Type: Expression Integer ---R --E 24 --S 25 of 504 ---Rd0104:= D(m0104,x) +d0104:= D(m0104,x) --R --R --R (25) @@ -546,21 +531,22 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 n --R (9b n + 10b n + 1)x --R Type: Expression Integer ---R --E 25 --S 26 of 504 ---Rt0105:= x*sin(a+b*log(c*x^n))^3 +t0105:= x*sin(a+b*log(c*x^n))^3 --R --R --R n 3 --R (26) x sin(b log(c x ) + a) --R Type: Expression Integer ---R --E 26 --S 27 of 504 ---Rr0105:= -6*b^3*n^3*x^2*cos(a+b*log(c*x^n))/(4+b^2*n^2)/(4+9*b^2*n^2)+12*b^2*n^2*x^2*sin(a+b*log(c*x^n))/(4+b^2*n^2)/(4+9*b^2*n^2)-3*b*n*x^2*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(4+9*b^2*n^2)+2*x^2*sin(a+b*log(c*x^n))^3/(4+9*b^2*n^2) +r0105:= -6*b^3*n^3*x^2*cos(a+b*log(c*x^n))/(4+b^2*n^2)/(4+9*b^2*n^2)+_ + 12*b^2*n^2*x^2*sin(a+b*log(c*x^n))/(4+b^2*n^2)/(4+9*b^2*n^2)-_ + 3*b*n*x^2*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(4+9*b^2*n^2)+_ + 2*x^2*sin(a+b*log(c*x^n))^3/(4+9*b^2*n^2) --R --R --R (27) @@ -576,11 +562,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R 9b n + 40b n + 16 --R Type: Expression Integer ---R --E 27 --S 28 of 504 ---Ra0105:= integrate(t0105,x) +a0105:= integrate(t0105,x) --R --R --R (28) @@ -598,11 +583,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R 9b n + 40b n + 16 --R Type: Union(Expression Integer,...) ---R --E 28 --S 29 of 504 ---Rm0105:= a0105-r0105 +m0105:= a0105-r0105 --R --R --R (29) @@ -629,11 +613,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R 9b n + 40b n + 16 --R Type: Expression Integer ---R --E 29 --S 30 of 504 ---Rd0105:= D(m0105,x) +d0105:= D(m0105,x) --R --R --R (30) @@ -681,21 +664,22 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 n --R (9b n + 40b n + 16)x --R Type: Expression Integer ---R --E 30 --S 31 of 504 ---Rt0106:= x^2*sin(a+b*log(c*x^n))^3 +t0106:= x^2*sin(a+b*log(c*x^n))^3 --R --R --R 2 n 3 --R (31) x sin(b log(c x ) + a) --R Type: Expression Integer ---R --E 31 --S 32 of 504 ---Rr0106:= -2/3*b^3*n^3*x^3*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(9+b^2*n^2)+2*b^2*n^2*x^3*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(9+b^2*n^2)-b*n*x^3*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(3+3*b^2*n^2)+x^3*sin(a+b*log(c*x^n))^3/(3+3*b^2*n^2) +r0106:= -2/3*b^3*n^3*x^3*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(9+b^2*n^2)+_ + 2*b^2*n^2*x^3*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(9+b^2*n^2)-_ + b*n*x^3*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(3+3*b^2*n^2)+_ + x^3*sin(a+b*log(c*x^n))^3/(3+3*b^2*n^2) --R --R --R (32) @@ -711,11 +695,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R 3b n + 30b n + 27 --R Type: Expression Integer ---R --E 32 --S 33 of 504 ---Ra0106:= integrate(t0106,x) +a0106:= integrate(t0106,x) --R --R --R (33) @@ -733,11 +716,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R 3b n + 30b n + 27 --R Type: Union(Expression Integer,...) ---R --E 33 --S 34 of 504 ---Rm0106:= a0106-r0106 +m0106:= a0106-r0106 --R --R --R (34) @@ -764,11 +746,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R 3b n + 30b n + 27 --R Type: Expression Integer ---R --E 34 --S 35 of 504 ---Rd0106:= D(m0106,x) +d0106:= D(m0106,x) --R --R --R (35) @@ -816,11 +797,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 n --R (3b n + 30b n + 27)x --R Type: Expression Integer ---R --E 35 --S 36 of 504 ---Rt0107:= sin(a+b*log(c*x^n))^3/x^2 +t0107:= sin(a+b*log(c*x^n))^3/x^2 --R --R --R n 3 @@ -829,11 +809,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 --R x --R Type: Expression Integer ---R --E 36 --S 37 of 504 ---Rr0107:= -6*b^3*n^3*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)/x-6*b^2*n^2*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)/x-3*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(1+9*b^2*n^2)/x-sin(a+b*log(c*x^n))^3/(1+9*b^2*n^2)/x +r0107:= -6*b^3*n^3*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)/x-_ + 6*b^2*n^2*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)/x-_ + 3*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(1+9*b^2*n^2)/x-_ + sin(a+b*log(c*x^n))^3/(1+9*b^2*n^2)/x --R --R --R (37) @@ -849,11 +831,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R (9b n + 10b n + 1)x --R Type: Expression Integer ---R --E 37 --S 38 of 504 ---Ra0107:= integrate(t0107,x) +a0107:= integrate(t0107,x) --R --R --R (38) @@ -871,11 +852,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R (9b n + 10b n + 1)x --R Type: Union(Expression Integer,...) ---R --E 38 --S 39 of 504 ---Rm0107:= a0107-r0107 +m0107:= a0107-r0107 --R --R --R (39) @@ -902,11 +882,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 --R (9b n + 10b n + 1)x --R Type: Expression Integer ---R --E 39 --S 40 of 504 ---Rd0107:= D(m0107,x) +d0107:= D(m0107,x) --R --R --R (40) @@ -954,21 +933,23 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 2 n --R (9b n + 10b n + 1)x x --R Type: Expression Integer ---R --E 40 --S 41 of 504 ---Rt0108:= x^m*sin(a+b*log(c*x^n))^3 +t0108:= x^m*sin(a+b*log(c*x^n))^3 --R --R --R m n 3 --R (41) x sin(b log(c x ) + a) --R Type: Expression Integer ---R --E 41 --S 42 of 504 ---Rr0108:= -6*b^3*n^3*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)/((1+m)^2+9*b^2*n^2)+6*b^2*(1+m)*n^2*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)/((1+m)^2+9*b^2*n^2)-3*b*n*x^(1+m)*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/((1+m)^2+9*b^2*n^2)+(1+m)*x^(1+m)*sin(a+b*log(c*x^n))^3/((1+m)^2+9*b^2*n^2) +r0108:= -6*b^3*n^3*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)/((1+m)^2+_ + 9*b^2*n^2)+6*b^2*(1+m)*n^2*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+_ + b^2*n^2)/((1+m)^2+9*b^2*n^2)-3*b*n*x^(1+m)*cos(a+b*log(c*x^n))*_ + sin(a+b*log(c*x^n))^2/((1+m)^2+9*b^2*n^2)+(1+m)*x^(1+m)*_ + sin(a+b*log(c*x^n))^3/((1+m)^2+9*b^2*n^2) --R --R --R (42) @@ -987,11 +968,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 2 2 2 4 3 2 --R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 --R Type: Expression Integer ---R --E 42 --S 43 of 504 ---Ra0108:= integrate(t0108,x) +a0108:= integrate(t0108,x) --R --R --R (43) @@ -1016,11 +996,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 2 2 2 4 3 2 --R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 --R Type: Union(Expression Integer,...) ---R --E 43 --S 44 of 504 ---Rm0108:= a0108-r0108 +m0108:= a0108-r0108 --R --R --R (44) @@ -1060,11 +1039,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 2 2 2 4 3 2 --R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 --R Type: Expression Integer ---R --E 44 --S 45 of 504 ---Rd0108:= D(m0108,x) +d0108:= D(m0108,x) --R --R --R (45) @@ -1133,70 +1111,63 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4 4 2 2 2 2 2 4 3 2 n --R (9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1)x --R Type: Expression Integer ---R --E 45 --S 46 of 504 ---Rt0109:= sin(log(9+17*x)) +t0109:= sin(log(9+17*x)) --R --R --R (46) sin(log(17x + 9)) --R Type: Expression Integer ---R --E 46 --S 47 of 504 ---Rr0109:= -1/34*(9+17*x)*(cos(log(9+17*x))-sin(log(9+17*x))) +r0109:= -1/34*(9+17*x)*(cos(log(9+17*x))-sin(log(9+17*x))) --R --R --R (17x + 9)sin(log(17x + 9)) + (- 17x - 9)cos(log(17x + 9)) --R (47) --------------------------------------------------------- --R 34 --R Type: Expression Integer ---R --E 47 --S 48 of 504 ---Ra0109:= integrate(t0109,x) +a0109:= integrate(t0109,x) --R --R --R (17x + 9)sin(log(17x + 9)) + (- 17x - 9)cos(log(17x + 9)) --R (48) --------------------------------------------------------- --R 34 --R Type: Union(Expression Integer,...) ---R --E 48 --S 49 of 504 ---Rm0109:= a0109-r0109 +m0109:= a0109-r0109 --R --R --R (49) 0 --R Type: Expression Integer ---R --E 49 --S 50 of 504 ---Rd0109:= D(m0109,x) +d0109:= D(m0109,x) --R --R --R (50) 0 --R Type: Expression Integer ---R --E 50 --S 51 of 504 ---Rt0110:= cos(a+b*x)^(1/2) +t0110:= cos(a+b*x)^(1/2) --R --R --R +------------+ --R (51) \|cos(b x + a) --R Type: Expression Integer ---R --E 51 --S 52 of 504 ---Rr0110:= 2*EllipticE(1/2*a+1/2*b*x,2)/b +r0110:= 2*EllipticE(1/2*a+1/2*b*x,2)/b --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -1204,6 +1175,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -1211,11 +1183,10 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 52 --S 53 of 504 ---Ra0110:= integrate(t0110,x) +a0110:= integrate(t0110,x) --R --R --R x @@ -1223,43 +1194,27 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R (52) | \|cos(%H b + a) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 53 --S 54 of 504 ---Rm0110:= a0110-r0110 ---R ---R ---R x ---R ++ +-------------+ ---R (53) | \|cos(%H b + a) d%H - r0110 ---R ++ ---R Type: Expression Integer ---R +--m0110:= a0110-r0110 --E 54 --S 55 of 504 ---Rd0110:= D(m0110,x) ---R ---R ---R +------------+ ---R (54) \|cos(b x + a) ---R Type: Expression Integer ---R +--d0110:= D(m0110,x) --E 55 --S 56 of 504 ---Rt0111:= cos(a+b*x)^(3/2) +t0111:= cos(a+b*x)^(3/2) --R --R --R +------------+ ---R (55) cos(b x + a)\|cos(b x + a) +--R (53) cos(b x + a)\|cos(b x + a) --R Type: Expression Integer ---R --E 56 --S 57 of 504 ---Rr0111:= 2/3*(EllipticF(1/2*a+1/2*b*x,2)+cos(a+b*x)^(1/2)*sin(a+b*x))/b +r0111:= 2/3*(EllipticF(1/2*a+1/2*b*x,2)+cos(a+b*x)^(1/2)*sin(a+b*x))/b --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -1267,6 +1222,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Polynomial Fraction Integer @@ -1274,55 +1230,38 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 57 --S 58 of 504 ---Ra0111:= integrate(t0111,x) +a0111:= integrate(t0111,x) --R --R --R x --R ++ +-------------+ ---R (56) | cos(%H b + a)\|cos(%H b + a) d%H +--R (54) | cos(%H b + a)\|cos(%H b + a) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 58 --S 59 of 504 ---Rm0111:= a0111-r0111 ---R ---R ---R x ---R ++ +-------------+ ---R (57) | cos(%H b + a)\|cos(%H b + a) d%H - r0111 ---R ++ ---R Type: Expression Integer ---R +--m0111:= a0111-r0111 --E 59 --S 60 of 504 ---Rd0111:= D(m0111,x) ---R ---R ---R +------------+ ---R (58) cos(b x + a)\|cos(b x + a) ---R Type: Expression Integer ---R +--d0111:= D(m0111,x) --E 60 --S 61 of 504 ---Rt0112:= cos(a+b*x)^(5/2) +t0112:= cos(a+b*x)^(5/2) --R --R --R 2 +------------+ ---R (59) cos(b x + a) \|cos(b x + a) +--R (55) cos(b x + a) \|cos(b x + a) --R Type: Expression Integer ---R --E 61 --S 62 of 504 ---Rr0112:= 2/5*(3*EllipticE(1/2*a+1/2*b*x,2)+cos(a+b*x)^(3/2)*sin(a+b*x))/b +r0112:= 2/5*(3*EllipticE(1/2*a+1/2*b*x,2)+cos(a+b*x)^(3/2)*sin(a+b*x))/b --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -1330,6 +1269,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -1337,57 +1277,40 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 62 --S 63 of 504 ---Ra0112:= integrate(t0112,x) +a0112:= integrate(t0112,x) --R --R --R x --R ++ 2 +-------------+ ---R (60) | cos(%H b + a) \|cos(%H b + a) d%H +--R (56) | cos(%H b + a) \|cos(%H b + a) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 63 --S 64 of 504 ---Rm0112:= a0112-r0112 ---R ---R ---R x ---R ++ 2 +-------------+ ---R (61) | cos(%H b + a) \|cos(%H b + a) d%H - r0112 ---R ++ ---R Type: Expression Integer ---R +--m0112:= a0112-r0112 --E 64 --S 65 of 504 ---Rd0112:= D(m0112,x) ---R ---R ---R 2 +------------+ ---R (62) cos(b x + a) \|cos(b x + a) ---R Type: Expression Integer ---R +--d0112:= D(m0112,x) --E 65 --S 66 of 504 ---Rt0113:= 1/cos(a+b*x)^(1/2) +t0113:= 1/cos(a+b*x)^(1/2) --R --R --R 1 ---R (63) --------------- +--R (57) --------------- --R +------------+ --R \|cos(b x + a) --R Type: Expression Integer ---R --E 66 --S 67 of 504 ---Rr0113:= 2*EllipticF(1/2*a+1/2*b*x,2)/b +r0113:= 2*EllipticF(1/2*a+1/2*b*x,2)/b --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -1395,6 +1318,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Polynomial Fraction Integer @@ -1402,61 +1326,41 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 67 --S 68 of 504 ---Ra0113:= integrate(t0113,x) +a0113:= integrate(t0113,x) --R --R --R x --R ++ 1 ---R (64) | ---------------- d%H +--R (58) | ---------------- d%H --R ++ +-------------+ --R \|cos(%H b + a) --R Type: Union(Expression Integer,...) ---R --E 68 --S 69 of 504 ---Rm0113:= a0113-r0113 ---R ---R ---R x ---R ++ 1 ---R (65) | ---------------- d%H - r0113 ---R ++ +-------------+ ---R \|cos(%H b + a) ---R Type: Expression Integer ---R +--m0113:= a0113-r0113 --E 69 --S 70 of 504 ---Rd0113:= D(m0113,x) ---R ---R ---R 1 ---R (66) --------------- ---R +------------+ ---R \|cos(b x + a) ---R Type: Expression Integer ---R +--d0113:= D(m0113,x) --E 70 --S 71 of 504 ---Rt0114:= 1/cos(a+b*x)^(3/2) +t0114:= 1/cos(a+b*x)^(3/2) --R --R --R 1 ---R (67) --------------------------- +--R (59) --------------------------- --R +------------+ --R cos(b x + a)\|cos(b x + a) --R Type: Expression Integer ---R --E 71 --S 72 of 504 ---Rr0114:= -2*EllipticE(1/2*a+1/2*b*x,2)/b+2*sin(a+b*x)/b/cos(a+b*x)^(1/2) +r0114:= -2*EllipticE(1/2*a+1/2*b*x,2)/b+2*sin(a+b*x)/b/cos(a+b*x)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -1464,6 +1368,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -1471,61 +1376,41 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 72 --S 73 of 504 ---Ra0114:= integrate(t0114,x) +a0114:= integrate(t0114,x) --R --R --R x --R ++ 1 ---R (68) | ----------------------------- d%H +--R (60) | ----------------------------- d%H --R ++ +-------------+ --R cos(%H b + a)\|cos(%H b + a) --R Type: Union(Expression Integer,...) ---R --E 73 --S 74 of 504 ---Rm0114:= a0114-r0114 ---R ---R ---R x ---R ++ 1 ---R (69) | ----------------------------- d%H - r0114 ---R ++ +-------------+ ---R cos(%H b + a)\|cos(%H b + a) ---R Type: Expression Integer ---R +--m0114:= a0114-r0114 --E 74 --S 75 of 504 ---Rd0114:= D(m0114,x) ---R ---R ---R 1 ---R (70) --------------------------- ---R +------------+ ---R cos(b x + a)\|cos(b x + a) ---R Type: Expression Integer ---R +--d0114:= D(m0114,x) --E 75 --S 76 of 504 ---Rt0115:= 1/cos(a+b*x)^(5/2) +t0115:= 1/cos(a+b*x)^(5/2) --R --R --R 1 ---R (71) ---------------------------- +--R (61) ---------------------------- --R 2 +------------+ --R cos(b x + a) \|cos(b x + a) --R Type: Expression Integer ---R --E 76 --S 77 of 504 ---Rr0115:= 2/3*EllipticF(1/2*a+1/2*b*x,2)/b+2/3*sin(a+b*x)/b/cos(a+b*x)^(3/2) +r0115:= 2/3*EllipticF(1/2*a+1/2*b*x,2)/b+2/3*sin(a+b*x)/b/cos(a+b*x)^(3/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -1533,6 +1418,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Polynomial Fraction Integer @@ -1540,59 +1426,39 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 77 --S 78 of 504 ---Ra0115:= integrate(t0115,x) +a0115:= integrate(t0115,x) --R --R --R x --R ++ 1 ---R (72) | ------------------------------ d%H +--R (62) | ------------------------------ d%H --R ++ 2 +-------------+ --R cos(%H b + a) \|cos(%H b + a) --R Type: Union(Expression Integer,...) ---R --E 78 --S 79 of 504 ---Rm0115:= a0115-r0115 ---R ---R ---R x ---R ++ 1 ---R (73) | ------------------------------ d%H - r0115 ---R ++ 2 +-------------+ ---R cos(%H b + a) \|cos(%H b + a) ---R Type: Expression Integer ---R +--m0115:= a0115-r0115 --E 79 --S 80 of 504 ---Rd0115:= D(m0115,x) ---R ---R ---R 1 ---R (74) ---------------------------- ---R 2 +------------+ ---R cos(b x + a) \|cos(b x + a) ---R Type: Expression Integer ---R +--d0115:= D(m0115,x) --E 80 --S 81 of 504 ---Rt0116:= (a*cos(x))^(1/2) +t0116:= (a*cos(x))^(1/2) --R --R --R +--------+ ---R (75) \|a cos(x) +--R (63) \|a cos(x) --R Type: Expression Integer ---R --E 81 --S 82 of 504 ---Rr0116:= 2*(a*cos(x))^(1/2)*EllipticE(1/2*x,2)/cos(x)^(1/2) +r0116:= 2*(a*cos(x))^(1/2)*EllipticE(1/2*x,2)/cos(x)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -1600,6 +1466,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -1607,56 +1474,40 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 82 --S 83 of 504 ---Ra0116:= integrate(t0116,x) +a0116:= integrate(t0116,x) --R --R --R x --R ++ +---------+ ---R (76) | \|a cos(%H) d%H +--R (64) | \|a cos(%H) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 83 --S 84 of 504 ---Rm0116:= a0116-r0116 ---R ---R ---R x ---R ++ +---------+ ---R (77) | \|a cos(%H) d%H - r0116 ---R ++ ---R Type: Expression Integer ---R +--m0116:= a0116-r0116 --E 84 --S 85 of 504 ---Rd0116:= D(m0116,x) ---R ---R ---R +--------+ ---R (78) \|a cos(x) ---R Type: Expression Integer ---R +--d0116:= D(m0116,x) --E 85 --S 86 of 504 ---Rt0117:= (a*cos(x)^3)^(1/2) +t0117:= (a*cos(x)^3)^(1/2) --R --R --R +---------+ --R | 3 ---R (79) \|a cos(x) +--R (65) \|a cos(x) --R Type: Expression Integer ---R --E 86 --S 87 of 504 ---Rr0117:= 2/3*(a*cos(x)^3)^(1/2)*(EllipticF(1/2*x,2)+cos(x)^(1/2)*sin(x))/cos(x)^(3/2) +r0117:= 2/3*(a*cos(x)^3)^(1/2)*_ + (EllipticF(1/2*x,2)+cos(x)^(1/2)*sin(x))/cos(x)^(3/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -1664,6 +1515,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Polynomial Fraction Integer @@ -1671,56 +1523,39 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 87 --S 88 of 504 ---Ra0117:= integrate(t0117,x) +a0117:= integrate(t0117,x) --R --R --R x +----------+ --R ++ | 3 ---R (80) | \|a cos(%H) d%H +--R (66) | \|a cos(%H) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 88 --S 89 of 504 ---Rm0117:= a0117-r0117 ---R ---R ---R x +----------+ ---R ++ | 3 ---R (81) | \|a cos(%H) d%H - r0117 ---R ++ ---R Type: Expression Integer ---R +--m0117:= a0117-r0117 --E 89 --S 90 of 504 ---Rd0117:= D(m0117,x) ---R ---R ---R +---------+ ---R | 3 ---R (82) \|a cos(x) ---R Type: Expression Integer ---R +--d0117:= D(m0117,x) --E 90 --S 91 of 504 ---Rt0118:= (a*cos(x))^(3/2) +t0118:= (a*cos(x))^(3/2) --R --R --R +--------+ ---R (83) a cos(x)\|a cos(x) +--R (67) a cos(x)\|a cos(x) --R Type: Expression Integer ---R --E 91 --S 92 of 504 ---Rr0118:= 2/3*a^2*(cos(x)^(1/2)*EllipticF(1/2*x,2)+cos(x)*sin(x))/(a*cos(x))^(1/2) +r0118:= 2/3*a^2*(cos(x)^(1/2)*_ + EllipticF(1/2*x,2)+cos(x)*sin(x))/(a*cos(x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -1728,6 +1563,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Polynomial Fraction Integer @@ -1735,56 +1571,41 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 92 --S 93 of 504 ---Ra0118:= integrate(t0118,x) +a0118:= integrate(t0118,x) --R --R --R x --R ++ +---------+ ---R (84) | a cos(%H)\|a cos(%H) d%H +--R (68) | a cos(%H)\|a cos(%H) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 93 --S 94 of 504 ---Rm0118:= a0118-r0118 ---R ---R ---R x ---R ++ +---------+ ---R (85) | a cos(%H)\|a cos(%H) d%H - r0118 ---R ++ ---R Type: Expression Integer ---R +--m0118:= a0118-r0118 --E 94 --S 95 of 504 ---Rd0118:= D(m0118,x) ---R ---R ---R +--------+ ---R (86) a cos(x)\|a cos(x) ---R Type: Expression Integer ---R +--d0118:= D(m0118,x) --E 95 --S 96 of 504 ---Rt0119:= (a*cos(x)^3)^(3/2) +t0119:= (a*cos(x)^3)^(3/2) --R --R --R +---------+ --R 3 | 3 ---R (87) a cos(x) \|a cos(x) +--R (69) a cos(x) \|a cos(x) --R Type: Expression Integer ---R --E 96 --S 97 of 504 ---Rr0119:= 2/45*a*(a*cos(x)^3)^(1/2)*(21*EllipticE(1/2*x,2)+7*cos(x)^(3/2)*sin(x)+5*cos(x)^(7/2)*sin(x))/cos(x)^(3/2) +r0119:= 2/45*a*(a*cos(x)^3)^(1/2)*_ + (21*EllipticE(1/2*x,2)+7*cos(x)^(3/2)*sin(x)+_ + 5*cos(x)^(7/2)*sin(x))/cos(x)^(3/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -1792,6 +1613,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -1799,58 +1621,40 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 97 --S 98 of 504 ---Ra0119:= integrate(t0119,x) +a0119:= integrate(t0119,x) --R --R --R x +----------+ --R ++ 3 | 3 ---R (88) | a cos(%H) \|a cos(%H) d%H +--R (70) | a cos(%H) \|a cos(%H) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 98 --S 99 of 504 ---Rm0119:= a0119-r0119 ---R ---R ---R x +----------+ ---R ++ 3 | 3 ---R (89) | a cos(%H) \|a cos(%H) d%H - r0119 ---R ++ ---R Type: Expression Integer ---R +--m0119:= a0119-r0119 --E 99 --S 100 of 504 ---Rd0119:= D(m0119,x) ---R ---R ---R +---------+ ---R 3 | 3 ---R (90) a cos(x) \|a cos(x) ---R Type: Expression Integer ---R +--d0119:= D(m0119,x) --E 100 --S 101 of 504 ---Rt0120:= 1/(a*cos(x))^(1/2) +t0120:= 1/(a*cos(x))^(1/2) --R --R --R 1 ---R (91) ----------- +--R (71) ----------- --R +--------+ --R \|a cos(x) --R Type: Expression Integer ---R --E 101 --S 102 of 504 ---Rr0120:= 2*cos(x)^(1/2)*EllipticF(1/2*x,2)/(a*cos(x))^(1/2) +r0120:= 2*cos(x)^(1/2)*EllipticF(1/2*x,2)/(a*cos(x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -1858,6 +1662,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Polynomial Fraction Integer @@ -1865,109 +1670,86 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 102 --S 103 of 504 ---Ra0120:= integrate(t0120,x) +a0120:= integrate(t0120,x) --R --R --R x --R ++ 1 ---R (92) | ------------ d%H +--R (72) | ------------ d%H --R ++ +---------+ --R \|a cos(%H) --R Type: Union(Expression Integer,...) ---R --E 103 --S 104 of 504 ---Rm0120:= a0120-r0120 ---R ---R ---R x ---R ++ 1 ---R (93) | ------------ d%H - r0120 ---R ++ +---------+ ---R \|a cos(%H) ---R Type: Expression Integer ---R +--m0120:= a0120-r0120 --E 104 --S 105 of 504 ---Rd0120:= D(m0120,x) ---R ---R ---R 1 ---R (94) ----------- ---R +--------+ ---R \|a cos(x) ---R Type: Expression Integer ---R +--d0120:= D(m0120,x) --E 105 --S 106 of 504 ---Rt0121:= 1/(a*cos(x)^2)^(1/2) +t0121:= 1/(a*cos(x)^2)^(1/2) --R --R --R 1 ---R (95) ------------ +--R (73) ------------ --R +---------+ --R | 2 --R \|a cos(x) --R Type: Expression Integer ---R --E 106 --S 107 of 504 ---Rr0121:= atanh(sin(x))*cos(x)/(a*cos(x)^2)^(1/2) +r0121:= atanh(sin(x))*cos(x)/(a*cos(x)^2)^(1/2) --R --R --R cos(x)atanh(sin(x)) ---R (96) ------------------- +--R (74) ------------------- --R +---------+ --R | 2 --R \|a cos(x) --R Type: Expression Integer ---R --E 107 --S 108 of 504 ---Ra0121:= integrate(t0121,x) +a0121:= integrate(t0121,x) --R --R --R +---+ +-+ --R sin(x) - cos(x) - 1 sin(x)\|- a \|a --R log(-------------------) 2atan(----------------) --R sin(x) + cos(x) + 1 a cos(x) + a ---R (97) [------------------------,- -----------------------] +--R (75) [------------------------,- -----------------------] --R +-+ +---+ --R \|a \|- a --R Type: Union(List Expression Integer,...) ---R --E 108 --S 109 of 504 ---Rm0121a:= a0121.1-r0121 +m0121a:= a0121.1-r0121 --R --R --R +---------+ --R sin(x) - cos(x) - 1 | 2 +-+ --R log(-------------------)\|a cos(x) - cos(x)\|a atanh(sin(x)) --R sin(x) + cos(x) + 1 ---R (98) -------------------------------------------------------------- +--R (76) -------------------------------------------------------------- --R +---------+ --R +-+ | 2 --R \|a \|a cos(x) --R Type: Expression Integer ---R --E 109 --S 110 of 504 ---Rd0121a:= D(m0121a,x) +d0121a:= D(m0121a,x) --R --R ---R (99) +--R (77) --R 4 2 2 2 +-+ --R (2sin(x) + (2cos(x) + 2cos(x) - 2)sin(x) - 2cos(x) - 2cos(x))\|a --R * @@ -1987,30 +1769,28 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R | 2 --R \|a cos(x) --R Type: Expression Integer ---R --E 110 --S 111 of 504 ---Rm0121b:= a0121.2-r0121 +m0121b:= a0121.2-r0121 --R --R ---R +---+ +-+ +---------+ ---R sin(x)\|- a \|a | 2 +---+ ---R - 2atan(----------------)\|a cos(x) - cos(x)\|- a atanh(sin(x)) ---R a cos(x) + a ---R (100) ----------------------------------------------------------------- ---R +---------+ ---R +---+ | 2 ---R \|- a \|a cos(x) +--R +---+ +-+ +---------+ +--R sin(x)\|- a \|a | 2 +---+ +--R - 2atan(----------------)\|a cos(x) - cos(x)\|- a atanh(sin(x)) +--R a cos(x) + a +--R (78) ----------------------------------------------------------------- +--R +---------+ +--R +---+ | 2 +--R \|- a \|a cos(x) --R Type: Expression Integer ---R --E 111 --S 112 of 504 ---Rd0121b:= D(m0121b,x) +d0121b:= D(m0121b,x) --R --R ---R (101) +--R (79) --R 4 2 2 2 +-+ --R (2sin(x) + (2cos(x) + 2cos(x) - 2)sin(x) - 2cos(x) - 2cos(x))\|a --R * @@ -2030,24 +1810,22 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R | 2 --R \|a cos(x) --R Type: Expression Integer ---R --E 112 --S 113 of 504 ---Rt0122:= 1/(a*cos(x)^3)^(1/2) +t0122:= 1/(a*cos(x)^3)^(1/2) --R --R ---R 1 ---R (102) ------------ ---R +---------+ ---R | 3 ---R \|a cos(x) +--R 1 +--R (80) ------------ +--R +---------+ +--R | 3 +--R \|a cos(x) --R Type: Expression Integer ---R --E 113 --S 114 of 504 ---Rr0122:= -2*cos(x)*(cos(x)^(1/2)*EllipticE(1/2*x,2)-sin(x))/(a*cos(x)^3)^(1/2) +r0122:= -2*cos(x)*(cos(x)^(1/2)*EllipticE(1/2*x,2)-sin(x))/(a*cos(x)^3)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -2055,6 +1833,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -2062,55 +1841,34 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 114 --S 115 of 504 ---Ra0122:= integrate(t0122,x) +a0122:= integrate(t0122,x) --R --R ---R x ---R ++ 1 ---R (103) | ------------- d%H ---R ++ +----------+ ---R | 3 ---R \|a cos(%H) +--R x +--R ++ 1 +--R (81) | ------------- d%H +--R ++ +----------+ +--R | 3 +--R \|a cos(%H) --R Type: Union(Expression Integer,...) ---R --E 115 --S 116 of 504 ---Rm0122:= a0122-r0122 ---R ---R ---R x ---R ++ 1 ---R (104) | ------------- d%H - r0122 ---R ++ +----------+ ---R | 3 ---R \|a cos(%H) ---R Type: Expression Integer ---R +--m0122:= a0122-r0122 --E 116 --S 117 of 504 ---Rd0122:= D(m0122,x) ---R ---R ---R 1 ---R (105) ------------ ---R +---------+ ---R | 3 ---R \|a cos(x) ---R Type: Expression Integer ---R +--d0122:= D(m0122,x) --E 117 --S 118 of 504 ---Rt0123:= 1/(a+b*cos(c+d*x))^4 +t0123:= 1/(a+b*cos(c+d*x))^4 --R --R ---R (106) +--R (82) --R 1 --R / --R 4 4 3 3 2 2 2 @@ -2119,14 +1877,17 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 3 4 --R 4a b cos(d x + c) + a --R Type: Expression Integer ---R --E 118 --S 119 of 504 ---Rr0123:= a*(2*a^2+3*b^2)*atan((a-b)*tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/(a^2-b^2)^(7/2)/d-1/3*b*sin(c+d*x)/(a^2-b^2)/d/(a+b*cos(c+d*x))^3-5/6*a*b*sin(c+d*x)/(a^2-b^2)^2/d/(a+b*cos(c+d*x))^2-1/6*b*(11*a^2+4*b^2)*sin(c+d*x)/(a^2-b^2)^3/d/(a+b*cos(c+d*x)) +r0123:= a*(2*a^2+3*b^2)*atan((a-b)*tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/_ + (a^2-b^2)^(7/2)/d-1/3*b*sin(c+d*x)/(a^2-b^2)/d/_ + (a+b*cos(c+d*x))^3-5/6*a*b*sin(c+d*x)/(a^2-b^2)^2/d/_ + (a+b*cos(c+d*x))^2-1/6*b*(11*a^2+4*b^2)*sin(c+d*x)/_ + (a^2-b^2)^3/d/(a+b*cos(c+d*x)) --R --R ---R (107) +--R (83) --R 5 3 3 3 2 4 4 2 2 --R (18a b + 12a b )cos(d x + c) + (54a b + 36a b )cos(d x + c) --R + @@ -2167,14 +1928,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R | 2 2 --R \|- b + a --R Type: Expression Integer ---R --E 119 --S 120 of 504 ---Ra0123:= integrate(t0123,x) +a0123:= integrate(t0123,x) --R --R ---R (108) +--R (84) --R [ --R 5 3 3 3 2 4 4 2 2 --R (9a b + 6a b )cos(d x + c) + (27a b + 18a b )cos(d x + c) @@ -2254,14 +2014,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R \|- b + a --R ] --R Type: Union(List Expression Integer,...) ---R --E 120 --S 121 of 504 ---Rm0123a:= a0123.1-r0123 +m0123a:= a0123.1-r0123 --R --R ---R (109) +--R (85) --R +---------+ --R 2 3 | 2 2 --R (3a b + 2a )\|- b + a @@ -2284,14 +2043,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 6 2 4 4 2 6 | 2 2 | 2 2 --R (2b - 6a b + 6a b - 2a )d\|- b + a \|b - a --R Type: Expression Integer ---R --E 121 --S 122 of 504 ---Rd0123a:= D(m0123a,x) +d0123a:= D(m0123a,x) --R --R ---R (110) +--R (86) --R 4 2 3 3 2 4 2 --R (- 3a b + 3a b - 2a b + 2a b)sin(d x + c) --R + @@ -2398,14 +2156,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R * --R sin(d x + c) --R Type: Expression Integer ---R --E 122 --S 123 of 504 ---Rm0123b:= a0123.2-r0123 +m0123b:= a0123.2-r0123 --R --R ---R (111) +--R (87) --R +---------+ --R | 2 2 --R 2 3 sin(d x + c)\|- b + a @@ -2424,14 +2181,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 6 2 4 4 2 6 | 2 2 --R (b - 3a b + 3a b - a )d\|- b + a --R Type: Expression Integer ---R --E 123 --S 124 of 504 ---Rd0123b:= D(m0123b,x) +d0123b:= D(m0123b,x) --R --R ---R (112) +--R (88) --R 3 2 2 3 4 2 --R (3a b - 3a b + 2a b - 2a )sin(d x + c) --R + @@ -2482,21 +2238,20 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 8 7 2 6 3 5 5 3 6 2 7 8 --R 2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a --R Type: Expression Integer ---R --E 124 --S 125 of 504 ---Rt0124:= (a+b*cos(c+d*x))^(1/2) +t0124:= (a+b*cos(c+d*x))^(1/2) --R --R ---R +------------------+ ---R (113) \|b cos(d x + c) + a +--R +------------------+ +--R (89) \|b cos(d x + c) + a --R Type: Expression Integer ---R --E 125 --S 126 of 504 ---Rr0124:= 2*(a+b*cos(c+d*x))^(1/2)*EllipticE(1/2*c+1/2*d*x,2*b/(a+b))/d/((a+b*cos(c+d*x))/(a+b))^(1/2) +r0124:= 2*(a+b*cos(c+d*x))^(1/2)*_ + EllipticE(1/2*c+1/2*d*x,2*b/(a+b))/d/((a+b*cos(c+d*x))/(a+b))^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -2504,6 +2259,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -2511,57 +2267,41 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 126 --S 127 of 504 ---Ra0124:= integrate(t0124,x) +a0124:= integrate(t0124,x) --R --R ---R x ---R ++ +-------------------+ ---R (114) | \|b cos(%H d + c) + a d%H ---R ++ +--R x +--R ++ +-------------------+ +--R (90) | \|b cos(%H d + c) + a d%H +--R ++ --R Type: Union(Expression Integer,...) ---R --E 127 --S 128 of 504 ---Rm0124:= a0124-r0124 ---R ---R ---R x ---R ++ +-------------------+ ---R (115) | \|b cos(%H d + c) + a d%H - r0124 ---R ++ ---R Type: Expression Integer ---R +--m0124:= a0124-r0124 --E 128 --S 129 of 504 ---Rd0124:= D(m0124,x) ---R ---R ---R +------------------+ ---R (116) \|b cos(d x + c) + a ---R Type: Expression Integer ---R +--d0124:= D(m0124,x) --E 129 --S 130 of 504 ---Rt0125:= 1/(a+b*cos(x))^(1/2) +t0125:= 1/(a+b*cos(x))^(1/2) --R --R ---R 1 ---R (117) --------------- ---R +------------+ ---R \|b cos(x) + a +--R 1 +--R (91) --------------- +--R +------------+ +--R \|b cos(x) + a --R Type: Expression Integer ---R --E 130 --S 131 of 504 ---Rr0125:= 2*((a+b*cos(x))/(a+b))^(1/2)*EllipticF(1/2*x,2*b/(a+b))/(a+b*cos(x))^(1/2) +r0125:= 2*((a+b*cos(x))/(a+b))^(1/2)*_ + EllipticF(1/2*x,2*b/(a+b))/(a+b*cos(x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -2569,6 +2309,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Polynomial Fraction Integer @@ -2576,61 +2317,43 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 131 --S 132 of 504 ---Ra0125:= integrate(t0125,x) +a0125:= integrate(t0125,x) --R --R ---R x ---R ++ 1 ---R (118) | ---------------- d%H ---R ++ +-------------+ ---R \|b cos(%H) + a +--R x +--R ++ 1 +--R (92) | ---------------- d%H +--R ++ +-------------+ +--R \|b cos(%H) + a --R Type: Union(Expression Integer,...) ---R --E 132 --S 133 of 504 ---Rm0125:= a0125-r0125 ---R ---R ---R x ---R ++ 1 ---R (119) | ---------------- d%H - r0125 ---R ++ +-------------+ ---R \|b cos(%H) + a ---R Type: Expression Integer ---R +--m0125:= a0125-r0125 --E 133 --S 134 of 504 ---Rd0125:= D(m0125,x) ---R ---R ---R 1 ---R (120) --------------- ---R +------------+ ---R \|b cos(x) + a ---R Type: Expression Integer ---R +--d0125:= D(m0125,x) --E 134 --S 135 of 504 ---Rt0126:= 1/(a+b*cos(x))^(3/2) +t0126:= 1/(a+b*cos(x))^(3/2) --R --R ---R 1 ---R (121) ----------------------------- ---R +------------+ ---R (b cos(x) + a)\|b cos(x) + a +--R 1 +--R (93) ----------------------------- +--R +------------+ +--R (b cos(x) + a)\|b cos(x) + a --R Type: Expression Integer ---R --E 135 --S 136 of 504 ---Rr0126:= 2*(a+b*cos(x))^(1/2)*EllipticE(1/2*x,2*b/(a+b))/(a^2-b^2)/((a+b*cos(x))/(a+b))^(1/2)-2*b*sin(x)/(a^2-b^2)/(a+b*cos(x))^(1/2) +r0126:= 2*(a+b*cos(x))^(1/2)*_ + EllipticE(1/2*x,2*b/(a+b))/(a^2-b^2)/((a+b*cos(x))/(a+b))^(1/2)-_ + 2*b*sin(x)/(a^2-b^2)/(a+b*cos(x))^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -2638,6 +2361,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -2645,61 +2369,46 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 136 --S 137 of 504 ---Ra0126:= integrate(t0126,x) +a0126:= integrate(t0126,x) --R --R ---R x ---R ++ 1 ---R (122) | ------------------------------- d%H ---R ++ +-------------+ ---R (b cos(%H) + a)\|b cos(%H) + a +--R x +--R ++ 1 +--R (94) | ------------------------------- d%H +--R ++ +-------------+ +--R (b cos(%H) + a)\|b cos(%H) + a --R Type: Union(Expression Integer,...) ---R --E 137 --S 138 of 504 ---Rm0126:= a0126-r0126 ---R ---R ---R x ---R ++ 1 ---R (123) | ------------------------------- d%H - r0126 ---R ++ +-------------+ ---R (b cos(%H) + a)\|b cos(%H) + a ---R Type: Expression Integer ---R +--m0126:= a0126-r0126 --E 138 --S 139 of 504 ---Rd0126:= D(m0126,x) ---R ---R ---R 1 ---R (124) ----------------------------- ---R +------------+ ---R (b cos(x) + a)\|b cos(x) + a ---R Type: Expression Integer ---R +--d0126:= D(m0126,x) --E 139 --S 140 of 504 ---Rt0127:= 1/(a+b*cos(x))^(5/2) +t0127:= 1/(a+b*cos(x))^(5/2) --R --R ---R 1 ---R (125) --------------------------------------------- ---R 2 2 2 +------------+ ---R (b cos(x) + 2a b cos(x) + a )\|b cos(x) + a +--R 1 +--R (95) --------------------------------------------- +--R 2 2 2 +------------+ +--R (b cos(x) + 2a b cos(x) + a )\|b cos(x) + a --R Type: Expression Integer ---R --E 140 --S 141 of 504 ---Rr0127:= 8/3*a*(a+b*cos(x))^(1/2)*EllipticE(1/2*x,2*b/(a+b))/(a^2-b^2)^2/((a+b*cos(x))/(a+b))^(1/2)-2/3*((a+b*cos(x))/(a+b))^(1/2)*EllipticF(1/2*x,2*b/(a+b))/(a^2-b^2)/(a+b*cos(x))^(1/2)-2/3*b*sin(x)/(a^2-b^2)/(a+b*cos(x))^(3/2)-8/3*a*b*sin(x)/(a^2-b^2)^2/(a+b*cos(x))^(1/2) +r0127:= 8/3*a*(a+b*cos(x))^(1/2)*EllipticE(1/2*x,2*b/(a+b))/_ + (a^2-b^2)^2/((a+b*cos(x))/(a+b))^(1/2)-_ + 2/3*((a+b*cos(x))/(a+b))^(1/2)*EllipticF(1/2*x,2*b/(a+b))/_ + (a^2-b^2)/(a+b*cos(x))^(1/2)-2/3*b*sin(x)/_ + (a^2-b^2)/(a+b*cos(x))^(3/2)-8/3*a*b*sin(x)/(a^2-b^2)^2/_ + (a+b*cos(x))^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -2707,6 +2416,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -2714,237 +2424,203 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 141 --S 142 of 504 ---Ra0127:= integrate(t0127,x) +a0127:= integrate(t0127,x) --R --R ---R x ---R ++ 1 ---R (126) | ------------------------------------------------ d%H ---R ++ 2 2 2 +-------------+ ---R (b cos(%H) + 2a b cos(%H) + a )\|b cos(%H) + a +--R x +--R ++ 1 +--R (96) | ------------------------------------------------ d%H +--R ++ 2 2 2 +-------------+ +--R (b cos(%H) + 2a b cos(%H) + a )\|b cos(%H) + a --R Type: Union(Expression Integer,...) ---R --E 142 --S 143 of 504 ---Rm0127:= a0127-r0127 ---R ---R ---R x ---R ++ 1 ---R (127) | ------------------------------------------------ d%H - r0127 ---R ++ 2 2 2 +-------------+ ---R (b cos(%H) + 2a b cos(%H) + a )\|b cos(%H) + a ---R Type: Expression Integer ---R +--m0127:= a0127-r0127 --E 143 --S 144 of 504 ---Rd0127:= D(m0127,x) ---R ---R ---R 1 ---R (128) --------------------------------------------- ---R 2 2 2 +------------+ ---R (b cos(x) + 2a b cos(x) + a )\|b cos(x) + a ---R Type: Expression Integer ---R +--d0127:= D(m0127,x) --E 144 --S 145 of 504 ---Rt0128:= (a+a*cos(c+d*x))^(1/2) +t0128:= (a+a*cos(c+d*x))^(1/2) --R --R ---R +------------------+ ---R (129) \|a cos(d x + c) + a +--R +------------------+ +--R (97) \|a cos(d x + c) + a --R Type: Expression Integer ---R --E 145 --S 146 of 504 ---Rr0128:= 2*a*sin(c+d*x)/d/(a+a*cos(c+d*x))^(1/2) +r0128:= 2*a*sin(c+d*x)/d/(a+a*cos(c+d*x))^(1/2) --R --R ---R 2a sin(d x + c) ---R (130) ---------------------- ---R +------------------+ ---R d\|a cos(d x + c) + a +--R 2a sin(d x + c) +--R (98) ---------------------- +--R +------------------+ +--R d\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 146 --S 147 of 504 ---Ra0128:= integrate(t0128,x) +a0128:= integrate(t0128,x) --R --R ---R +------------------+ ---R 2sin(d x + c)\|a cos(d x + c) + a ---R (131) ---------------------------------- ---R d cos(d x + c) + d +--R +------------------+ +--R 2sin(d x + c)\|a cos(d x + c) + a +--R (99) ---------------------------------- +--R d cos(d x + c) + d --R Type: Union(Expression Integer,...) ---R --E 147 --S 148 of 504 ---Rm0128:= a0128-r0128 +m0128:= a0128-r0128 --R --R ---R (132) 0 +--R (100) 0 --R Type: Expression Integer ---R --E 148 --S 149 of 504 ---Rd0128:= D(m0128,x) +d0128:= D(m0128,x) --R --R ---R (133) 0 +--R (101) 0 --R Type: Expression Integer ---R --E 149 --S 150 of 504 ---Rt0129:= (a+a*cos(c+d*x))^(3/2) +t0129:= (a+a*cos(c+d*x))^(3/2) --R --R --R +------------------+ ---R (134) (a cos(d x + c) + a)\|a cos(d x + c) + a +--R (102) (a cos(d x + c) + a)\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 150 --S 151 of 504 ---Rr0129:= 2/3*a^2*sin(c+d*x)*(5+cos(c+d*x))/(a*(1+cos(c+d*x)))^(1/2)/d +r0129:= 2/3*a^2*sin(c+d*x)*(5+cos(c+d*x))/(a*(1+cos(c+d*x)))^(1/2)/d --R --R --R 2 2 --R (2a cos(d x + c) + 10a )sin(d x + c) ---R (135) ------------------------------------ +--R (103) ------------------------------------ --R +------------------+ --R 3d\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 151 --S 152 of 504 ---Ra0129:= integrate(t0129,x) +a0129:= integrate(t0129,x) --R --R --R +------------------+ --R (2a cos(d x + c) + 10a)sin(d x + c)\|a cos(d x + c) + a ---R (136) -------------------------------------------------------- +--R (104) -------------------------------------------------------- --R 3d cos(d x + c) + 3d --R Type: Union(Expression Integer,...) ---R --E 152 --S 153 of 504 ---Rm0129:= a0129-r0129 +m0129:= a0129-r0129 --R --R ---R (137) 0 +--R (105) 0 --R Type: Expression Integer ---R --E 153 --S 154 of 504 ---Rd0129:= D(m0129,x) +d0129:= D(m0129,x) --R --R ---R (138) 0 +--R (106) 0 --R Type: Expression Integer ---R --E 154 --S 155 of 504 ---Rt0130:= (a+a*cos(c+d*x))^(5/2) +t0130:= (a+a*cos(c+d*x))^(5/2) --R --R --R 2 2 2 2 +------------------+ ---R (139) (a cos(d x + c) + 2a cos(d x + c) + a )\|a cos(d x + c) + a +--R (107) (a cos(d x + c) + 2a cos(d x + c) + a )\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 155 --S 156 of 504 ---Rr0130:= 2/15*a^3*sin(c+d*x)*(43+14*cos(c+d*x)+3*cos(c+d*x)^2)/(a*(1+cos(c+d*x)))^(1/2)/d +r0130:= 2/15*a^3*sin(c+d*x)*(43+14*cos(c+d*x)+_ + 3*cos(c+d*x)^2)/(a*(1+cos(c+d*x)))^(1/2)/d --R --R --R 3 2 3 3 --R (6a cos(d x + c) + 28a cos(d x + c) + 86a )sin(d x + c) ---R (140) -------------------------------------------------------- +--R (108) -------------------------------------------------------- --R +------------------+ --R 15d\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 156 --S 157 of 504 ---Ra0130:= integrate(t0130,x) +a0130:= integrate(t0130,x) --R --R ---R (141) +--R (109) --R 2 2 2 2 +------------------+ --R (6a cos(d x + c) + 28a cos(d x + c) + 86a )sin(d x + c)\|a cos(d x + c) + a --R ----------------------------------------------------------------------------- --R 15d cos(d x + c) + 15d --R Type: Union(Expression Integer,...) ---R --E 157 --S 158 of 504 ---Rm0130:= a0130-r0130 +m0130:= a0130-r0130 --R --R ---R (142) 0 +--R (110) 0 --R Type: Expression Integer ---R --E 158 --S 159 of 504 ---Rd0130:= D(m0130,x) +d0130:= D(m0130,x) --R --R ---R (143) 0 +--R (111) 0 --R Type: Expression Integer ---R --E 159 --S 160 of 504 ---Rt0131:= 1/(a+a*cos(c+d*x))^(1/2) +t0131:= 1/(a+a*cos(c+d*x))^(1/2) --R --R --R 1 ---R (144) --------------------- +--R (112) --------------------- --R +------------------+ --R \|a cos(d x + c) + a --R Type: Expression Integer ---R --E 160 --S 161 of 504 ---Rr0131:= 2*atanh(sin(1/2*c+1/2*d*x))*cos(1/2*c+1/2*d*x)/d/(a+a*cos(c+d*x))^(1/2) +r0131:= 2*atanh(sin(1/2*c+1/2*d*x))*cos(1/2*c+1/2*d*x)/d/_ + (a+a*cos(c+d*x))^(1/2) --R --R --R d x + c d x + c --R 2cos(-------)atanh(sin(-------)) --R 2 2 ---R (145) -------------------------------- +--R (113) -------------------------------- --R +------------------+ --R d\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 161 --S 162 of 504 ---Ra0131:= integrate(t0131,x) +a0131:= integrate(t0131,x) --R --R ---R (146) +--R (114) --R [ --R +-+ --R |2 @@ -2984,14 +2660,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2d --R ] --R Type: Union(List Expression Integer,...) ---R --E 162 --S 163 of 504 ---Rm0131a:= a0131.1-r0131 +m0131a:= a0131.1-r0131 --R --R ---R (147) +--R (115) --R +-+ --R |2 +------------------+ --R |- \|a cos(d x + c) + a @@ -3015,14 +2690,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +------------------+ --R 2d\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 163 --S 164 of 504 ---Rd0131a:= D(m0131a,x) +d0131a:= D(m0131a,x) --R --R ---R (148) +--R (116) --R d x + c d x + c 2 d x + c 2 --R (2cos(-------)sin(-------) - 2cos(-------))sin(d x + c) --R 2 2 2 @@ -3130,14 +2804,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R sin(d x + c) |- --R \|a --R Type: Expression Integer ---R --E 164 --S 165 of 504 ---Rm0131b:= a0131.2-r0131 +m0131b:= a0131.2-r0131 --R --R ---R (149) +--R (117) --R +-+ --R |2 +------------------+ --R |- \|a cos(d x + c) + a @@ -3161,14 +2834,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +------------------+ --R 2d\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 165 --S 166 of 504 ---Rd0131b:= D(m0131b,x) +d0131b:= D(m0131b,x) --R --R ---R (150) +--R (118) --R d x + c d x + c d x + c 2 --R (- 4cos(-------)cos(d x + c) + 12cos(-------))sin(-------) --R 2 2 2 @@ -3346,26 +3018,26 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R sin(d x + c) |- --R \|a --R Type: Expression Integer ---R --E 166 --S 167 of 504 ---Rt0132:= 1/(a+a*cos(c+d*x))^(3/2) +t0132:= 1/(a+a*cos(c+d*x))^(3/2) --R --R --R 1 ---R (151) ----------------------------------------- +--R (119) ----------------------------------------- --R +------------------+ --R (a cos(d x + c) + a)\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 167 --S 168 of 504 ---Rr0132:= 1/2*atanh(sin(1/2*c+1/2*d*x))*cos(1/2*c+1/2*d*x)/a/d/(a+a*cos(c+d*x))^(1/2)+1/2*sin(c+d*x)/d/(a+a*cos(c+d*x))^(3/2) +r0132:= 1/2*atanh(sin(1/2*c+1/2*d*x))*_ + cos(1/2*c+1/2*d*x)/a/d/(a+a*cos(c+d*x))^(1/2)+_ + 1/2*sin(c+d*x)/d/(a+a*cos(c+d*x))^(3/2) --R --R ---R (152) +--R (120) --R d x + c d x + c d x + c --R (cos(-------)cos(d x + c) + cos(-------))atanh(sin(-------)) + sin(d x + c) --R 2 2 2 @@ -3373,14 +3045,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +------------------+ --R (2a d cos(d x + c) + 2a d)\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 168 --S 169 of 504 ---Ra0132:= integrate(t0132,x) +a0132:= integrate(t0132,x) --R --R ---R (153) +--R (121) --R [ --R 2 +--+ --R (cos(d x + c) + 2cos(d x + c) + 1)\|2a @@ -3416,14 +3087,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4a d cos(d x + c) + 8a d cos(d x + c) + 4a d --R ] --R Type: Union(List Expression Integer,...) ---R --E 169 --S 170 of 504 ---Rm0132a:= a0132.1-r0132 +m0132a:= a0132.1-r0132 --R --R ---R (154) +--R (122) --R +--+ +------------------+ --R \|2a \|a cos(d x + c) + a --R * @@ -3443,14 +3113,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 +------------------+ --R 8a d\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 170 --S 171 of 504 ---Rd0132a:= D(m0132a,x) +d0132a:= D(m0132a,x) --R --R ---R (155) +--R (123) --R d x + c d x + c 2 d x + c 2 --R (2cos(-------)sin(-------) - 2cos(-------))sin(d x + c) --R 2 2 2 @@ -3569,14 +3238,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +--+ --R sin(d x + c)\|2a --R Type: Expression Integer ---R --E 171 --S 172 of 504 ---Rm0132b:= a0132.2-r0132 +m0132b:= a0132.2-r0132 --R --R ---R (156) +--R (124) --R - --R +----+ +------------------+ --R \|- 2a \|a cos(d x + c) + a @@ -3593,14 +3261,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 +------------------+ --R 4a d\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 172 --S 173 of 504 ---Rd0132b:= D(m0132b,x) +d0132b:= D(m0132b,x) --R --R ---R (157) +--R (125) --R d x + c d x + c 2 d x + c 3 --R (- cos(-------)sin(-------) + cos(-------))sin(d x + c) --R 2 2 2 @@ -3678,26 +3345,26 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +------------------+ --R \|a cos(d x + c) + a --R Type: Expression Integer ---R --E 173 --S 174 of 504 ---Rt0133:= 1/(a+a*cos(c+d*x))^(5/2) +t0133:= 1/(a+a*cos(c+d*x))^(5/2) --R --R --R 1 ---R (158) ------------------------------------------------------------- +--R (126) ------------------------------------------------------------- --R 2 2 2 2 +------------------+ --R (a cos(d x + c) + 2a cos(d x + c) + a )\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 174 --S 175 of 504 ---Rr0133:= 3/16*atanh(sin(1/2*c+1/2*d*x))*cos(1/2*c+1/2*d*x)/a^2/d/(a+a*cos(c+d*x))^(1/2)+1/4*sin(c+d*x)/d/(a+a*cos(c+d*x))^(5/2)+3/16*sin(c+d*x)/a/d/(a+a*cos(c+d*x))^(3/2) +r0133:= 3/16*atanh(sin(1/2*c+1/2*d*x))*cos(1/2*c+1/2*d*x)/a^2/d/_ + (a+a*cos(c+d*x))^(1/2)+1/4*sin(c+d*x)/d/_ + (a+a*cos(c+d*x))^(5/2)+3/16*sin(c+d*x)/a/d/(a+a*cos(c+d*x))^(3/2) --R --R ---R (159) +--R (127) --R d x + c 2 d x + c --R 3cos(-------)cos(d x + c) + 6cos(-------)cos(d x + c) --R 2 2 @@ -3715,14 +3382,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 2 2 +------------------+ --R (16a d cos(d x + c) + 32a d cos(d x + c) + 16a d)\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 175 --S 176 of 504 ---Ra0133:= integrate(t0133,x) +a0133:= integrate(t0133,x) --R --R ---R (160) +--R (128) --R [ --R 3 2 +--+ --R (3cos(d x + c) + 9cos(d x + c) + 9cos(d x + c) + 3)\|2a @@ -3758,14 +3424,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 32a d cos(d x + c) + 96a d cos(d x + c) + 96a d cos(d x + c) + 32a d --R ] --R Type: Union(List Expression Integer,...) ---R --E 176 --S 177 of 504 ---Rm0133a:= a0133.1-r0133 +m0133a:= a0133.1-r0133 --R --R ---R (161) +--R (129) --R +--+ +------------------+ --R 3\|2a \|a cos(d x + c) + a --R * @@ -3785,14 +3450,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 3 +------------------+ --R 64a d\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 177 --S 178 of 504 ---Rd0133a:= D(m0133a,x) +d0133a:= D(m0133a,x) --R --R ---R (162) +--R (130) --R d x + c d x + c 2 d x + c 2 --R (6cos(-------)sin(-------) - 6cos(-------))sin(d x + c) --R 2 2 2 @@ -3911,14 +3575,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +--+ --R sin(d x + c)\|2a --R Type: Expression Integer ---R --E 178 --S 179 of 504 ---Rm0133b:= a0133.2-r0133 +m0133b:= a0133.2-r0133 --R --R ---R (163) +--R (131) --R - --R +----+ +------------------+ --R 3\|- 2a \|a cos(d x + c) + a @@ -3935,14 +3598,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 3 +------------------+ --R 32a d\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 179 --S 180 of 504 ---Rd0133b:= D(m0133b,x) +d0133b:= D(m0133b,x) --R --R ---R (164) +--R (132) --R d x + c d x + c 2 d x + c 3 --R (- 3cos(-------)sin(-------) + 3cos(-------))sin(d x + c) --R 2 2 2 @@ -4020,40 +3682,38 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +------------------+ --R \|a cos(d x + c) + a --R Type: Expression Integer ---R --E 180 --S 181 of 504 ---Rt0134:= 1/(a-a*cos(c+d*x))^(3/2) +t0134:= 1/(a-a*cos(c+d*x))^(3/2) --R --R --R 1 ---R (165) - ------------------------------------------- +--R (133) - ------------------------------------------- --R +--------------------+ --R (a cos(d x + c) - a)\|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 181 --S 182 of 504 ---Rr0134:= -1/2*atanh(cos(1/2*c+1/2*d*x))*sin(1/2*c+1/2*d*x)/a/d/(a-a*cos(c+d*x))^(1/2)-1/2*sin(c+d*x)/d/(a-a*cos(c+d*x))^(3/2) +r0134:= -1/2*atanh(cos(1/2*c+1/2*d*x))*sin(1/2*c+1/2*d*x)/a/d/_ + (a-a*cos(c+d*x))^(1/2)-1/2*sin(c+d*x)/d/(a-a*cos(c+d*x))^(3/2) --R --R --R d x + c d x + c --R (- cos(d x + c) + 1)sin(-------)atanh(cos(-------)) + sin(d x + c) --R 2 2 ---R (166) ------------------------------------------------------------------ +--R (134) ------------------------------------------------------------------ --R +--------------------+ --R (2a d cos(d x + c) - 2a d)\|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 182 --S 183 of 504 ---Ra0134:= integrate(t0134,x) +a0134:= integrate(t0134,x) --R --R ---R (167) +--R (135) --R [ --R +--+ --R (cos(d x + c) - 1)\|2a @@ -4082,14 +3742,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4a d cos(d x + c) - 4a d --R ] --R Type: Union(List Expression Integer,...) ---R --E 183 --S 184 of 504 ---Rm0134a:= a0134.1-r0134 +m0134a:= a0134.1-r0134 --R --R ---R (168) +--R (136) --R +--+ +--------------------+ --R (cos(d x + c) - 1)\|2a \|- a cos(d x + c) + a --R * @@ -4108,14 +3767,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 +--------------------+ --R (8a d cos(d x + c) - 8a d)\|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 184 --S 185 of 504 ---Rd0134a:= D(m0134a,x) +d0134a:= D(m0134a,x) --R --R ---R (169) +--R (137) --R d x + c 2 d x + c 2 --R ((- 4cos(-------) + 4)cos(d x + c) - 12cos(-------) + 12) --R 2 2 @@ -4296,14 +3954,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +--------------------+ --R \|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 185 --S 186 of 504 ---Rm0134b:= a0134.2-r0134 +m0134b:= a0134.2-r0134 --R --R ---R (170) +--R (138) --R +----+ +--------------------+ --R (cos(d x + c) - 1)\|- 2a \|- a cos(d x + c) + a --R * @@ -4322,14 +3979,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 +--------------------+ --R (4a d cos(d x + c) - 4a d)\|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 186 --S 187 of 504 ---Rd0134b:= D(m0134b,x) +d0134b:= D(m0134b,x) --R --R ---R (171) +--R (139) --R d x + c 2 d x + c 2 --R ((cos(-------) - 1)cos(d x + c) - cos(-------) + 1) --R 2 2 @@ -4384,26 +4040,26 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +--------------------+ +------------------+ --R \|- a cos(d x + c) + a \|a cos(d x + c) + a --R Type: Expression Integer ---R --E 187 --S 188 of 504 ---Rt0135:= 1/(a-a*cos(c+d*x))^(5/2) +t0135:= 1/(a-a*cos(c+d*x))^(5/2) --R --R --R 1 ---R (172) --------------------------------------------------------------- +--R (140) --------------------------------------------------------------- --R 2 2 2 2 +--------------------+ --R (a cos(d x + c) - 2a cos(d x + c) + a )\|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 188 --S 189 of 504 ---Rr0135:= -3/16*atanh(cos(1/2*c+1/2*d*x))*sin(1/2*c+1/2*d*x)/a^2/d/(a-a*cos(c+d*x))^(1/2)-1/4*sin(c+d*x)/d/(a-a*cos(c+d*x))^(5/2)-3/16*sin(c+d*x)/a/d/(a-a*cos(c+d*x))^(3/2) +r0135:= -3/16*atanh(cos(1/2*c+1/2*d*x))*sin(1/2*c+1/2*d*x)/a^2/d/_ + (a-a*cos(c+d*x))^(1/2)-1/4*sin(c+d*x)/d/_ + (a-a*cos(c+d*x))^(5/2)-3/16*sin(c+d*x)/a/d/(a-a*cos(c+d*x))^(3/2) --R --R ---R (173) +--R (141) --R 2 d x + c d x + c --R (- 3cos(d x + c) + 6cos(d x + c) - 3)sin(-------)atanh(cos(-------)) --R 2 2 @@ -4413,14 +4069,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 2 2 +--------------------+ --R (16a d cos(d x + c) - 32a d cos(d x + c) + 16a d)\|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 189 --S 190 of 504 ---Ra0135:= integrate(t0135,x) +a0135:= integrate(t0135,x) --R --R ---R (174) +--R (142) --R [ --R 2 +--+ --R (3cos(d x + c) - 6cos(d x + c) + 3)\|2a @@ -4452,14 +4107,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 32a d cos(d x + c) - 64a d cos(d x + c) + 32a d --R ] --R Type: Union(List Expression Integer,...) ---R --E 190 --S 191 of 504 ---Rm0135a:= a0135.1-r0135 +m0135a:= a0135.1-r0135 --R --R ---R (175) +--R (143) --R 2 +--+ +--------------------+ --R (3cos(d x + c) - 6cos(d x + c) + 3)\|2a \|- a cos(d x + c) + a --R * @@ -4484,14 +4138,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 3 2 3 3 +--------------------+ --R (64a d cos(d x + c) - 128a d cos(d x + c) + 64a d)\|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 191 --S 192 of 504 ---Rd0135a:= D(m0135a,x) +d0135a:= D(m0135a,x) --R --R ---R (176) +--R (144) --R d x + c 2 d x + c 2 --R ((32cos(-------) - 32)cos(d x + c) + 96cos(-------) - 96) --R 2 2 @@ -4713,14 +4366,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +--------------------+ --R \|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 192 --S 193 of 504 ---Rm0135b:= a0135.2-r0135 +m0135b:= a0135.2-r0135 --R --R ---R (177) +--R (145) --R 2 +----+ +--------------------+ --R (3cos(d x + c) - 6cos(d x + c) + 3)\|- 2a \|- a cos(d x + c) + a --R * @@ -4741,14 +4393,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 3 2 3 3 +--------------------+ --R (32a d cos(d x + c) - 64a d cos(d x + c) + 32a d)\|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 193 --S 194 of 504 ---Rd0135b:= D(m0135b,x) +d0135b:= D(m0135b,x) --R --R ---R (178) +--R (146) --R d x + c 2 2 --R (3cos(-------) - 3)cos(d x + c) --R 2 @@ -4826,21 +4477,19 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +--------------------+ +------------------+ --R \|- a cos(d x + c) + a \|a cos(d x + c) + a --R Type: Expression Integer ---R --E 194 --S 195 of 504 ---Rt0136:= (b*cos(c+d*x))^(1/2) +t0136:= (b*cos(c+d*x))^(1/2) --R --R --R +--------------+ ---R (179) \|b cos(d x + c) +--R (147) \|b cos(d x + c) --R Type: Expression Integer ---R --E 195 --S 196 of 504 ---Rr0136:= 2*(b*cos(c+d*x))^(1/2)*EllipticE(1/2*c+1/2*d*x,2)/d/cos(c+d*x)^(1/2) +r0136:= 2*(b*cos(c+d*x))^(1/2)*EllipticE(1/2*c+1/2*d*x,2)/d/cos(c+d*x)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -4848,6 +4497,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -4855,55 +4505,39 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 196 --S 197 of 504 ---Ra0136:= integrate(t0136,x) +a0136:= integrate(t0136,x) --R --R --R x --R ++ +---------------+ ---R (180) | \|b cos(%H d + c) d%H +--R (148) | \|b cos(%H d + c) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 197 --S 198 of 504 ---Rm0136:= a0136-r0136 ---R ---R ---R x ---R ++ +---------------+ ---R (181) | \|b cos(%H d + c) d%H - r0136 ---R ++ ---R Type: Expression Integer ---R +--m0136:= a0136-r0136 --E 198 --S 199 of 504 ---Rd0136:= D(m0136,x) ---R ---R ---R +--------------+ ---R (182) \|b cos(d x + c) ---R Type: Expression Integer ---R +--d0136:= D(m0136,x) --E 199 --S 200 of 504 ---Rt0137:= (b*cos(c+d*x))^(3/2) +t0137:= (b*cos(c+d*x))^(3/2) --R --R --R +--------------+ ---R (183) b cos(d x + c)\|b cos(d x + c) +--R (149) b cos(d x + c)\|b cos(d x + c) --R Type: Expression Integer ---R --E 200 --S 201 of 504 ---Rr0137:= 2/3*b^2*(cos(c+d*x)^(1/2)*EllipticF(1/2*c+1/2*d*x,2)+cos(c+d*x)*sin(c+d*x))/d/(b*cos(c+d*x))^(1/2) +r0137:= 2/3*b^2*(cos(c+d*x)^(1/2)*EllipticF(1/2*c+1/2*d*x,2)+_ + cos(c+d*x)*sin(c+d*x))/d/(b*cos(c+d*x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -4911,6 +4545,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Polynomial Fraction Integer @@ -4918,55 +4553,39 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 201 --S 202 of 504 ---Ra0137:= integrate(t0137,x) +a0137:= integrate(t0137,x) --R --R --R x --R ++ +---------------+ ---R (184) | b cos(%H d + c)\|b cos(%H d + c) d%H +--R (150) | b cos(%H d + c)\|b cos(%H d + c) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 202 --S 203 of 504 ---Rm0137:= a0137-r0137 ---R ---R ---R x ---R ++ +---------------+ ---R (185) | b cos(%H d + c)\|b cos(%H d + c) d%H - r0137 ---R ++ ---R Type: Expression Integer ---R +--m0137:= a0137-r0137 --E 203 --S 204 of 504 ---Rd0137:= D(m0137,x) ---R ---R ---R +--------------+ ---R (186) b cos(d x + c)\|b cos(d x + c) ---R Type: Expression Integer ---R +--d0137:= D(m0137,x) --E 204 --S 205 of 504 ---Rt0138:= (b*cos(c+d*x))^(5/2) +t0138:= (b*cos(c+d*x))^(5/2) --R --R --R 2 2 +--------------+ ---R (187) b cos(d x + c) \|b cos(d x + c) +--R (151) b cos(d x + c) \|b cos(d x + c) --R Type: Expression Integer ---R --E 205 --S 206 of 504 ---Rr0138:= 2/5*b^2*(b*cos(c+d*x))^(1/2)*(3*EllipticE(1/2*c+1/2*d*x,2)+cos(c+d*x)^(3/2)*sin(c+d*x))/d/cos(c+d*x)^(1/2) +r0138:= 2/5*b^2*(b*cos(c+d*x))^(1/2)*(3*EllipticE(1/2*c+1/2*d*x,2)+_ + cos(c+d*x)^(3/2)*sin(c+d*x))/d/cos(c+d*x)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -4974,6 +4593,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -4981,57 +4601,40 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 206 --S 207 of 504 ---Ra0138:= integrate(t0138,x) +a0138:= integrate(t0138,x) --R --R --R x --R ++ 2 2 +---------------+ ---R (188) | b cos(%H d + c) \|b cos(%H d + c) d%H +--R (152) | b cos(%H d + c) \|b cos(%H d + c) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 207 --S 208 of 504 ---Rm0138:= a0138-r0138 ---R ---R ---R x ---R ++ 2 2 +---------------+ ---R (189) | b cos(%H d + c) \|b cos(%H d + c) d%H - r0138 ---R ++ ---R Type: Expression Integer ---R +--m0138:= a0138-r0138 --E 208 --S 209 of 504 ---Rd0138:= D(m0138,x) ---R ---R ---R 2 2 +--------------+ ---R (190) b cos(d x + c) \|b cos(d x + c) ---R Type: Expression Integer ---R +--d0138:= D(m0138,x) --E 209 --S 210 of 504 ---Rt0139:= 1/(b*cos(c+d*x))^(1/2) +t0139:= 1/(b*cos(c+d*x))^(1/2) --R --R --R 1 ---R (191) ----------------- +--R (153) ----------------- --R +--------------+ --R \|b cos(d x + c) --R Type: Expression Integer ---R --E 210 --S 211 of 504 ---Rr0139:= 2*cos(c+d*x)^(1/2)*EllipticF(1/2*c+1/2*d*x,2)/d/(b*cos(c+d*x))^(1/2) +r0139:= 2*cos(c+d*x)^(1/2)*EllipticF(1/2*c+1/2*d*x,2)/d/(b*cos(c+d*x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -5039,6 +4642,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Polynomial Fraction Integer @@ -5046,61 +4650,42 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 211 --S 212 of 504 ---Ra0139:= integrate(t0139,x) +a0139:= integrate(t0139,x) --R --R --R x --R ++ 1 ---R (192) | ------------------ d%H +--R (154) | ------------------ d%H --R ++ +---------------+ --R \|b cos(%H d + c) --R Type: Union(Expression Integer,...) ---R --E 212 --S 213 of 504 ---Rm0139:= a0139-r0139 ---R ---R ---R x ---R ++ 1 ---R (193) | ------------------ d%H - r0139 ---R ++ +---------------+ ---R \|b cos(%H d + c) ---R Type: Expression Integer ---R +--m0139:= a0139-r0139 --E 213 --S 214 of 504 ---Rd0139:= D(m0139,x) ---R ---R ---R 1 ---R (194) ----------------- ---R +--------------+ ---R \|b cos(d x + c) ---R Type: Expression Integer ---R +--d0139:= D(m0139,x) --E 214 --S 215 of 504 ---Rt0140:= 1/(b*cos(c+d*x))^(3/2) +t0140:= 1/(b*cos(c+d*x))^(3/2) --R --R --R 1 ---R (195) ------------------------------- +--R (155) ------------------------------- --R +--------------+ --R b cos(d x + c)\|b cos(d x + c) --R Type: Expression Integer ---R --E 215 --S 216 of 504 ---Rr0140:= -2/b*(cos(c+d*x)*EllipticE(1/2*c+1/2*d*x,2)-sin(c+d*x)*cos(c+d*x)^(1/2))/d/cos(c+d*x)^(1/2)/(b*cos(c+d*x))^(1/2) +r0140:= -2/b*(cos(c+d*x)*EllipticE(1/2*c+1/2*d*x,2)-_ + sin(c+d*x)*cos(c+d*x)^(1/2))/d/cos(c+d*x)^(1/2)/(b*cos(c+d*x))^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -5108,6 +4693,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -5115,61 +4701,42 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 216 --S 217 of 504 ---Ra0140:= integrate(t0140,x) +a0140:= integrate(t0140,x) --R --R --R x --R ++ 1 ---R (196) | --------------------------------- d%H +--R (156) | --------------------------------- d%H --R ++ +---------------+ --R b cos(%H d + c)\|b cos(%H d + c) --R Type: Union(Expression Integer,...) ---R --E 217 --S 218 of 504 ---Rm0140:= a0140-r0140 ---R ---R ---R x ---R ++ 1 ---R (197) | --------------------------------- d%H - r0140 ---R ++ +---------------+ ---R b cos(%H d + c)\|b cos(%H d + c) ---R Type: Expression Integer ---R +--m0140:= a0140-r0140 --E 218 --S 219 of 504 ---Rd0140:= D(m0140,x) ---R ---R ---R 1 ---R (198) ------------------------------- ---R +--------------+ ---R b cos(d x + c)\|b cos(d x + c) ---R Type: Expression Integer ---R +--d0140:= D(m0140,x) --E 219 --S 220 of 504 ---Rt0141:= 1/(b*cos(c+d*x))^(5/2) +t0141:= 1/(b*cos(c+d*x))^(5/2) --R --R --R 1 ---R (199) -------------------------------- +--R (157) -------------------------------- --R 2 2 +--------------+ --R b cos(d x + c) \|b cos(d x + c) --R Type: Expression Integer ---R --E 220 --S 221 of 504 ---Rr0141:= 2/3/b^2*(cos(c+d*x)^(3/2)*EllipticF(1/2*c+1/2*d*x,2)+sin(c+d*x))/d/cos(c+d*x)/(b*cos(c+d*x))^(1/2) +r0141:= 2/3/b^2*(cos(c+d*x)^(3/2)*EllipticF(1/2*c+1/2*d*x,2)+_ + sin(c+d*x))/d/cos(c+d*x)/(b*cos(c+d*x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -5177,6 +4744,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Polynomial Fraction Integer @@ -5184,61 +4752,46 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 221 --S 222 of 504 ---Ra0141:= integrate(t0141,x) +a0141:= integrate(t0141,x) --R --R --R x --R ++ 1 ---R (200) | ---------------------------------- d%H +--R (158) | ---------------------------------- d%H --R ++ 2 2 +---------------+ --R b cos(%H d + c) \|b cos(%H d + c) --R Type: Union(Expression Integer,...) ---R --E 222 --S 223 of 504 ---Rm0141:= a0141-r0141 ---R ---R ---R x ---R ++ 1 ---R (201) | ---------------------------------- d%H - r0141 ---R ++ 2 2 +---------------+ ---R b cos(%H d + c) \|b cos(%H d + c) ---R Type: Expression Integer ---R +--m0141:= a0141-r0141 --E 223 --S 224 of 504 ---Rd0141:= D(m0141,x) ---R ---R ---R 1 ---R (202) -------------------------------- ---R 2 2 +--------------+ ---R b cos(d x + c) \|b cos(d x + c) ---R Type: Expression Integer ---R +--d0141:= D(m0141,x) --E 224 --S 225 of 504 ---Rt0142:= x^2/(a+b*cos(x)) +t0142:= x^2/(a+b*cos(x)) --R --R --R 2 --R x ---R (203) ------------ +--R (159) ------------ --R b cos(x) + a --R Type: Expression Integer ---R --E 225 --S 226 of 504 ---Rr0142:= -(%i*x^2*log((-a+(a^2-b^2)^(1/2)-b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-%i*x^2*log((a+(a^2-b^2)^(1/2)+b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+2*x*polylog(2,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-2*x*polylog(2,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+2*%i*polylog(3,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-2*%i*polylog(3,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +r0142:= -(%i*x^2*log((-a+(a^2-b^2)^(1/2)-b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-_ + %i*x^2*log((a+(a^2-b^2)^(1/2)+b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+_ + 2*x*polylog(2,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 2*x*polylog(2,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+_ + 2*%i*polylog(3,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 2*%i*polylog(3,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -5246,6 +4799,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -5253,59 +4807,47 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 226 --S 227 of 504 ---Ra0142:= integrate(t0142,x) +a0142:= integrate(t0142,x) --R --R --R x 2 --R ++ %H ---R (204) | ------------- d%H +--R (160) | ------------- d%H --R ++ b cos(%H) + a --R Type: Union(Expression Integer,...) ---R --E 227 --S 228 of 504 ---Rm0142:= a0142-r0142 ---R ---R ---R x 2 ---R ++ %H ---R (205) | ------------- d%H - r0142 ---R ++ b cos(%H) + a ---R Type: Expression Integer ---R +--m0142:= a0142-r0142 --E 228 --S 229 of 504 ---Rd0142:= D(m0142,x) ---R ---R ---R 2 ---R x ---R (206) ------------ ---R b cos(x) + a ---R Type: Expression Integer ---R +--d0142:= D(m0142,x) --E 229 --S 230 of 504 ---Rt0143:= x^3/(a+b*cos(x)) +t0143:= x^3/(a+b*cos(x)) --R --R --R 3 --R x ---R (207) ------------ +--R (161) ------------ --R b cos(x) + a --R Type: Expression Integer ---R --E 230 --S 231 of 504 ---Rr0143:= -(%i*x^3*log((-a+(a^2-b^2)^(1/2)-b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-%i*x^3*log((a+(a^2-b^2)^(1/2)+b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+3*x^2*polylog(2,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-3*x^2*polylog(2,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+6*%i*x*polylog(3,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-6*%i*x*polylog(3,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))-6*polylog(4,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))+6*polylog(4,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +r0143:= -(%i*x^3*log((-a+(a^2-b^2)^(1/2)-b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-_ + %i*x^3*log((a+(a^2-b^2)^(1/2)+b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+_ + 3*x^2*polylog(2,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 3*x^2*polylog(2,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+_ + 6*%i*x*polylog(3,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 6*%i*x*polylog(3,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))-_ + 6*polylog(4,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))+_ + 6*polylog(4,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -5313,6 +4855,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -5320,87 +4863,66 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 231 --S 232 of 504 ---Ra0143:= integrate(t0143,x) +a0143:= integrate(t0143,x) --R --R --R x 3 --R ++ %H ---R (208) | ------------- d%H +--R (162) | ------------- d%H --R ++ b cos(%H) + a --R Type: Union(Expression Integer,...) ---R --E 232 --S 233 of 504 ---Rm0143:= a0143-r0143 ---R ---R ---R x 3 ---R ++ %H ---R (209) | ------------- d%H - r0143 ---R ++ b cos(%H) + a ---R Type: Expression Integer ---R +--m0143:= a0143-r0143 --E 233 --S 234 of 504 ---Rd0143:= D(m0143,x) ---R ---R ---R 3 ---R x ---R (210) ------------ ---R b cos(x) + a ---R Type: Expression Integer ---R +--d0143:= D(m0143,x) --E 234 --S 235 of 504 ---Rt0144:= x/(a-a*cos(x)) +t0144:= x/(a-a*cos(x)) --R --R --R x ---R (211) - ------------ +--R (163) - ------------ --R a cos(x) - a --R Type: Expression Integer ---R --E 235 --S 236 of 504 ---Rr0144:= -x*cot(1/2*x)/a+2*log(sin(1/2*x))/a +r0144:= -x*cot(1/2*x)/a+2*log(sin(1/2*x))/a --R --R --R x x --R 2log(sin(-)) - x cot(-) --R 2 2 ---R (212) ----------------------- +--R (164) ----------------------- --R a --R Type: Expression Integer ---R --E 236 --S 237 of 504 ---Ra0144:= integrate(t0144,x) +a0144:= integrate(t0144,x) --R --R --R sin(x) 2 --R 2sin(x)log(----------) - sin(x)log(----------) - x cos(x) - x --R cos(x) + 1 cos(x) + 1 ---R (213) ------------------------------------------------------------- +--R (165) ------------------------------------------------------------- --R a sin(x) --R Type: Union(Expression Integer,...) ---R --E 237 --S 238 of 504 ---Rm0144:= a0144-r0144 +m0144:= a0144-r0144 --R --R ---R (214) +--R (166) --R sin(x) x 2 --R 2sin(x)log(----------) - 2sin(x)log(sin(-)) - sin(x)log(----------) --R cos(x) + 1 2 cos(x) + 1 @@ -5411,14 +4933,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R a sin(x) --R Type: Expression Integer ---R --E 238 --S 239 of 504 ---Rd0144:= D(m0144,x) +d0144:= D(m0144,x) --R --R ---R (215) +--R (167) --R x 3 --R 2sin(-)sin(x) --R 2 @@ -5442,23 +4963,26 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R (2a cos(x) + 2a)sin(-)sin(x) --R 2 --R Type: Expression Integer ---R --E 239 --S 240 of 504 ---Rt0145:= x/(a+b*cos(x))^2 +t0145:= x/(a+b*cos(x))^2 --R --R --R x ---R (216) ---------------------------- +--R (168) ---------------------------- --R 2 2 2 --R b cos(x) + 2a b cos(x) + a --R Type: Expression Integer ---R --E 240 --S 241 of 504 ---Rr0145:= -%i*a*x*log(1+b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+%i*a*x*log(1+b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-log(a+b*cos(x))/(a^2-b^2)-a*polylog(2,-b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+a*polylog(2,-b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-b*x*sin(x)/(a^2-b^2)/(a+b*cos(x)) +r0145:= -%i*a*x*log(1+b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+_ + %i*a*x*log(1+b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-_ + log(a+b*cos(x))/(a^2-b^2)-_ + a*polylog(2,-b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+_ + a*polylog(2,-b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-_ + b*x*sin(x)/(a^2-b^2)/(a+b*cos(x)) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -5466,6 +4990,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -5473,62 +4998,43 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 241 --S 242 of 504 ---Ra0145:= integrate(t0145,x) +a0145:= integrate(t0145,x) --R --R --R x --R ++ %H ---R (217) | ------------------------------ d%H +--R (169) | ------------------------------ d%H --R ++ 2 2 2 --R b cos(%H) + 2a b cos(%H) + a --R Type: Union(Expression Integer,...) ---R --E 242 --S 243 of 504 ---Rm0145:= a0145-r0145 ---R ---R ---R x ---R ++ %H ---R (218) | ------------------------------ d%H - r0145 ---R ++ 2 2 2 ---R b cos(%H) + 2a b cos(%H) + a ---R Type: Expression Integer ---R +--m0145:= a0145-r0145 --E 243 --S 244 of 504 ---Rd0145:= D(m0145,x) ---R ---R ---R x ---R (219) ---------------------------- ---R 2 2 2 ---R b cos(x) + 2a b cos(x) + a ---R Type: Expression Integer ---R +--d0145:= D(m0145,x) --E 244 --S 245 of 504 ---Rt0146:= x*(a+a*cos(c+d*x))^(1/2) +t0146:= x*(a+a*cos(c+d*x))^(1/2) --R --R --R +------------------+ ---R (220) x\|a cos(d x + c) + a +--R (170) x\|a cos(d x + c) + a --R Type: Expression Integer ---R --E 245 --S 246 of 504 ---Rr0146:= 2*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*(2*cos(1/2*c+1/2*d*x)+d*x*sin(1/2*c+1/2*d*x))/d^2 +r0146:= 2*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*_ + sec(1/2*c+1/2*d*x)*(2*cos(1/2*c+1/2*d*x)+d*x*sin(1/2*c+1/2*d*x))/d^2 --R --R ---R (221) +--R (171) --R +-+ d x + c d x + c +-+ d x + c d x + c --R (2d x\|2 sec(-------)sin(-------) + 4\|2 cos(-------)sec(-------)) --R 2 2 2 2 @@ -5541,96 +5047,43 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 --R d --R Type: Expression Integer ---R --E 246 --S 247 of 504 ---Ra0146:= integrate(t0146,x) +a0146:= integrate(t0146,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 247 --S 248 of 504 ---Rm0146:= a0146-r0146 ---R ---R ---R (222) ---R +-+ d x + c d x + c +-+ d x + c d x + c ---R (- 2d x\|2 sec(-------)sin(-------) - 4\|2 cos(-------)sec(-------)) ---R 2 2 2 2 ---R * ---R +---------------+ ---R | d x + c 2 ---R |a cos(-------) ---R \| 2 ---R + ---R 2 ---R a0146 d ---R / ---R 2 ---R d ---R Type: Expression Integer ---R +--m0146:= a0146-r0146 --E 248 --S 249 of 504 ---Rd0146:= D(m0146,x) ---R ---R ---R (223) ---R +-+ d x + c 2 d x + c d x + c ---R - a d x\|2 cos(-------) sec(-------)sin(-------) ---R 2 2 2 ---R + ---R +-+ d x + c 3 d x + c ---R - 2a\|2 cos(-------) sec(-------) ---R 2 2 ---R * ---R d x + c ---R tan(-------) ---R 2 ---R + ---R +-+ d x + c d x + c d x + c 2 ---R a d x\|2 cos(-------)sec(-------)sin(-------) ---R 2 2 2 ---R + ---R +-+ d x + c 2 d x + c d x + c ---R 2a\|2 cos(-------) sec(-------)sin(-------) ---R 2 2 2 ---R + ---R +-+ d x + c 3 d x + c ---R - a d x\|2 cos(-------) sec(-------) ---R 2 2 ---R / ---R +---------------+ ---R | d x + c 2 ---R d |a cos(-------) ---R \| 2 ---R Type: Expression Integer ---R +--d0146:= D(m0146,x) --E 249 --S 250 of 504 ---Rt0147:= x^2*(a+a*cos(c+d*x))^(1/2) +t0147:= x^2*(a+a*cos(c+d*x))^(1/2) --R --R --R 2 +------------------+ ---R (224) x \|a cos(d x + c) + a +--R (172) x \|a cos(d x + c) + a --R Type: Expression Integer ---R --E 250 --S 251 of 504 ---Rr0147:= 2*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*(4*d*x*cos(1/2*c+1/2*d*x)-(8-d^2*x^2)*sin(1/2*c+1/2*d*x))/d^3 +r0147:= 2*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*_ + (4*d*x*cos(1/2*c+1/2*d*x)-(8-d^2*x^2)*sin(1/2*c+1/2*d*x))/d^3 --R --R ---R (225) +--R (173) --R 2 2 +-+ d x + c d x + c --R (2d x - 16)\|2 sec(-------)sin(-------) --R 2 2 @@ -5647,102 +5100,45 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 3 --R d --R Type: Expression Integer ---R --E 251 --S 252 of 504 ---Ra0147:= integrate(t0147,x) +a0147:= integrate(t0147,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 252 --S 253 of 504 ---Rm0147:= a0147-r0147 ---R ---R ---R (226) ---R 2 2 +-+ d x + c d x + c ---R (- 2d x + 16)\|2 sec(-------)sin(-------) ---R 2 2 ---R + ---R +-+ d x + c d x + c ---R - 8d x\|2 cos(-------)sec(-------) ---R 2 2 ---R * ---R +---------------+ ---R | d x + c 2 ---R |a cos(-------) ---R \| 2 ---R + ---R 3 ---R a0147 d ---R / ---R 3 ---R d ---R Type: Expression Integer ---R +--m0147:= a0147-r0147 --E 253 --S 254 of 504 ---Rd0147:= D(m0147,x) ---R ---R ---R (227) ---R 2 2 +-+ d x + c 2 d x + c d x + c ---R (- a d x + 8a)\|2 cos(-------) sec(-------)sin(-------) ---R 2 2 2 ---R + ---R +-+ d x + c 3 d x + c ---R - 4a d x\|2 cos(-------) sec(-------) ---R 2 2 ---R * ---R d x + c ---R tan(-------) ---R 2 ---R + ---R 2 2 +-+ d x + c d x + c d x + c 2 ---R (a d x - 8a)\|2 cos(-------)sec(-------)sin(-------) ---R 2 2 2 ---R + ---R +-+ d x + c 2 d x + c d x + c ---R 4a d x\|2 cos(-------) sec(-------)sin(-------) ---R 2 2 2 ---R + ---R 2 2 +-+ d x + c 3 d x + c ---R - a d x \|2 cos(-------) sec(-------) ---R 2 2 ---R / ---R +---------------+ ---R 2 | d x + c 2 ---R d |a cos(-------) ---R \| 2 ---R Type: Expression Integer ---R +--d0147:= D(m0147,x) --E 254 --S 255 of 504 ---Rt0148:= (a+a*cos(c+d*x))^(1/2)/x +t0148:= (a+a*cos(c+d*x))^(1/2)/x --R --R --R +------------------+ --R \|a cos(d x + c) + a ---R (228) --------------------- +--R (174) --------------------- --R x --R Type: Expression Integer ---R --E 255 --S 256 of 504 ---Rr0148:= 2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*(cos(1/2*c)*Ci(1/2*d*x)-sin(1/2*c)*Si(1/2*d*x)) +r0148:= 2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*_ + (cos(1/2*c)*Ci(1/2*d*x)-sin(1/2*c)*Si(1/2*d*x)) --R --R ---R (229) +--R (175) --R +-+ d x d x + c c +-+ d x c d x + c --R (- \|2 Si(---)sec(-------)sin(-) + \|2 Ci(---)cos(-)sec(-------)) --R 2 2 2 2 2 2 @@ -5752,103 +5148,47 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R |a cos(-------) --R \| 2 --R Type: Expression Integer ---R --E 256 --S 257 of 504 ---Ra0148:= integrate(t0148,x) +a0148:= integrate(t0148,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 257 --S 258 of 504 ---Rm0148:= a0148-r0148 ---R ---R ---R (230) ---R +-+ d x d x + c c +-+ d x c d x + c ---R (\|2 Si(---)sec(-------)sin(-) - \|2 Ci(---)cos(-)sec(-------)) ---R 2 2 2 2 2 2 ---R * ---R +---------------+ ---R | d x + c 2 ---R |a cos(-------) ---R \| 2 ---R + ---R a0148 ---R Type: Expression Integer ---R +--m0148:= a0148-r0148 --E 258 --S 259 of 504 ---Rd0148:= D(m0148,x) ---R ---R ---R (231) ---R +-+ d x d x + c 2 d x + c c ---R a d x\|2 Si(---)cos(-------) sec(-------)sin(-) ---R 2 2 2 2 ---R + ---R +-+ d x c d x + c 2 d x + c ---R - a d x\|2 Ci(---)cos(-)cos(-------) sec(-------) ---R 2 2 2 2 ---R * ---R d x + c ---R tan(-------) ---R 2 ---R + ---R +-+ d x d x + c d x + c c ---R - a d x\|2 Si(---)cos(-------)sec(-------)sin(-) ---R 2 2 2 2 ---R + ---R +-+ d x c d x + c d x + c ---R a d x\|2 Ci(---)cos(-)cos(-------)sec(-------) ---R 2 2 2 2 ---R * ---R d x + c ---R sin(-------) ---R 2 ---R + ---R +-+ d x + c 2 d x + c c d x ---R 2a\|2 cos(-------) sec(-------)sin(-)sin(---) ---R 2 2 2 2 ---R + ---R +-+ c d x d x + c 2 d x + c ---R - 2a\|2 cos(-)cos(---)cos(-------) sec(-------) ---R 2 2 2 2 ---R / ---R +---------------+ ---R | d x + c 2 ---R 2x |a cos(-------) ---R \| 2 ---R Type: Expression Integer ---R +--d0148:= D(m0148,x) --E 259 --S 260 of 504 ---Rt0149:= (a+a*cos(c+d*x))^(1/2)/x^2 +t0149:= (a+a*cos(c+d*x))^(1/2)/x^2 --R --R --R +------------------+ --R \|a cos(d x + c) + a ---R (232) --------------------- +--R (176) --------------------- --R 2 --R x --R Type: Expression Integer ---R --E 260 --S 261 of 504 ---Rr0149:= -1/2*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*(2*cos(1/2*c+1/2*d*x)/x+d*Ci(1/2*d*x)*sin(1/2*c)+d*cos(1/2*c)*Si(1/2*d*x))*2^(1/2) +r0149:= -1/2*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*_ + (2*cos(1/2*c+1/2*d*x)/x+d*Ci(1/2*d*x)*sin(1/2*c)+_ + d*cos(1/2*c)*Si(1/2*d*x))*2^(1/2) --R --R ---R (233) +--R (177) --R +-+ d x d x + c c --R - d x\|2 Ci(---)sec(-------)sin(-) --R 2 2 2 @@ -5864,121 +5204,47 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 2x --R Type: Expression Integer ---R --E 261 --S 262 of 504 ---Ra0149:= integrate(t0149,x) +a0149:= integrate(t0149,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 262 --S 263 of 504 ---Rm0149:= a0149-r0149 ---R ---R ---R (234) ---R +-+ d x d x + c c ---R d x\|2 Ci(---)sec(-------)sin(-) ---R 2 2 2 ---R + ---R +-+ d x + c +-+ d x c d x + c ---R (2\|2 cos(-------) + d x\|2 Si(---)cos(-))sec(-------) ---R 2 2 2 2 ---R * ---R +---------------+ ---R | d x + c 2 ---R |a cos(-------) ---R \| 2 ---R + ---R 2a0149 x ---R / ---R 2x ---R Type: Expression Integer ---R +--m0149:= a0149-r0149 --E 263 --S 264 of 504 ---Rd0149:= D(m0149,x) ---R ---R ---R (235) ---R 2 2 +-+ d x d x + c 2 d x + c c ---R a d x \|2 Ci(---)cos(-------) sec(-------)sin(-) ---R 2 2 2 2 ---R + ---R +-+ d x + c 3 2 2 +-+ d x c d x + c 2 ---R (2a d x\|2 cos(-------) + a d x \|2 Si(---)cos(-)cos(-------) ) ---R 2 2 2 2 ---R * ---R d x + c ---R sec(-------) ---R 2 ---R * ---R d x + c ---R tan(-------) ---R 2 ---R + ---R 2 2 +-+ d x d x + c d x + c c ---R - a d x \|2 Ci(---)cos(-------)sec(-------)sin(-) ---R 2 2 2 2 ---R + ---R +-+ d x + c 2 2 2 +-+ d x c d x + c ---R (- 4a d x\|2 cos(-------) - a d x \|2 Si(---)cos(-)cos(-------)) ---R 2 2 2 2 ---R * ---R d x + c ---R sec(-------) ---R 2 ---R * ---R d x + c ---R sin(-------) ---R 2 ---R + ---R +-+ c d x + c 2 d x + c d x ---R 2a d x\|2 cos(-)cos(-------) sec(-------)sin(---) ---R 2 2 2 2 ---R + ---R +-+ d x d x + c 2 d x + c c ---R 2a d x\|2 cos(---)cos(-------) sec(-------)sin(-) ---R 2 2 2 2 ---R + ---R +-+ d x + c 3 d x + c ---R - 4a\|2 cos(-------) sec(-------) ---R 2 2 ---R / ---R +---------------+ ---R 2 | d x + c 2 ---R 4x |a cos(-------) ---R \| 2 ---R Type: Expression Integer ---R +--d0149:= D(m0149,x) --E 264 --S 265 of 504 ---Rt0150:= (a+a*cos(c+d*x))^(1/2)/x^3 +t0150:= (a+a*cos(c+d*x))^(1/2)/x^3 --R --R --R +------------------+ --R \|a cos(d x + c) + a ---R (236) --------------------- +--R (178) --------------------- --R 3 --R x --R Type: Expression Integer ---R --E 265 --S 266 of 504 ---Rr0150:= -1/8*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*(4*cos(1/2*c+1/2*d*x)/x^2+d^2*cos(1/2*c)*Ci(1/2*d*x)-2*d*sin(1/2*c+1/2*d*x)/x-d^2*sin(1/2*c)*Si(1/2*d*x)) +r0150:= -1/8*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*_ + (4*cos(1/2*c+1/2*d*x)/x^2+d^2*cos(1/2*c)*Ci(1/2*d*x)-_ + 2*d*sin(1/2*c+1/2*d*x)/x-d^2*sin(1/2*c)*Si(1/2*d*x)) --R --R ---R (237) +--R (179) --R +-+ d x + c d x + c 2 2 +-+ d x d x + c c --R 2d x\|2 sec(-------)sin(-------) + d x \|2 Si(---)sec(-------)sin(-) --R 2 2 2 2 2 @@ -5995,136 +5261,43 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 --R 8x --R Type: Expression Integer ---R --E 266 --S 267 of 504 ---Ra0150:= integrate(t0150,x) +a0150:= integrate(t0150,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 267 --S 268 of 504 ---Rm0150:= a0150-r0150 ---R ---R ---R (238) ---R +-+ d x + c d x + c ---R - 2d x\|2 sec(-------)sin(-------) ---R 2 2 ---R + ---R 2 2 +-+ d x d x + c c ---R - d x \|2 Si(---)sec(-------)sin(-) ---R 2 2 2 ---R + ---R +-+ d x + c 2 2 +-+ d x c d x + c ---R (4\|2 cos(-------) + d x \|2 Ci(---)cos(-))sec(-------) ---R 2 2 2 2 ---R * ---R +---------------+ ---R | d x + c 2 ---R |a cos(-------) ---R \| 2 ---R + ---R 2 ---R 8a0150 x ---R / ---R 2 ---R 8x ---R Type: Expression Integer ---R +--m0150:= a0150-r0150 --E 268 --S 269 of 504 ---Rd0150:= D(m0150,x) ---R ---R ---R (239) ---R 2 2 +-+ d x + c 2 d x + c d x + c ---R - 2a d x \|2 cos(-------) sec(-------)sin(-------) ---R 2 2 2 ---R + ---R 3 3 +-+ d x d x + c 2 d x + c c ---R - a d x \|2 Si(---)cos(-------) sec(-------)sin(-) ---R 2 2 2 2 ---R + ---R +-+ d x + c 3 3 3 +-+ d x c d x + c 2 ---R (4a d x\|2 cos(-------) + a d x \|2 Ci(---)cos(-)cos(-------) ) ---R 2 2 2 2 ---R * ---R d x + c ---R sec(-------) ---R 2 ---R * ---R d x + c ---R tan(-------) ---R 2 ---R + ---R 2 2 +-+ d x + c d x + c d x + c 2 ---R 2a d x \|2 cos(-------)sec(-------)sin(-------) ---R 2 2 2 ---R + ---R 3 3 +-+ d x d x + c d x + c c ---R a d x \|2 Si(---)cos(-------)sec(-------)sin(-) ---R 2 2 2 2 ---R + ---R +-+ d x + c 2 3 3 +-+ d x c d x + c ---R (- 4a d x\|2 cos(-------) - a d x \|2 Ci(---)cos(-)cos(-------)) ---R 2 2 2 2 ---R * ---R d x + c ---R sec(-------) ---R 2 ---R * ---R d x + c ---R sin(-------) ---R 2 ---R + ---R 2 2 +-+ d x + c 2 d x + c c d x ---R - 2a d x \|2 cos(-------) sec(-------)sin(-)sin(---) ---R 2 2 2 2 ---R + ---R 2 2 +-+ d x + c 3 ---R (- 2a d x - 16a)\|2 cos(-------) ---R 2 ---R + ---R 2 2 +-+ c d x d x + c 2 ---R 2a d x \|2 cos(-)cos(---)cos(-------) ---R 2 2 2 ---R * ---R d x + c ---R sec(-------) ---R 2 ---R / ---R +---------------+ ---R 3 | d x + c 2 ---R 16x |a cos(-------) ---R \| 2 ---R Type: Expression Integer ---R +--d0150:= D(m0150,x) --E 269 --S 270 of 504 ---Rt0151:= x*(a-a*cos(c+d*x))^(1/2) +t0151:= x*(a-a*cos(c+d*x))^(1/2) --R --R --R +--------------------+ ---R (240) x\|- a cos(d x + c) + a +--R (180) x\|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 270 --S 271 of 504 ---Rr0151:= -2*2^(1/2)*csc(1/2*c+1/2*d*x)*(d*x*cos(1/2*c+1/2*d*x)-2*sin(1/2*c+1/2*d*x))*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)/d^2 +r0151:= -2*2^(1/2)*csc(1/2*c+1/2*d*x)*(d*x*cos(1/2*c+1/2*d*x)-_ + 2*sin(1/2*c+1/2*d*x))*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)/d^2 --R --R ---R (241) +--R (181) --R +-+ d x + c d x + c +-+ d x + c d x + c --R (4\|2 csc(-------)sin(-------) - 2d x\|2 cos(-------)csc(-------)) --R 2 2 2 2 @@ -6137,88 +5310,44 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 --R d --R Type: Expression Integer ---R --E 271 --S 272 of 504 ---Ra0151:= integrate(t0151,x) +a0151:= integrate(t0151,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 272 --S 273 of 504 ---Rm0151:= a0151-r0151 ---R ---R ---R (242) ---R +-+ d x + c d x + c +-+ d x + c d x + c ---R (- 4\|2 csc(-------)sin(-------) + 2d x\|2 cos(-------)csc(-------)) ---R 2 2 2 2 ---R * ---R +---------------+ ---R | d x + c 2 ---R |a sin(-------) ---R \| 2 ---R + ---R 2 ---R a0151 d ---R / ---R 2 ---R d ---R Type: Expression Integer ---R +--m0151:= a0151-r0151 --E 273 --S 274 of 504 ---Rd0151:= D(m0151,x) ---R ---R ---R (243) ---R +-+ d x + c +-+ d x + c d x + c 3 ---R (2a\|2 cot(-------) - a d x\|2 )csc(-------)sin(-------) ---R 2 2 2 ---R + ---R +-+ d x + c d x + c +-+ d x + c d x + c ---R (- a d x\|2 cos(-------)cot(-------) - 2a\|2 cos(-------))csc(-------) ---R 2 2 2 2 ---R * ---R d x + c 2 ---R sin(-------) ---R 2 ---R + ---R +-+ d x + c 2 d x + c d x + c ---R a d x\|2 cos(-------) csc(-------)sin(-------) ---R 2 2 2 ---R / ---R +---------------+ ---R | d x + c 2 ---R d |a sin(-------) ---R \| 2 ---R Type: Expression Integer ---R +--d0151:= D(m0151,x) --E 274 --S 275 of 504 ---Rt0152:= x^2*(a-a*cos(c+d*x))^(1/2) +t0152:= x^2*(a-a*cos(c+d*x))^(1/2) --R --R --R 2 +--------------------+ ---R (244) x \|- a cos(d x + c) + a +--R (182) x \|- a cos(d x + c) + a --R Type: Expression Integer ---R --E 275 --S 276 of 504 ---Rr0152:= 2*2^(1/2)*csc(1/2*c+1/2*d*x)*(8*cos(1/2*c+1/2*d*x)-d*x*(d*x*cos(1/2*c+1/2*d*x)-4*sin(1/2*c+1/2*d*x)))*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)/d^3 +r0152:= 2*2^(1/2)*csc(1/2*c+1/2*d*x)*(8*cos(1/2*c+1/2*d*x)-_ + d*x*(d*x*cos(1/2*c+1/2*d*x)-4*sin(1/2*c+1/2*d*x)))*_ + (a*sin(1/2*c+1/2*d*x)^2)^(1/2)/d^3 --R --R ---R (245) +--R (183) --R +-+ d x + c d x + c --R 8d x\|2 csc(-------)sin(-------) --R 2 2 @@ -6235,94 +5364,45 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 3 --R d --R Type: Expression Integer ---R --E 276 --S 277 of 504 ---Ra0152:= integrate(t0152,x) +a0152:= integrate(t0152,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 277 --S 278 of 504 ---Rm0152:= a0152-r0152 ---R ---R ---R (246) ---R +-+ d x + c d x + c ---R - 8d x\|2 csc(-------)sin(-------) ---R 2 2 ---R + ---R 2 2 +-+ d x + c d x + c ---R (2d x - 16)\|2 cos(-------)csc(-------) ---R 2 2 ---R * ---R +---------------+ ---R | d x + c 2 ---R |a sin(-------) ---R \| 2 ---R + ---R 3 ---R a0152 d ---R / ---R 3 ---R d ---R Type: Expression Integer ---R +--m0152:= a0152-r0152 --E 278 --S 279 of 504 ---Rd0152:= D(m0152,x) ---R ---R ---R (247) ---R +-+ d x + c 2 2 +-+ d x + c d x + c 3 ---R (4a d x\|2 cot(-------) - a d x \|2 )csc(-------)sin(-------) ---R 2 2 2 ---R + ---R 2 2 +-+ d x + c d x + c +-+ d x + c ---R ((- a d x + 8a)\|2 cos(-------)cot(-------) - 4a d x\|2 cos(-------)) ---R 2 2 2 ---R * ---R d x + c d x + c 2 ---R csc(-------)sin(-------) ---R 2 2 ---R + ---R 2 2 +-+ d x + c 2 d x + c d x + c ---R (a d x - 8a)\|2 cos(-------) csc(-------)sin(-------) ---R 2 2 2 ---R / ---R +---------------+ ---R 2 | d x + c 2 ---R d |a sin(-------) ---R \| 2 ---R Type: Expression Integer ---R +--d0152:= D(m0152,x) --E 279 --S 280 of 504 ---Rt0153:= (a-a*cos(c+d*x))^(1/2)/x +t0153:= (a-a*cos(c+d*x))^(1/2)/x --R --R --R +--------------------+ --R \|- a cos(d x + c) + a ---R (248) ----------------------- +--R (184) ----------------------- --R x --R Type: Expression Integer ---R --E 280 --S 281 of 504 ---Rr0153:= 2^(1/2)*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*(Ci(1/2*d*x)*sin(1/2*c)+cos(1/2*c)*Si(1/2*d*x)) +r0153:= 2^(1/2)*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*_ + (Ci(1/2*d*x)*sin(1/2*c)+cos(1/2*c)*Si(1/2*d*x)) --R --R ---R (249) +--R (185) --R +-+ d x d x + c c +-+ d x c d x + c --R (\|2 Ci(---)csc(-------)sin(-) + \|2 Si(---)cos(-)csc(-------)) --R 2 2 2 2 2 2 @@ -6332,99 +5412,47 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R |a sin(-------) --R \| 2 --R Type: Expression Integer ---R --E 281 --S 282 of 504 ---Ra0153:= integrate(t0153,x) +a0153:= integrate(t0153,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 282 --S 283 of 504 ---Rm0153:= a0153-r0153 ---R ---R ---R (250) ---R +-+ d x d x + c c +-+ d x c d x + c ---R (- \|2 Ci(---)csc(-------)sin(-) - \|2 Si(---)cos(-)csc(-------)) ---R 2 2 2 2 2 2 ---R * ---R +---------------+ ---R | d x + c 2 ---R |a sin(-------) ---R \| 2 ---R + ---R a0153 ---R Type: Expression Integer ---R +--m0153:= a0153-r0153 --E 283 --S 284 of 504 ---Rd0153:= D(m0153,x) ---R ---R ---R (251) ---R +-+ c d x + c d x ---R - 2a\|2 cos(-)csc(-------)sin(---) ---R 2 2 2 ---R + ---R +-+ d x d x + c +-+ d x d x + c c ---R (a d x\|2 Ci(---)cot(-------) - 2a\|2 cos(---))csc(-------)sin(-) ---R 2 2 2 2 2 ---R + ---R +-+ d x c d x + c d x + c ---R a d x\|2 Si(---)cos(-)cot(-------)csc(-------) ---R 2 2 2 2 ---R * ---R d x + c 2 ---R sin(-------) ---R 2 ---R + ---R +-+ d x d x + c d x + c c ---R - a d x\|2 Ci(---)cos(-------)csc(-------)sin(-) ---R 2 2 2 2 ---R + ---R +-+ d x c d x + c d x + c ---R - a d x\|2 Si(---)cos(-)cos(-------)csc(-------) ---R 2 2 2 2 ---R * ---R d x + c ---R sin(-------) ---R 2 ---R / ---R +---------------+ ---R | d x + c 2 ---R 2x |a sin(-------) ---R \| 2 ---R Type: Expression Integer ---R +--d0153:= D(m0153,x) --E 284 --S 285 of 504 ---Rt0154:= (a-a*cos(c+d*x))^(1/2)/x^2 +t0154:= (a-a*cos(c+d*x))^(1/2)/x^2 --R --R --R +--------------------+ --R \|- a cos(d x + c) + a ---R (252) ----------------------- +--R (186) ----------------------- --R 2 --R x --R Type: Expression Integer ---R --E 285 --S 286 of 504 ---Rr0154:= 1/2*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*(d*cos(1/2*c)*Ci(1/2*d*x)-2*sin(1/2*c+1/2*d*x)/x-d*sin(1/2*c)*Si(1/2*d*x))*2^(1/2) +r0154:= 1/2*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*_ + (d*cos(1/2*c)*Ci(1/2*d*x)-2*sin(1/2*c+1/2*d*x)/x-_ + d*sin(1/2*c)*Si(1/2*d*x))*2^(1/2) --R --R ---R (253) +--R (187) --R +-+ d x + c d x + c +-+ d x d x + c c --R - 2\|2 csc(-------)sin(-------) - d x\|2 Si(---)csc(-------)sin(-) --R 2 2 2 2 2 @@ -6440,117 +5468,47 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 2x --R Type: Expression Integer ---R --E 286 --S 287 of 504 ---Ra0154:= integrate(t0154,x) +a0154:= integrate(t0154,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 287 --S 288 of 504 ---Rm0154:= a0154-r0154 ---R ---R ---R (254) ---R +-+ d x + c d x + c +-+ d x d x + c c ---R 2\|2 csc(-------)sin(-------) + d x\|2 Si(---)csc(-------)sin(-) ---R 2 2 2 2 2 ---R + ---R +-+ d x c d x + c ---R - d x\|2 Ci(---)cos(-)csc(-------) ---R 2 2 2 ---R * ---R +---------------+ ---R | d x + c 2 ---R |a sin(-------) ---R \| 2 ---R + ---R 2a0154 x ---R / ---R 2x ---R Type: Expression Integer ---R +--m0154:= a0154-r0154 --E 288 --S 289 of 504 ---Rd0154:= D(m0154,x) ---R ---R ---R (255) ---R +-+ d x + c +-+ d x + c d x + c 3 ---R (- 2a d x\|2 cot(-------) - 4a\|2 )csc(-------)sin(-------) ---R 2 2 2 ---R + ---R +-+ d x + c c d x ---R 2a d x\|2 csc(-------)sin(-)sin(---) ---R 2 2 2 ---R + ---R 2 2 +-+ d x d x + c d x + c c ---R - a d x \|2 Si(---)cot(-------)csc(-------)sin(-) ---R 2 2 2 2 ---R + ---R 2 2 +-+ d x c d x + c +-+ d x + c ---R a d x \|2 Ci(---)cos(-)cot(-------) + 4a d x\|2 cos(-------) ---R 2 2 2 2 ---R + ---R +-+ c d x ---R - 2a d x\|2 cos(-)cos(---) ---R 2 2 ---R * ---R d x + c ---R csc(-------) ---R 2 ---R * ---R d x + c 2 ---R sin(-------) ---R 2 ---R + ---R 2 2 +-+ d x d x + c d x + c c ---R a d x \|2 Si(---)cos(-------)csc(-------)sin(-) ---R 2 2 2 2 ---R + ---R 2 2 +-+ d x c d x + c d x + c ---R - a d x \|2 Ci(---)cos(-)cos(-------)csc(-------) ---R 2 2 2 2 ---R * ---R d x + c ---R sin(-------) ---R 2 ---R / ---R +---------------+ ---R 2 | d x + c 2 ---R 4x |a sin(-------) ---R \| 2 ---R Type: Expression Integer ---R +--d0154:= D(m0154,x) --E 289 --S 290 of 504 ---Rt0155:= (a-a*cos(c+d*x))^(1/2)/x^3 +t0155:= (a-a*cos(c+d*x))^(1/2)/x^3 --R --R --R +--------------------+ --R \|- a cos(d x + c) + a ---R (256) ----------------------- +--R (188) ----------------------- --R 3 --R x --R Type: Expression Integer ---R --E 290 --S 291 of 504 ---Rr0155:= -1/8*2^(1/2)*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*(2*d*cos(1/2*c+1/2*d*x)/x+d^2*Ci(1/2*d*x)*sin(1/2*c)+4*sin(1/2*c+1/2*d*x)/x^2+d^2*cos(1/2*c)*Si(1/2*d*x)) +r0155:= -1/8*2^(1/2)*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*_ + (2*d*cos(1/2*c+1/2*d*x)/x+d^2*Ci(1/2*d*x)*sin(1/2*c)+_ + 4*sin(1/2*c+1/2*d*x)/x^2+d^2*cos(1/2*c)*Si(1/2*d*x)) --R --R ---R (257) +--R (189) --R +-+ d x + c d x + c 2 2 +-+ d x d x + c c --R - 4\|2 csc(-------)sin(-------) - d x \|2 Ci(---)csc(-------)sin(-) --R 2 2 2 2 2 @@ -6567,126 +5525,40 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 --R 8x --R Type: Expression Integer ---R --E 291 --S 292 of 504 ---Ra0155:= integrate(t0155,x) +a0155:= integrate(t0155,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 292 --S 293 of 504 ---Rm0155:= a0155-r0155 ---R ---R ---R (258) ---R +-+ d x + c d x + c 2 2 +-+ d x d x + c c ---R 4\|2 csc(-------)sin(-------) + d x \|2 Ci(---)csc(-------)sin(-) ---R 2 2 2 2 2 ---R + ---R +-+ d x + c 2 2 +-+ d x c d x + c ---R (2d x\|2 cos(-------) + d x \|2 Si(---)cos(-))csc(-------) ---R 2 2 2 2 ---R * ---R +---------------+ ---R | d x + c 2 ---R |a sin(-------) ---R \| 2 ---R + ---R 2 ---R 8a0155 x ---R / ---R 2 ---R 8x ---R Type: Expression Integer ---R +--m0155:= a0155-r0155 --E 293 --S 294 of 504 ---Rd0155:= D(m0155,x) ---R ---R ---R (259) ---R +-+ d x + c 2 2 +-+ d x + c ---R (- 4a d x\|2 cot(-------) + (- 2a d x - 16a)\|2 )csc(-------) ---R 2 2 ---R * ---R d x + c 3 ---R sin(-------) ---R 2 ---R + ---R 2 2 +-+ c d x + c d x ---R 2a d x \|2 cos(-)csc(-------)sin(---) ---R 2 2 2 ---R + ---R 3 3 +-+ d x d x + c 2 2 +-+ d x d x + c ---R (- a d x \|2 Ci(---)cot(-------) + 2a d x \|2 cos(---))csc(-------) ---R 2 2 2 2 ---R * ---R c ---R sin(-) ---R 2 ---R + ---R 2 2 +-+ d x + c 3 3 +-+ d x c d x + c ---R (- 2a d x \|2 cos(-------) - a d x \|2 Si(---)cos(-))cot(-------) ---R 2 2 2 2 ---R + ---R +-+ d x + c ---R 4a d x\|2 cos(-------) ---R 2 ---R * ---R d x + c ---R csc(-------) ---R 2 ---R * ---R d x + c 2 ---R sin(-------) ---R 2 ---R + ---R 3 3 +-+ d x d x + c d x + c c ---R a d x \|2 Ci(---)cos(-------)csc(-------)sin(-) ---R 2 2 2 2 ---R + ---R 2 2 +-+ d x + c 2 3 3 +-+ d x c d x + c ---R (2a d x \|2 cos(-------) + a d x \|2 Si(---)cos(-)cos(-------)) ---R 2 2 2 2 ---R * ---R d x + c ---R csc(-------) ---R 2 ---R * ---R d x + c ---R sin(-------) ---R 2 ---R / ---R +---------------+ ---R 3 | d x + c 2 ---R 16x |a sin(-------) ---R \| 2 ---R Type: Expression Integer ---R +--d0155:= D(m0155,x) --E 294 --S 295 of 504 ---Rt0156:= (1+cos(x)^2)^(1/2) +t0156:= (1+cos(x)^2)^(1/2) --R --R --R +-----------+ --R | 2 ---R (260) \|cos(x) + 1 +--R (190) \|cos(x) + 1 --R Type: Expression Integer ---R --E 295 --S 296 of 504 ---Rr0156:= 2^(1/2)*EllipticE(x,1/2) +r0156:= 2^(1/2)*EllipticE(x,1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -6694,6 +5566,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Variable x @@ -6701,57 +5574,39 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 296 --S 297 of 504 ---Ra0156:= integrate(t0156,x) +a0156:= integrate(t0156,x) --R --R --R x +------------+ --R ++ | 2 ---R (261) | \|cos(%H) + 1 d%H +--R (191) | \|cos(%H) + 1 d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 297 --S 298 of 504 ---Rm0156:= a0156-r0156 ---R ---R ---R x +------------+ ---R ++ | 2 ---R (262) | \|cos(%H) + 1 d%H - r0156 ---R ++ ---R Type: Expression Integer ---R +--m0156:= a0156-r0156 --E 298 --S 299 of 504 ---Rd0156:= D(m0156,x) ---R ---R ---R +-----------+ ---R | 2 ---R (263) \|cos(x) + 1 ---R Type: Expression Integer ---R +--d0156:= D(m0156,x) --E 299 --S 300 of 504 ---Rt0157:= (-1-cos(x)^2)^(1/2) +t0157:= (-1-cos(x)^2)^(1/2) --R --R --R +-------------+ --R | 2 ---R (264) \|- cos(x) - 1 +--R (192) \|- cos(x) - 1 --R Type: Expression Integer ---R --E 300 --S 301 of 504 ---Rr0157:= 2^(1/2)*(-3-cos(2*x))^(1/2)*EllipticE(x,1/2)/(3+cos(2*x))^(1/2) +r0157:= 2^(1/2)*(-3-cos(2*x))^(1/2)*EllipticE(x,1/2)/(3+cos(2*x))^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -6759,6 +5614,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Variable x @@ -6766,14 +5622,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 301 --S 302 of 504 ---Ra0157:= integrate(t0157,x) +a0157:= integrate(t0157,x) --R --R ---R (265) +--R (193) --R +---+ 2 +---+ --R x\|- 1 x\|- 1 --R (2(%e ) - 2%e ) @@ -6796,87 +5651,30 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R x\|- 1 x\|- 1 --R 2(%e ) - 2%e --R Type: Union(Expression Integer,...) ---R --E 302 --S 303 of 504 ---Rm0157:= a0157-r0157 ---R ---R ---R (266) ---R +---+ 2 +---+ ---R x\|- 1 x\|- 1 ---R (2(%e ) - 2%e ) ---R * ---R +----------------------------------+ ---R +---+ 2 | +---+ 4 +---+ 2 ---R x %H\|- 1 | %H\|- 1 %H\|- 1 ---R ++ (4(%e ) + 4)\|(%e ) + 6(%e ) + 1 ---R | --------------------------------------------------------- d%H ---R ++ +---+ 6 +---+ 4 +---+ 2 ---R %H\|- 1 %H\|- 1 %H\|- 1 ---R (%e ) + 6(%e ) + (%e ) ---R + ---R +--------------------------------+ ---R +---+ | +---+ 4 +---+ 2 +---+ 2 ---R x\|- 1 | x\|- 1 x\|- 1 x\|- 1 ---R (%e + 1)\|(%e ) + 6(%e ) + 1 - 2r0157 (%e ) ---R + ---R +---+ ---R x\|- 1 ---R 2r0157 %e ---R / ---R +---+ 2 +---+ ---R x\|- 1 x\|- 1 ---R 2(%e ) - 2%e ---R Type: Expression Integer ---R +--m0157:= a0157-r0157 --E 303 --S 304 of 504 ---Rd0157:= D(m0157,x) ---R ---R ---R (267) ---R +---+ 7 +---+ 6 +---+ 5 ---R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 ---R \|- 1 (%e ) - 2\|- 1 (%e ) - \|- 1 (%e ) ---R + ---R +---+ 4 +---+ 3 ---R +---+ x\|- 1 +---+ x\|- 1 ---R (- 12\|- 1 + 8)(%e ) + (- \|- 1 - 16)(%e ) ---R + ---R +---+ 2 +---+ ---R +---+ x\|- 1 +---+ x\|- 1 ---R (- 2\|- 1 + 16)(%e ) + (\|- 1 - 16)%e + 8 ---R / ---R +---+ 4 +---+ 3 +---+ 2 ---R x\|- 1 x\|- 1 x\|- 1 ---R (2(%e ) - 4(%e ) + 2(%e ) ) ---R * ---R +--------------------------------+ ---R | +---+ 4 +---+ 2 ---R | x\|- 1 x\|- 1 ---R \|(%e ) + 6(%e ) + 1 ---R Type: Expression Integer ---R +--d0157:= D(m0157,x) --E 304 --S 305 of 504 ---Rt0158:= 1/(1+cos(x)^2)^(1/2) +t0158:= 1/(1+cos(x)^2)^(1/2) --R --R --R 1 ---R (268) -------------- +--R (194) -------------- --R +-----------+ --R | 2 --R \|cos(x) + 1 --R Type: Expression Integer ---R --E 305 --S 306 of 504 ---Rr0158:= 1/2*EllipticF(x,1/2)*2^(1/2) +r0158:= 1/2*EllipticF(x,1/2)*2^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -6884,6 +5682,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Variable x @@ -6891,65 +5690,43 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 306 --S 307 of 504 ---Ra0158:= integrate(t0158,x) +a0158:= integrate(t0158,x) --R --R --R x --R ++ 1 ---R (269) | --------------- d%H +--R (195) | --------------- d%H --R ++ +------------+ --R | 2 --R \|cos(%H) + 1 --R Type: Union(Expression Integer,...) ---R --E 307 --S 308 of 504 ---Rm0158:= a0158-r0158 ---R ---R ---R x ---R ++ 1 ---R (270) | --------------- d%H - r0158 ---R ++ +------------+ ---R | 2 ---R \|cos(%H) + 1 ---R Type: Expression Integer ---R +--m0158:= a0158-r0158 --E 308 --S 309 of 504 ---Rd0158:= D(m0158,x) ---R ---R ---R 1 ---R (271) -------------- ---R +-----------+ ---R | 2 ---R \|cos(x) + 1 ---R Type: Expression Integer ---R +--d0158:= D(m0158,x) --E 309 --S 310 of 504 ---Rt0159:= 1/(-1-cos(x)^2)^(1/2) +t0159:= 1/(-1-cos(x)^2)^(1/2) --R --R --R 1 ---R (272) ---------------- +--R (196) ---------------- --R +-------------+ --R | 2 --R \|- cos(x) - 1 --R Type: Expression Integer ---R --E 310 --S 311 of 504 ---Rr0159:= 1/2*(3+cos(2*x))^(1/2)*EllipticF(x,1/2)*2^(1/2)/(-3-cos(2*x))^(1/2) +r0159:= 1/2*(3+cos(2*x))^(1/2)*EllipticF(x,1/2)*2^(1/2)/(-3-cos(2*x))^(1/2) --R --R There are no library operations named EllipticF --R Use HyperDoc Browse or issue @@ -6957,6 +5734,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Variable x @@ -6964,71 +5742,49 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 311 --S 312 of 504 ---Ra0159:= integrate(t0159,x) +a0159:= integrate(t0159,x) --R --R --R +----------------------------------+ --R | +---+ 4 +---+ 2 --R x | %H\|- 1 %H\|- 1 --R ++ 2\|(%e ) + 6(%e ) + 1 ---R (273) | ---------------------------------------------- d%H +--R (197) | ---------------------------------------------- d%H --R ++ +---+ 6 +---+ 4 +---+ 2 --R %H\|- 1 %H\|- 1 %H\|- 1 --R (%e ) + 6(%e ) + (%e ) --R Type: Union(Expression Integer,...) ---R --E 312 --S 313 of 504 ---Rm0159:= a0159-r0159 ---R ---R ---R +----------------------------------+ ---R | +---+ 4 +---+ 2 ---R x | %H\|- 1 %H\|- 1 ---R ++ 2\|(%e ) + 6(%e ) + 1 ---R (274) | ---------------------------------------------- d%H - r0159 ---R ++ +---+ 6 +---+ 4 +---+ 2 ---R %H\|- 1 %H\|- 1 %H\|- 1 ---R (%e ) + 6(%e ) + (%e ) ---R Type: Expression Integer ---R +--m0159:= a0159-r0159 --E 313 --S 314 of 504 ---Rd0159:= D(m0159,x) ---R ---R ---R +--------------------------------+ ---R | +---+ 4 +---+ 2 ---R | x\|- 1 x\|- 1 ---R 2\|(%e ) + 6(%e ) + 1 ---R (275) ------------------------------------------- ---R +---+ 6 +---+ 4 +---+ 2 ---R x\|- 1 x\|- 1 x\|- 1 ---R (%e ) + 6(%e ) + (%e ) ---R Type: Expression Integer ---R +--d0159:= D(m0159,x) --E 314 --S 315 of 504 ---Rt0160:= x/(a+b*cos(x)^2) +t0160:= x/(a+b*cos(x)^2) --R --R --R x ---R (276) ------------- +--R (198) ------------- --R 2 --R b cos(x) + a --R Type: Expression Integer ---R --E 315 --S 316 of 504 ---Rr0160:= -1/4*(2*%i*x*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*%i*x*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+polylog(2,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/a^(1/2)/(a+b)^(1/2) +r0160:= -1/4*(2*%i*x*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*%i*x))/_ + (-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*%i*x*log((2*a+b+2*a^(1/2)*_ + (a+b)^(1/2)+b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + polylog(2,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*_ + (a+b)^(1/2))))/a^(1/2)/(a+b)^(1/2) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -7036,6 +5792,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -7043,62 +5800,50 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 316 --S 317 of 504 ---Ra0160:= integrate(t0160,x) +a0160:= integrate(t0160,x) --R --R --R x --R ++ %H ---R (277) | -------------- d%H +--R (199) | -------------- d%H --R ++ 2 --R b cos(%H) + a --R Type: Union(Expression Integer,...) ---R --E 317 --S 318 of 504 ---Rm0160:= a0160-r0160 ---R ---R ---R x ---R ++ %H ---R (278) | -------------- d%H - r0160 ---R ++ 2 ---R b cos(%H) + a ---R Type: Expression Integer ---R +--m0160:= a0160-r0160 --E 318 --S 319 of 504 ---Rd0160:= D(m0160,x) ---R ---R ---R x ---R (279) ------------- ---R 2 ---R b cos(x) + a ---R Type: Expression Integer ---R +--d0160:= D(m0160,x) --E 319 --S 320 of 504 ---Rt0161:= x^2/(a+b*cos(x)^2) +t0161:= x^2/(a+b*cos(x)^2) --R --R --R 2 --R x ---R (280) ------------- +--R (200) ------------- --R 2 --R b cos(x) + a --R Type: Expression Integer ---R --E 320 --S 321 of 504 ---Rr0161:= -1/4*(2*%i*x^2*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*%i*x^2*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+2*x*polylog(2,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*x*polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+%i*polylog(3,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-%i*polylog(3,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/a^(1/2)/(a+b)^(1/2) +r0161:= -1/4*(2*%i*x^2*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-_ + b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 2*%i*x^2*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*%i*x))/_ + (2*a+b+2*a^(1/2)*(a+b)^(1/2)))+2*x*polylog(2,b*exp(2*%i*x)/_ + (-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*x*_ + polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + %i*polylog(3,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + %i*polylog(3,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/_ + a^(1/2)/(a+b)^(1/2) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -7106,6 +5851,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -7113,63 +5859,52 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 321 --S 322 of 504 ---Ra0161:= integrate(t0161,x) +a0161:= integrate(t0161,x) --R --R --R x 2 --R ++ %H ---R (281) | -------------- d%H +--R (201) | -------------- d%H --R ++ 2 --R b cos(%H) + a --R Type: Union(Expression Integer,...) ---R --E 322 --S 323 of 504 ---Rm0161:= a0161-r0161 ---R ---R ---R x 2 ---R ++ %H ---R (282) | -------------- d%H - r0161 ---R ++ 2 ---R b cos(%H) + a ---R Type: Expression Integer ---R +--m0161:= a0161-r0161 --E 323 --S 324 of 504 ---Rd0161:= D(m0161,x) ---R ---R ---R 2 ---R x ---R (283) ------------- ---R 2 ---R b cos(x) + a ---R Type: Expression Integer ---R +--d0161:= D(m0161,x) --E 324 --S 325 of 504 ---Rt0162:= x^3/(a+b*cos(x)^2) +t0162:= x^3/(a+b*cos(x)^2) --R --R --R 3 --R x ---R (284) ------------- +--R (202) ------------- --R 2 --R b cos(x) + a --R Type: Expression Integer ---R --E 325 --S 326 of 504 ---Rr0162:= 1/8*(-4*%i*x^3*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+4*%i*x^3*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-6*x^2*polylog(2,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+6*x^2*polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-6*%i*x*polylog(3,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+6*%i*x*polylog(3,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+3*polylog(4,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-3*polylog(4,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/a^(1/2)/(a+b)^(1/2) +r0162:= 1/8*(-4*%i*x^3*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-_ + b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 4*%i*x^3*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+_ + b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-_ + 6*x^2*polylog(2,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 6*x^2*polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-_ + 6*%i*x*polylog(3,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 6*%i*x*polylog(3,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + 3*polylog(4,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 3*polylog(4,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/_ + a^(1/2)/(a+b)^(1/2) --R --R There are no library operations named polylog --R Use HyperDoc Browse or issue @@ -7177,6 +5912,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -7184,65 +5920,49 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 326 --S 327 of 504 ---Ra0162:= integrate(t0162,x) +a0162:= integrate(t0162,x) --R --R --R x 3 --R ++ %H ---R (285) | -------------- d%H +--R (203) | -------------- d%H --R ++ 2 --R b cos(%H) + a --R Type: Union(Expression Integer,...) ---R --E 327 --S 328 of 504 ---Rm0162:= a0162-r0162 ---R ---R ---R x 3 ---R ++ %H ---R (286) | -------------- d%H - r0162 ---R ++ 2 ---R b cos(%H) + a ---R Type: Expression Integer ---R +--m0162:= a0162-r0162 --E 328 --S 329 of 504 ---Rd0162:= D(m0162,x) ---R ---R ---R 3 ---R x ---R (287) ------------- ---R 2 ---R b cos(x) + a ---R Type: Expression Integer ---R +--d0162:= D(m0162,x) --E 329 --S 330 of 504 ---Rt0163:= 1/(a+b*cos(x)^3) +t0163:= 1/(a+b*cos(x)^3) --R --R --R 1 ---R (288) ------------- +--R (204) ------------- --R 3 --R b cos(x) + a --R Type: Expression Integer ---R --E 330 --S 331 of 504 ---Rr0163:= 2/3*atan((a^(1/3)-b^(1/3))*tan(1/2*x)/(a^(2/3)-b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atan((a^(1/3)-(-1)^(2/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+2/3*atan((a^(1/3)+(-1)^(1/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) +r0163:= 2/3*atan((a^(1/3)-b^(1/3))*tan(1/2*x)/(a^(2/3)-b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atan((a^(1/3)-(-1)^(2/3)*_ + b^(1/3))*tan(1/2*x)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/a^(2/3)/_ + (a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+2/3*atan((a^(1/3)+(-1)^(1/3)*_ + b^(1/3))*tan(1/2*x)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) --R --R ---R (289) +--R (205) --R +---------------+ +-------------------+ --R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 --R 2\|- \|b + \|a \|\|- 1 \|b + \|a @@ -7285,14 +6005,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 --R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a --R Type: Expression Integer ---R --E 331 --S 332 of 504 ---Ra0163:= integrate(t0163,x) +a0163:= integrate(t0163,x) --R --R ---R (290) +--R (206) --R ROOT --R 2 2 --R (6b - 6a ) @@ -7618,7 +6337,6 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 2 --R Type: Union(Expression Integer,...) ---R --E 332 --S 333 of 504 @@ -7630,22 +6348,23 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --E 334 --S 335 of 504 ---Rt0164:= 1/(a+b*cos(x)^4) +t0164:= 1/(a+b*cos(x)^4) --R --R --R 1 ---R (291) ------------- +--R (207) ------------- --R 4 --R b cos(x) + a --R Type: Expression Integer ---R --E 335 --S 336 of 504 ---Rr0164:= 1/2*atan(a^(1/4)*tan(x)/(a^(1/2)-(-b)^(1/2))^(1/2))/a^(3/4)/(a^(1/2)-(-b)^(1/2))^(1/2)+1/2*atan(a^(1/4)*tan(x)/(a^(1/2)+(-b)^(1/2))^(1/2))/a^(3/4)/(a^(1/2)+(-b)^(1/2))^(1/2) +r0164:= 1/2*atan(a^(1/4)*tan(x)/(a^(1/2)-(-b)^(1/2))^(1/2))/a^(3/4)/_ + (a^(1/2)-(-b)^(1/2))^(1/2)+1/2*atan(a^(1/4)*tan(x)/(a^(1/2)+_ + (-b)^(1/2))^(1/2))/a^(3/4)/(a^(1/2)+(-b)^(1/2))^(1/2) --R --R ---R (292) +--R (208) --R +-------------+ 4+-+ --R | +-+ +---+ tan(x)\|a --R \|\|a + \|- b atan(----------------) @@ -7664,14 +6383,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4+-+3 | +-+ +---+ | +-+ +---+ --R 2\|a \|\|a - \|- b \|\|a + \|- b --R Type: Expression Integer ---R --E 336 --S 337 of 504 ---Ra0164:= integrate(t0164,x) +a0164:= integrate(t0164,x) --R --R ---R (293) +--R (209) --R +-------------------------------------------+ --R | +------------------------+ --R | 2 | b @@ -7770,14 +6488,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 2 --R Type: Union(Expression Integer,...) ---R --E 337 --S 338 of 504 ---Rm0164:= a0164-r0164 +m0164:= a0164-r0164 --R --R ---R (294) +--R (210) --R +-------------------------------------------+ --R | +------------------------+ --R | 2 | b @@ -7908,14 +6625,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4+-+3 | +-+ +---+ | +-+ +---+ --R 2\|a \|\|a - \|- b \|\|a + \|- b --R Type: Expression Integer ---R --E 338 --S 339 of 504 ---Rd0164:= D(m0164,x) +d0164:= D(m0164,x) --R --R ---R (295) +--R (211) --R 4 4 --R - b cos(x) tan(x) --R + @@ -7952,26 +6668,28 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 4 2 2 2 2 4 2 +-+ --R (2a sin(x) + 4a cos(x) sin(x) + (2a b + 2a )cos(x) )tan(x) \|a --R Type: Expression Integer ---R --E 339 --S 340 of 504 ---Rt0165:= 1/(a+b*cos(x)^6) +t0165:= 1/(a+b*cos(x)^6) --R --R --R 1 ---R (296) ------------- +--R (212) ------------- --R 6 --R b cos(x) + a --R Type: Expression Integer ---R --E 340 --S 341 of 504 ---Rr0165:= 1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-(-1)^(1/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-(-1)^(1/3)*b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2) +r0165:= 1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+_ + b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-_ + (-1)^(1/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-_ + (-1)^(1/3)*b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+_ + (-1)^(2/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2) --R --R ---R (297) +--R (213) --R +-----------+ +------------------+ 6+-+ --R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|a --R \|\|b + \|a \|\|- 1 \|b + \|a atan(----------------------) @@ -7997,14 +6715,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ --R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a --R Type: Expression Integer ---R --E 341 --S 342 of 504 ---Ra0165:= integrate(t0165,x) +a0165:= integrate(t0165,x) --R --R ---R (298) +--R (214) --R ROOT --R 2 --R (12a b + 12a ) @@ -8209,14 +6926,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 2 --R Type: Union(Expression Integer,...) ---R --E 342 --S 343 of 504 ---Rm0165:= a0165-r0165 +m0165:= a0165-r0165 --R --R ---R (299) +--R (215) --R +-------------------+ +-----------+ +------------------+ --R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ --R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a @@ -8469,730 +7185,34 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ --R 6\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a --R Type: Expression Integer ---R --E 343 --S 344 of 504 ---Rd0165:= D(m0165,x) ---R ---R ---R (300) ---R 3+---+2 3+---+ 6 6 ---R (- 3b \|- 1 + 3b\|- 1 - 3b)cos(x) tan(x) ---R + ---R 3+---+2 3+---+ 6 ---R (- 3a \|- 1 + 3a\|- 1 - 3a)sin(x) ---R + ---R 3+---+2 3+---+ 2 4 ---R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 4 2 ---R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((- 3b - 3a)\|- 1 + (3b + 3a)\|- 1 - 3b - 3a)cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((6b + 15a)\|- 1 + (- 6b - 15a)\|- 1 + 6b + 15a)sin(x) ---R + ---R 3+---+2 3+---+ 2 ---R ((18b + 45a)\|- 1 + (- 18b - 45a)\|- 1 + 18b + 45a)cos(x) ---R * ---R 4 ---R sin(x) ---R + ---R 3+---+2 3+---+ 4 ---R ((18b + 45a)\|- 1 + (- 18b - 45a)\|- 1 + 18b + 45a)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((6b + 15a)\|- 1 + (- 6b - 15a)\|- 1 + 6b + 15a)cos(x) ---R * ---R 3+-+6+-+4 ---R \|a \|a ---R + ---R 3+---+2 3+---+ 6 ---R (6a \|- 1 - 6a\|- 1 + 6a)sin(x) ---R + ---R 3+---+2 3+---+ 2 4 ---R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 4 2 ---R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((- 12b + 6a)\|- 1 + (12b - 6a)\|- 1 - 12b + 6a)cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 3+---+2 3+---+ 6 ---R (- 12a \|- 1 + 12a\|- 1 - 12a)sin(x) ---R + ---R 3+---+2 3+---+ 2 4 ---R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 4 2 ---R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((- 12b - 12a)\|- 1 + (12b + 12a)\|- 1 - 12b - 12a)cos(x) ---R * ---R 2 ---R tan(x) ---R * ---R 3+-+2 6+-+2 ---R \|a \|a ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((2a b + 20a )\|- 1 + (- 2a b - 20a )\|- 1 + 2a b + 20a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((6a b + 60a )\|- 1 + (- 6a b - 60a )\|- 1 + 6a b + 60a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((6a b + 60a )\|- 1 + (- 6a b - 60a )\|- 1 + 6a b + 60a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 ---R (- b - 8a b + 20a )\|- 1 + (b + 8a b - 20a )\|- 1 - b ---R + ---R 2 ---R - 8a b + 20a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R ((- a b - 10a )\|- 1 + (a b + 10a )\|- 1 - a b - 10a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R ((- 3a b - 30a )\|- 1 + (3a b + 30a )\|- 1 - 3a b - 30a )cos(x) ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R ((- 3a b - 30a )\|- 1 + (3a b + 30a )\|- 1 - 3a b - 30a )cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 ---R (- b - 11a b - 10a )\|- 1 + (b + 11a b + 10a )\|- 1 - b ---R + ---R 2 ---R - 11a b - 10a ---R * ---R 6 ---R cos(x) ---R * ---R 3+-+2 ---R \|b ---R + ---R 3+---+2 3+---+ 6 6 ---R (- 3b \|- 1 + 3b\|- 1 - 3b)cos(x) tan(x) ---R + ---R 3+---+2 3+---+ 6 ---R (- 3a \|- 1 + 3a\|- 1 - 3a)sin(x) ---R + ---R 3+---+2 3+---+ 2 4 ---R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 4 2 ---R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((- 3b - 3a)\|- 1 + (3b + 3a)\|- 1 - 3b - 3a)cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((15b + 6a)\|- 1 + (- 15b - 6a)\|- 1 + 15b + 6a)sin(x) ---R + ---R 3+---+2 3+---+ 2 ---R ((45b + 18a)\|- 1 + (- 45b - 18a)\|- 1 + 45b + 18a)cos(x) ---R * ---R 4 ---R sin(x) ---R + ---R 3+---+2 3+---+ 4 ---R ((45b + 18a)\|- 1 + (- 45b - 18a)\|- 1 + 45b + 18a)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((15b + 6a)\|- 1 + (- 15b - 6a)\|- 1 + 15b + 6a)cos(x) ---R * ---R 3+-+2 6+-+4 ---R \|a \|a ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R ((a b + 4a )\|- 1 + (- a b - 4a )\|- 1 + a b + 4a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (3a b + 12a )\|- 1 + (- 3a b - 12a )\|- 1 + 3a b ---R + ---R 2 ---R 12a ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (3a b + 12a )\|- 1 + (- 3a b - 12a )\|- 1 + 3a b ---R + ---R 2 ---R 12a ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (- 2b - 7a b + 4a )\|- 1 + (2b + 7a b - 4a )\|- 1 ---R + ---R 2 2 ---R - 2b - 7a b + 4a ---R * ---R 6 ---R cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 2a b - 8a )\|- 1 + (2a b + 8a )\|- 1 - 2a b - 8a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (- 6a b - 24a )\|- 1 + (6a b + 24a )\|- 1 - 6a b ---R + ---R 2 ---R - 24a ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (- 6a b - 24a )\|- 1 + (6a b + 24a )\|- 1 - 6a b ---R + ---R 2 ---R - 24a ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (- 2b - 10a b - 8a )\|- 1 + (2b + 10a b + 8a )\|- 1 ---R + ---R 2 2 ---R - 2b - 10a b - 8a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R * ---R 6+-+2 ---R \|a ---R + ---R 2 3+---+2 2 3+---+ ---R (10a b + 10a )\|- 1 + (- 10a b - 10a )\|- 1 + 10a b ---R + ---R 2 ---R 10a ---R * ---R 6 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (30a b + 30a )\|- 1 + (- 30a b - 30a )\|- 1 + 30a b ---R + ---R 2 ---R 30a ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (30a b + 30a )\|- 1 + (- 30a b - 30a )\|- 1 + 30a b ---R + ---R 2 ---R 30a ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (- 5b + 5a b + 10a )\|- 1 + (5b - 5a b - 10a )\|- 1 ---R + ---R 2 2 ---R - 5b + 5a b + 10a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R ((- 5a b - 5a )\|- 1 + (5a b + 5a )\|- 1 - 5a b - 5a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 15a b - 15a )\|- 1 + (15a b + 15a )\|- 1 - 15a b - 15a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 15a b - 15a )\|- 1 + (15a b + 15a )\|- 1 - 15a b - 15a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (- 5b - 10a b - 5a )\|- 1 + (5b + 10a b + 5a )\|- 1 ---R + ---R 2 2 ---R - 5b - 10a b - 5a ---R * ---R 6 ---R cos(x) ---R * ---R 3+-+ ---R \|a ---R * ---R 3+-+ ---R \|b ---R + ---R 2 6 6 ---R (- 3b - 3a b)cos(x) tan(x) ---R + ---R 2 6 2 2 4 ---R (- 3a b - 3a )sin(x) + (- 9a b - 9a )cos(x) sin(x) ---R + ---R 2 4 2 2 2 6 ---R (- 9a b - 9a )cos(x) sin(x) + (- 3b - 6a b - 3a )cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 3+---+2 3+---+ 2 2 6 ---R (18a b \|- 1 - 18a b\|- 1 + 3b + 24a b + 3a )sin(x) ---R + ---R 3+---+2 3+---+ 2 2 2 4 ---R (54a b \|- 1 - 54a b\|- 1 + 9b + 72a b + 9a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 2 4 2 ---R (54a b \|- 1 - 54a b\|- 1 + 9b + 72a b + 9a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 2 6 ---R (18a b \|- 1 - 18a b\|- 1 + 3b + 24a b + 3a )cos(x) ---R * ---R 6+-+4 ---R \|a ---R + ---R 3+---+2 3+---+ 2 6 ---R (3a b \|- 1 - 3a b\|- 1 + 6a b + 3a )sin(x) ---R + ---R 3+---+2 3+---+ 2 2 4 ---R (9a b \|- 1 - 9a b\|- 1 + 18a b + 9a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 4 2 ---R (9a b \|- 1 - 9a b\|- 1 + 18a b + 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 6 ---R ((- 6b + 3a b)\|- 1 + (6b - 3a b)\|- 1 - 12b + 3a )cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 3+---+2 3+---+ 2 6 ---R (- 6a b \|- 1 + 6a b\|- 1 - 12a b - 6a )sin(x) ---R + ---R 3+---+2 3+---+ 2 2 4 ---R (- 18a b \|- 1 + 18a b\|- 1 - 36a b - 18a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 4 2 ---R (- 18a b \|- 1 + 18a b\|- 1 - 36a b - 18a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (- 6b - 6a b)\|- 1 + (6b + 6a b)\|- 1 - 12b - 18a b ---R + ---R 2 ---R - 6a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R * ---R 3+-+6+-+2 ---R \|a \|a ---R + ---R 3+---+2 3+---+ 2 6 ---R (18a b \|- 1 - 18a b\|- 1 + 24a b + 6a )sin(x) ---R + ---R 3+---+2 3+---+ 2 2 4 ---R (54a b \|- 1 - 54a b\|- 1 + 72a b + 18a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 4 2 ---R (54a b \|- 1 - 54a b\|- 1 + 72a b + 18a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (- 9b + 18a b)\|- 1 + (9b - 18a b)\|- 1 - 12b + 21a b ---R + ---R 2 ---R 6a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R + ---R 3+---+2 3+---+ 2 6 ---R (- 9a b \|- 1 + 9a b\|- 1 - 12a b - 3a )sin(x) ---R + ---R 3+---+2 3+---+ 2 2 4 ---R (- 27a b \|- 1 + 27a b\|- 1 - 36a b - 9a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 4 2 ---R (- 27a b \|- 1 + 27a b\|- 1 - 36a b - 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R ((- 9b - 9a b)\|- 1 + (9b + 9a b)\|- 1 - 12b - 15a b - 3a ) ---R * ---R 6 ---R cos(x) ---R * ---R 3+-+2 ---R \|a ---R / ---R 2 3+---+2 2 3+---+ 2 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 4 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 2 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((3a b + 3a )\|- 1 + (- 3a b - 3a )\|- 1 + 3a b + 3a ) ---R * ---R 6 ---R cos(x) ---R * ---R 6 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((6a b + 15a )\|- 1 + (- 6a b - 15a )\|- 1 + 6a b + 15a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((18a b + 45a )\|- 1 + (- 18a b - 45a )\|- 1 + 18a b + 45a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((18a b + 45a )\|- 1 + (- 18a b - 45a )\|- 1 + 18a b + 45a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (6b + 21a b + 15a )\|- 1 + (- 6b - 21a b - 15a )\|- 1 ---R + ---R 2 2 ---R 6b + 21a b + 15a ---R * ---R 6 ---R cos(x) ---R * ---R 3+-+6+-+4 ---R \|a \|a ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (18a \|- 1 - 18a \|- 1 + 18a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 4 ---R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 2 ---R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((18a b + 18a )\|- 1 + (- 18a b - 18a )\|- 1 + 18a b + 18a ) ---R * ---R 6 ---R cos(x) ---R * ---R 4 3+-+2 6+-+2 ---R tan(x) \|a \|a ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((3a b + 30a )\|- 1 + (- 3a b - 30a )\|- 1 + 3a b + 30a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((9a b + 90a )\|- 1 + (- 9a b - 90a )\|- 1 + 9a b + 90a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((9a b + 90a )\|- 1 + (- 9a b - 90a )\|- 1 + 9a b + 90a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3 3+---+2 ---R (3a b + 33a b + 30a )\|- 1 ---R + ---R 2 2 3 3+---+ 2 2 3 ---R (- 3a b - 33a b - 30a )\|- 1 + 3a b + 33a b + 30a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R * ---R 3+-+2 ---R \|b ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 4 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 2 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((3a b + 3a )\|- 1 + (- 3a b - 3a )\|- 1 + 3a b + 3a ) ---R * ---R 6 ---R cos(x) ---R * ---R 6 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((15a b + 6a )\|- 1 + (- 15a b - 6a )\|- 1 + 15a b + 6a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((45a b + 18a )\|- 1 + (- 45a b - 18a )\|- 1 + 45a b + 18a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((45a b + 18a )\|- 1 + (- 45a b - 18a )\|- 1 + 45a b + 18a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (15b + 21a b + 6a )\|- 1 + (- 15b - 21a b - 6a )\|- 1 ---R + ---R 2 2 ---R 15b + 21a b + 6a ---R * ---R 6 ---R cos(x) ---R * ---R 3+-+2 6+-+4 ---R \|a \|a ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((3a b + 12a )\|- 1 + (- 3a b - 12a )\|- 1 + 3a b + 12a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((9a b + 36a )\|- 1 + (- 9a b - 36a )\|- 1 + 9a b + 36a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((9a b + 36a )\|- 1 + (- 9a b - 36a )\|- 1 + 9a b + 36a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3 3+---+2 ---R (3a b + 15a b + 12a )\|- 1 ---R + ---R 2 2 3 3+---+ 2 2 3 ---R (- 3a b - 15a b - 12a )\|- 1 + 3a b + 15a b + 12a ---R * ---R 6 ---R cos(x) ---R * ---R 4 6+-+2 ---R tan(x) \|a ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((15a b + 15a )\|- 1 + (- 15a b - 15a )\|- 1 + 15a b + 15a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((45a b + 45a )\|- 1 + (- 45a b - 45a )\|- 1 + 45a b + 45a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((45a b + 45a )\|- 1 + (- 45a b - 45a )\|- 1 + 45a b + 45a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3 3+---+2 ---R (15a b + 30a b + 15a )\|- 1 ---R + ---R 2 2 3 3+---+ 2 2 3 ---R (- 15a b - 30a b - 15a )\|- 1 + 15a b + 30a b + 15a ---R * ---R 6 ---R cos(x) ---R * ---R 2 3+-+ ---R tan(x) \|a ---R * ---R 3+-+ ---R \|b ---R + ---R 2 3 6 2 3 2 4 ---R (3a b + 3a )sin(x) + (9a b + 9a )cos(x) sin(x) ---R + ---R 2 3 4 2 2 2 3 6 ---R (9a b + 9a )cos(x) sin(x) + (3a b + 6a b + 3a )cos(x) ---R * ---R 6 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3 6 ---R (18a b \|- 1 - 18a b\|- 1 + 3a b + 24a b + 3a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3 2 4 ---R (54a b \|- 1 - 54a b\|- 1 + 9a b + 72a b + 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3 4 2 ---R (54a b \|- 1 - 54a b\|- 1 + 9a b + 72a b + 9a )cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 3 2 ---R (18a b + 18a b)\|- 1 + (- 18a b - 18a b)\|- 1 + 3b + 27a b ---R + ---R 2 3 ---R 27a b + 3a ---R * ---R 6 ---R cos(x) ---R * ---R 6+-+4 ---R \|a ---R + ---R 2 3+---+2 2 3+---+ 2 3 6 ---R (9a b \|- 1 - 9a b\|- 1 + 18a b + 9a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 2 4 ---R (27a b \|- 1 - 27a b\|- 1 + 54a b + 27a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 4 2 ---R (27a b \|- 1 - 27a b\|- 1 + 54a b + 27a )cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (9a b + 9a b)\|- 1 + (- 9a b - 9a b)\|- 1 + 18a b + 27a b ---R + ---R 3 ---R 9a ---R * ---R 6 ---R cos(x) ---R * ---R 4 3+-+6+-+2 ---R tan(x) \|a \|a ---R + ---R 2 3+---+2 2 3+---+ 2 3 6 ---R (27a b \|- 1 - 27a b\|- 1 + 36a b + 9a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 2 4 ---R (81a b \|- 1 - 81a b\|- 1 + 108a b + 27a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 4 2 ---R (81a b \|- 1 - 81a b\|- 1 + 108a b + 27a )cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 ---R (27a b + 27a b)\|- 1 + (- 27a b - 27a b)\|- 1 + 36a b ---R + ---R 2 3 ---R 45a b + 9a ---R * ---R 6 ---R cos(x) ---R * ---R 2 3+-+2 ---R tan(x) \|a ---R Type: Expression Integer ---R +--d0165:= D(m0165,x) --E 344 --S 345 of 504 ---Rt0166:= 1/(a+b*cos(x)^8) +t0166:= 1/(a+b*cos(x)^8) --R --R --R 1 ---R (301) ------------- +--R (216) ------------- --R 8 --R b cos(x) + a --R Type: Expression Integer ---R --E 345 --S 346 of 504 ---Rr0166:= 1/4*atan(a^(1/8)*tan(x)/(a^(1/4)+(-b)^(1/4))^(1/2))/a^(7/8)/(a^(1/4)+(-b)^(1/4))^(1/2)+1/4*atan(a^(1/4)*tan(x)/(a^(1/2)-a^(1/4)*(-b)^(1/4))^(1/2))/a^(3/4)/(a^(1/2)-a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atan(a^(1/4)*tan(x)/(a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2))/a^(3/4)/(a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atan(a^(1/4)*tan(x)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2))/a^(3/4)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2) +r0166:= 1/4*atan(a^(1/8)*tan(x)/(a^(1/4)+(-b)^(1/4))^(1/2))/a^(7/8)/_ + (a^(1/4)+(-b)^(1/4))^(1/2)+1/4*atan(a^(1/4)*tan(x)/(a^(1/2)-_ + a^(1/4)*(-b)^(1/4))^(1/2))/a^(3/4)/(a^(1/2)-a^(1/4)*_ + (-b)^(1/4))^(1/2)+1/4*atan(a^(1/4)*tan(x)/(a^(1/2)-%i*a^(1/4)*_ + (-b)^(1/4))^(1/2))/a^(3/4)/(a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2)+_ + 1/4*atan(a^(1/4)*tan(x)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2))/_ + a^(3/4)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2) --R --R ---R (302) +--R (217) --R +---------------------+ +-------------+ +-------------------+ --R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ --R \|a \|- %i\|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a @@ -9245,14 +7265,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R | 4+---+4+-+ +-+ --R \|%i\|- b \|a + \|a --R Type: Expression Complex Integer ---R --E 346 --S 347 of 504 ---Ra0166:= integrate(t0166,x) +a0166:= integrate(t0166,x) --R --R ---R (303) +--R (218) --R ROOT --R 2 --R (16a b + 16a ) @@ -9549,7 +7568,6 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 2 --R Type: Union(Expression Integer,...) ---R --E 347 --S 348 of 504 @@ -9561,22 +7579,26 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --E 349 --S 350 of 504 ---Rt0167:= 1/(a-b*cos(x)^3) +t0167:= 1/(a-b*cos(x)^3) --R --R --R 1 ---R (304) - ------------- +--R (219) - ------------- --R 3 --R b cos(x) - a --R Type: Expression Integer ---R --E 350 --S 351 of 504 ---Rr0167:= 2/3*atan((a^(1/3)+b^(1/3))*tan(1/2*x)/(a^(2/3)-b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atan((a^(1/3)+(-1)^(2/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+2/3*atan((a^(1/3)-(-1)^(1/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) +r0167:= 2/3*atan((a^(1/3)+b^(1/3))*tan(1/2*x)/(a^(2/3)-b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atan((a^(1/3)+_ + (-1)^(2/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)+(-1)^(1/3)*_ + b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+_ + 2/3*atan((a^(1/3)-(-1)^(1/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)-_ + (-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) --R --R ---R (305) +--R (220) --R - --R +---------------+ +-------------------+ --R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 @@ -9618,14 +7640,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 --R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a --R Type: Expression Integer ---R --E 351 --S 352 of 504 ---Ra0167:= integrate(t0167,x) +a0167:= integrate(t0167,x) --R --R ---R (306) +--R (221) --R - --R ROOT --R 2 2 @@ -9951,7 +7972,6 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 2 --R Type: Union(Expression Integer,...) ---R --E 352 --S 353 of 504 @@ -9963,22 +7983,25 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --E 354 --S 355 of 504 ---Rt0168:= 1/(a-b*cos(x)^6) +t0168:= 1/(a-b*cos(x)^6) --R --R --R 1 ---R (307) - ------------- +--R (222) - ------------- --R 6 --R b cos(x) - a --R Type: Expression Integer ---R --E 355 --S 356 of 504 ---Rr0168:= 1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2) +r0168:= 1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-b^(1/3))^(1/2))/a^(5/6)/_ + (a^(1/3)-b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+_ + (-1)^(1/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+(-1)^(1/3)*_ + b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-_ + (-1)^(2/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2) --R --R ---R (308) +--R (223) --R +-------------+ +-----------------+ 6+-+ --R | 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|a --R \|- \|b + \|a \|\|- 1 \|b + \|a atan(-----------------------) @@ -10004,14 +8027,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ --R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a --R Type: Expression Integer ---R --E 356 --S 357 of 504 ---Ra0168:= integrate(t0168,x) +a0168:= integrate(t0168,x) --R --R ---R (309) +--R (224) --R ROOT --R 2 --R (12a b - 12a ) @@ -10216,14 +8238,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 2 --R Type: Union(Expression Integer,...) ---R --E 357 --S 358 of 504 ---Rm0168:= a0168-r0168 +m0168:= a0168-r0168 --R --R ---R (310) +--R (225) --R +--------------------+ +-------------+ +-----------------+ --R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ --R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a @@ -10476,730 +8497,33 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ --R 6\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a --R Type: Expression Integer ---R --E 358 --S 359 of 504 ---Rd0168:= D(m0168,x) ---R ---R ---R (311) ---R 3+---+2 3+---+ 6 6 ---R (3b \|- 1 - 3b\|- 1 + 3b)cos(x) tan(x) ---R + ---R 3+---+2 3+---+ 6 ---R (- 3a \|- 1 + 3a\|- 1 - 3a)sin(x) ---R + ---R 3+---+2 3+---+ 2 4 ---R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 4 2 ---R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((3b - 3a)\|- 1 + (- 3b + 3a)\|- 1 + 3b - 3a)cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((- 6b + 15a)\|- 1 + (6b - 15a)\|- 1 - 6b + 15a)sin(x) ---R + ---R 3+---+2 3+---+ 2 ---R ((- 18b + 45a)\|- 1 + (18b - 45a)\|- 1 - 18b + 45a)cos(x) ---R * ---R 4 ---R sin(x) ---R + ---R 3+---+2 3+---+ 4 ---R ((- 18b + 45a)\|- 1 + (18b - 45a)\|- 1 - 18b + 45a)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((- 6b + 15a)\|- 1 + (6b - 15a)\|- 1 - 6b + 15a)cos(x) ---R * ---R 3+-+6+-+4 ---R \|a \|a ---R + ---R 3+---+2 3+---+ 6 ---R (6a \|- 1 - 6a\|- 1 + 6a)sin(x) ---R + ---R 3+---+2 3+---+ 2 4 ---R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 4 2 ---R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((12b + 6a)\|- 1 + (- 12b - 6a)\|- 1 + 12b + 6a)cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 3+---+2 3+---+ 6 ---R (- 12a \|- 1 + 12a\|- 1 - 12a)sin(x) ---R + ---R 3+---+2 3+---+ 2 4 ---R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 4 2 ---R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((12b - 12a)\|- 1 + (- 12b + 12a)\|- 1 + 12b - 12a)cos(x) ---R * ---R 2 ---R tan(x) ---R * ---R 3+-+2 6+-+2 ---R \|a \|a ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 2a b + 20a )\|- 1 + (2a b - 20a )\|- 1 - 2a b + 20a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 6a b + 60a )\|- 1 + (6a b - 60a )\|- 1 - 6a b + 60a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 6a b + 60a )\|- 1 + (6a b - 60a )\|- 1 - 6a b + 60a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 ---R (- b + 8a b + 20a )\|- 1 + (b - 8a b - 20a )\|- 1 - b ---R + ---R 2 ---R 8a b + 20a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R ((a b - 10a )\|- 1 + (- a b + 10a )\|- 1 + a b - 10a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R ((3a b - 30a )\|- 1 + (- 3a b + 30a )\|- 1 + 3a b - 30a )cos(x) ---R * ---R 4 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 ---R ((3a b - 30a )\|- 1 + (- 3a b + 30a )\|- 1 + 3a b - 30a )cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 ---R (- b + 11a b - 10a )\|- 1 + (b - 11a b + 10a )\|- 1 - b ---R + ---R 2 ---R 11a b - 10a ---R * ---R 6 ---R cos(x) ---R * ---R 3+-+2 ---R \|b ---R + ---R 3+---+2 3+---+ 6 6 ---R (- 3b \|- 1 + 3b\|- 1 - 3b)cos(x) tan(x) ---R + ---R 3+---+2 3+---+ 6 ---R (3a \|- 1 - 3a\|- 1 + 3a)sin(x) ---R + ---R 3+---+2 3+---+ 2 4 ---R (9a \|- 1 - 9a\|- 1 + 9a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 4 2 ---R (9a \|- 1 - 9a\|- 1 + 9a)cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((- 3b + 3a)\|- 1 + (3b - 3a)\|- 1 - 3b + 3a)cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((15b - 6a)\|- 1 + (- 15b + 6a)\|- 1 + 15b - 6a)sin(x) ---R + ---R 3+---+2 3+---+ 2 ---R ((45b - 18a)\|- 1 + (- 45b + 18a)\|- 1 + 45b - 18a)cos(x) ---R * ---R 4 ---R sin(x) ---R + ---R 3+---+2 3+---+ 4 ---R ((45b - 18a)\|- 1 + (- 45b + 18a)\|- 1 + 45b - 18a)cos(x) ---R * ---R 2 ---R sin(x) ---R + ---R 3+---+2 3+---+ 6 ---R ((15b - 6a)\|- 1 + (- 15b + 6a)\|- 1 + 15b - 6a)cos(x) ---R * ---R 3+-+2 6+-+4 ---R \|a \|a ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R ((a b - 4a )\|- 1 + (- a b + 4a )\|- 1 + a b - 4a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (3a b - 12a )\|- 1 + (- 3a b + 12a )\|- 1 + 3a b ---R + ---R 2 ---R - 12a ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (3a b - 12a )\|- 1 + (- 3a b + 12a )\|- 1 + 3a b ---R + ---R 2 ---R - 12a ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (2b - 7a b - 4a )\|- 1 + (- 2b + 7a b + 4a )\|- 1 ---R + ---R 2 2 ---R 2b - 7a b - 4a ---R * ---R 6 ---R cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 2a b + 8a )\|- 1 + (2a b - 8a )\|- 1 - 2a b + 8a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (- 6a b + 24a )\|- 1 + (6a b - 24a )\|- 1 - 6a b ---R + ---R 2 ---R 24a ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (- 6a b + 24a )\|- 1 + (6a b - 24a )\|- 1 - 6a b ---R + ---R 2 ---R 24a ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (2b - 10a b + 8a )\|- 1 + (- 2b + 10a b - 8a )\|- 1 ---R + ---R 2 2 ---R 2b - 10a b + 8a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R * ---R 6+-+2 ---R \|a ---R + ---R 2 3+---+2 2 3+---+ ---R (10a b - 10a )\|- 1 + (- 10a b + 10a )\|- 1 + 10a b ---R + ---R 2 ---R - 10a ---R * ---R 6 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (30a b - 30a )\|- 1 + (- 30a b + 30a )\|- 1 + 30a b ---R + ---R 2 ---R - 30a ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ ---R (30a b - 30a )\|- 1 + (- 30a b + 30a )\|- 1 + 30a b ---R + ---R 2 ---R - 30a ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (5b + 5a b - 10a )\|- 1 + (- 5b - 5a b + 10a )\|- 1 ---R + ---R 2 2 ---R 5b + 5a b - 10a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R ((- 5a b + 5a )\|- 1 + (5a b - 5a )\|- 1 - 5a b + 5a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 15a b + 15a )\|- 1 + (15a b - 15a )\|- 1 - 15a b + 15a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 15a b + 15a )\|- 1 + (15a b - 15a )\|- 1 - 15a b + 15a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (5b - 10a b + 5a )\|- 1 + (- 5b + 10a b - 5a )\|- 1 ---R + ---R 2 2 ---R 5b - 10a b + 5a ---R * ---R 6 ---R cos(x) ---R * ---R 3+-+ ---R \|a ---R * ---R 3+-+ ---R \|b ---R + ---R 2 6 6 ---R (- 3b + 3a b)cos(x) tan(x) ---R + ---R 2 6 2 2 4 ---R (3a b - 3a )sin(x) + (9a b - 9a )cos(x) sin(x) ---R + ---R 2 4 2 2 2 6 ---R (9a b - 9a )cos(x) sin(x) + (- 3b + 6a b - 3a )cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 3+---+2 3+---+ 2 2 6 ---R (- 18a b \|- 1 + 18a b\|- 1 + 3b - 24a b + 3a )sin(x) ---R + ---R 3+---+2 3+---+ 2 2 2 4 ---R (- 54a b \|- 1 + 54a b\|- 1 + 9b - 72a b + 9a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 2 4 2 ---R (- 54a b \|- 1 + 54a b\|- 1 + 9b - 72a b + 9a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 2 6 ---R (- 18a b \|- 1 + 18a b\|- 1 + 3b - 24a b + 3a )cos(x) ---R * ---R 6+-+4 ---R \|a ---R + ---R 3+---+2 3+---+ 2 6 ---R (- 3a b \|- 1 + 3a b\|- 1 - 6a b + 3a )sin(x) ---R + ---R 3+---+2 3+---+ 2 2 4 ---R (- 9a b \|- 1 + 9a b\|- 1 - 18a b + 9a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 4 2 ---R (- 9a b \|- 1 + 9a b\|- 1 - 18a b + 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 6 ---R ((- 6b - 3a b)\|- 1 + (6b + 3a b)\|- 1 - 12b + 3a )cos(x) ---R * ---R 4 ---R tan(x) ---R + ---R 3+---+2 3+---+ 2 6 ---R (6a b \|- 1 - 6a b\|- 1 + 12a b - 6a )sin(x) ---R + ---R 3+---+2 3+---+ 2 2 4 ---R (18a b \|- 1 - 18a b\|- 1 + 36a b - 18a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 4 2 ---R (18a b \|- 1 - 18a b\|- 1 + 36a b - 18a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (- 6b + 6a b)\|- 1 + (6b - 6a b)\|- 1 - 12b + 18a b ---R + ---R 2 ---R - 6a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R * ---R 3+-+6+-+2 ---R \|a \|a ---R + ---R 3+---+2 3+---+ 2 6 ---R (- 18a b \|- 1 + 18a b\|- 1 - 24a b + 6a )sin(x) ---R + ---R 3+---+2 3+---+ 2 2 4 ---R (- 54a b \|- 1 + 54a b\|- 1 - 72a b + 18a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 4 2 ---R (- 54a b \|- 1 + 54a b\|- 1 - 72a b + 18a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R (- 9b - 18a b)\|- 1 + (9b + 18a b)\|- 1 - 12b - 21a b ---R + ---R 2 ---R 6a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R + ---R 3+---+2 3+---+ 2 6 ---R (9a b \|- 1 - 9a b\|- 1 + 12a b - 3a )sin(x) ---R + ---R 3+---+2 3+---+ 2 2 4 ---R (27a b \|- 1 - 27a b\|- 1 + 36a b - 9a )cos(x) sin(x) ---R + ---R 3+---+2 3+---+ 2 4 2 ---R (27a b \|- 1 - 27a b\|- 1 + 36a b - 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 ---R ((- 9b + 9a b)\|- 1 + (9b - 9a b)\|- 1 - 12b + 15a b - 3a ) ---R * ---R 6 ---R cos(x) ---R * ---R 3+-+2 ---R \|a ---R / ---R 2 3+---+2 2 3+---+ 2 6 ---R (3a \|- 1 - 3a \|- 1 + 3a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 4 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 2 ---R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 3a b + 3a )\|- 1 + (3a b - 3a )\|- 1 - 3a b + 3a ) ---R * ---R 6 ---R cos(x) ---R * ---R 6 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 6a b + 15a )\|- 1 + (6a b - 15a )\|- 1 - 6a b + 15a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 18a b + 45a )\|- 1 + (18a b - 45a )\|- 1 - 18a b + 45a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 18a b + 45a )\|- 1 + (18a b - 45a )\|- 1 - 18a b + 45a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (6b - 21a b + 15a )\|- 1 + (- 6b + 21a b - 15a )\|- 1 ---R + ---R 2 2 ---R 6b - 21a b + 15a ---R * ---R 6 ---R cos(x) ---R * ---R 3+-+6+-+4 ---R \|a \|a ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (18a \|- 1 - 18a \|- 1 + 18a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 4 ---R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 2 ---R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((- 18a b + 18a )\|- 1 + (18a b - 18a )\|- 1 - 18a b + 18a ) ---R * ---R 6 ---R cos(x) ---R * ---R 4 3+-+2 6+-+2 ---R tan(x) \|a \|a ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((- 3a b + 30a )\|- 1 + (3a b - 30a )\|- 1 - 3a b + 30a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((- 9a b + 90a )\|- 1 + (9a b - 90a )\|- 1 - 9a b + 90a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((- 9a b + 90a )\|- 1 + (9a b - 90a )\|- 1 - 9a b + 90a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3 3+---+2 ---R (3a b - 33a b + 30a )\|- 1 ---R + ---R 2 2 3 3+---+ 2 2 3 ---R (- 3a b + 33a b - 30a )\|- 1 + 3a b - 33a b + 30a ---R * ---R 6 ---R cos(x) ---R * ---R 2 ---R tan(x) ---R * ---R 3+-+2 ---R \|b ---R + ---R 2 3+---+2 2 3+---+ 2 6 ---R (- 3a \|- 1 + 3a \|- 1 - 3a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 4 ---R (- 9a \|- 1 + 9a \|- 1 - 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 4 2 ---R (- 9a \|- 1 + 9a \|- 1 - 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((3a b - 3a )\|- 1 + (- 3a b + 3a )\|- 1 + 3a b - 3a ) ---R * ---R 6 ---R cos(x) ---R * ---R 6 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((15a b - 6a )\|- 1 + (- 15a b + 6a )\|- 1 + 15a b - 6a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((45a b - 18a )\|- 1 + (- 45a b + 18a )\|- 1 + 45a b - 18a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 ---R ((45a b - 18a )\|- 1 + (- 45a b + 18a )\|- 1 + 45a b - 18a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ ---R (- 15b + 21a b - 6a )\|- 1 + (15b - 21a b + 6a )\|- 1 ---R + ---R 2 2 ---R - 15b + 21a b - 6a ---R * ---R 6 ---R cos(x) ---R * ---R 3+-+2 6+-+4 ---R \|a \|a ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((3a b - 12a )\|- 1 + (- 3a b + 12a )\|- 1 + 3a b - 12a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((9a b - 36a )\|- 1 + (- 9a b + 36a )\|- 1 + 9a b - 36a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((9a b - 36a )\|- 1 + (- 9a b + 36a )\|- 1 + 9a b - 36a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3 3+---+2 ---R (- 3a b + 15a b - 12a )\|- 1 ---R + ---R 2 2 3 3+---+ 2 2 3 ---R (3a b - 15a b + 12a )\|- 1 - 3a b + 15a b - 12a ---R * ---R 6 ---R cos(x) ---R * ---R 4 6+-+2 ---R tan(x) \|a ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((15a b - 15a )\|- 1 + (- 15a b + 15a )\|- 1 + 15a b - 15a ) ---R * ---R 6 ---R sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((45a b - 45a )\|- 1 + (- 45a b + 45a )\|- 1 + 45a b - 45a ) ---R * ---R 2 4 ---R cos(x) sin(x) ---R + ---R 2 3 3+---+2 2 3 3+---+ 2 3 ---R ((45a b - 45a )\|- 1 + (- 45a b + 45a )\|- 1 + 45a b - 45a ) ---R * ---R 4 2 ---R cos(x) sin(x) ---R + ---R 2 2 3 3+---+2 ---R (- 15a b + 30a b - 15a )\|- 1 ---R + ---R 2 2 3 3+---+ 2 2 3 ---R (15a b - 30a b + 15a )\|- 1 - 15a b + 30a b - 15a ---R * ---R 6 ---R cos(x) ---R * ---R 2 3+-+ ---R tan(x) \|a ---R * ---R 3+-+ ---R \|b ---R + ---R 2 3 6 2 3 2 4 ---R (- 3a b + 3a )sin(x) + (- 9a b + 9a )cos(x) sin(x) ---R + ---R 2 3 4 2 2 2 3 6 ---R (- 9a b + 9a )cos(x) sin(x) + (3a b - 6a b + 3a )cos(x) ---R * ---R 6 ---R tan(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3 6 ---R (- 18a b \|- 1 + 18a b\|- 1 + 3a b - 24a b + 3a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3 2 4 ---R (- 54a b \|- 1 + 54a b\|- 1 + 9a b - 72a b + 9a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 2 3 4 2 ---R (- 54a b \|- 1 + 54a b\|- 1 + 9a b - 72a b + 9a )cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 3 2 ---R (18a b - 18a b)\|- 1 + (- 18a b + 18a b)\|- 1 - 3b + 27a b ---R + ---R 2 3 ---R - 27a b + 3a ---R * ---R 6 ---R cos(x) ---R * ---R 6+-+4 ---R \|a ---R + ---R 2 3+---+2 2 3+---+ 2 3 6 ---R (- 9a b \|- 1 + 9a b\|- 1 - 18a b + 9a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 2 4 ---R (- 27a b \|- 1 + 27a b\|- 1 - 54a b + 27a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 4 2 ---R (- 27a b \|- 1 + 27a b\|- 1 - 54a b + 27a )cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 2 ---R (9a b - 9a b)\|- 1 + (- 9a b + 9a b)\|- 1 + 18a b - 27a b ---R + ---R 3 ---R 9a ---R * ---R 6 ---R cos(x) ---R * ---R 4 3+-+6+-+2 ---R tan(x) \|a \|a ---R + ---R 2 3+---+2 2 3+---+ 2 3 6 ---R (- 27a b \|- 1 + 27a b\|- 1 - 36a b + 9a )sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 2 4 ---R (- 81a b \|- 1 + 81a b\|- 1 - 108a b + 27a )cos(x) sin(x) ---R + ---R 2 3+---+2 2 3+---+ 2 3 4 2 ---R (- 81a b \|- 1 + 81a b\|- 1 - 108a b + 27a )cos(x) sin(x) ---R + ---R 2 2 3+---+2 2 2 3+---+ 2 ---R (27a b - 27a b)\|- 1 + (- 27a b + 27a b)\|- 1 + 36a b ---R + ---R 2 3 ---R - 45a b + 9a ---R * ---R 6 ---R cos(x) ---R * ---R 2 3+-+2 ---R tan(x) \|a ---R Type: Expression Integer ---R +--d0168:= D(m0168,x) --E 359 --S 360 of 504 ---Rt0169:= 1/(a-b*cos(x)^8) +t0169:= 1/(a-b*cos(x)^8) --R --R --R 1 ---R (312) - ------------- +--R (226) - ------------- --R 8 --R b cos(x) - a --R Type: Expression Integer ---R --E 360 --S 361 of 504 ---Rr0169:= 1/4*atan(a^(1/8)*tan(x)/(a^(1/4)-b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)-b^(1/4))^(1/2)+1/4*atan(a^(1/8)*tan(x)/(a^(1/4)-%i*b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)-%i*b^(1/4))^(1/2)+1/4*atan(a^(1/8)*tan(x)/(a^(1/4)+%i*b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)+%i*b^(1/4))^(1/2)+1/4*atan(a^(1/8)*tan(x)/(a^(1/4)+b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)+b^(1/4))^(1/2) +r0169:= 1/4*atan(a^(1/8)*tan(x)/(a^(1/4)-b^(1/4))^(1/2))/a^(7/8)/_ + (a^(1/4)-b^(1/4))^(1/2)+1/4*atan(a^(1/8)*tan(x)/_ + (a^(1/4)-%i*b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)-%i*b^(1/4))^(1/2)+_ + 1/4*atan(a^(1/8)*tan(x)/(a^(1/4)+%i*b^(1/4))^(1/2))/a^(7/8)/_ + (a^(1/4)+%i*b^(1/4))^(1/2)+1/4*atan(a^(1/8)*tan(x)/_ + (a^(1/4)+b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)+b^(1/4))^(1/2) --R --R ---R (313) +--R (227) --R +---------------+ +-------------+ +-----------+ 8+-+ --R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a --R \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a atan(----------------) @@ -11232,14 +8556,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ --R 4\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a --R Type: Expression Complex Integer ---R --E 361 --S 362 of 504 ---Ra0169:= integrate(t0169,x) +a0169:= integrate(t0169,x) --R --R ---R (314) +--R (228) --R ROOT --R 2 --R (16a b - 16a ) @@ -11536,14 +8859,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 2 --R Type: Union(Expression Integer,...) ---R --E 362 --S 363 of 504 ---Rm0169:= a0169-r0169 +m0169:= a0169-r0169 --R --R ---R (315) +--R (229) --R +-------------+ +---------------+ +-------------+ +-----------+ --R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ --R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a @@ -11912,14 +9234,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ --R 4\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a --R Type: Expression Complex Integer ---R --E 363 --S 364 of 504 ---Rd0169:= D(m0169,x) +d0169:= D(m0169,x) --R --R ---R (316) +--R (230) --R 8 8 --R b cos(x) tan(x) --R + @@ -12052,26 +9373,26 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 4+-+3 --R tan(x) \|a --R Type: Expression Complex Integer ---R --E 364 --S 365 of 504 ---Rt0170:= 1/(1+cos(x)^3) +t0170:= 1/(1+cos(x)^3) --R --R --R 1 ---R (317) ----------- +--R (231) ----------- --R 3 --R cos(x) + 1 --R Type: Expression Integer ---R --E 365 --S 366 of 504 ---Rr0170:= -2/3*atan((-1)^(2/3)*(1+(-1)^(1/3))^(1/2)*tan(1/2*x))/(1+(-1)^(1/3))^(1/2)+2/3*atan((-1)^(1/3)*(1-(-1)^(2/3))^(1/2)*tan(1/2*x))/(1-(-1)^(2/3))^(1/2)+sin(x)/(3*cos(x)+3) +r0170:= -2/3*atan((-1)^(2/3)*(1+(-1)^(1/3))^(1/2)*tan(1/2*x))/_ + (1+(-1)^(1/3))^(1/2)+2/3*atan((-1)^(1/3)*(1-(-1)^(2/3))^(1/2)*_ + tan(1/2*x))/(1-(-1)^(2/3))^(1/2)+sin(x)/(3*cos(x)+3) --R --R ---R (318) +--R (232) --R +-------------+ +----------+ --R | 3+---+2 3+---+2 x |3+---+ --R (- 2cos(x) - 2)\|- \|- 1 + 1 atan(\|- 1 tan(-)\|\|- 1 + 1 ) @@ -12090,14 +9411,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R | 3+---+2 |3+---+ --R (3cos(x) + 3)\|- \|- 1 + 1 \|\|- 1 + 1 --R Type: Expression Integer ---R --E 366 --S 367 of 504 ---Ra0170:= integrate(t0170,x) +a0170:= integrate(t0170,x) --R --R ---R (319) +--R (233) --R %pi x 4 %pi x 2 %pi x 2 --R cos(---)sin(-) + (2cos(---)cos(-) - 2cos(---))sin(-) --R 12 2 12 2 12 2 @@ -12606,43 +9926,39 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 12\|3 cos(-) + 6\|3 --R 2 --R Type: Union(Expression Integer,...) ---R ---R ---R --E 367 --S 368 of 504 ---Rt0171:= 1/(1+cos(x)^4) +t0171:= 1/(1+cos(x)^4) --R --R --R 1 ---R (320) ----------- +--R (234) ----------- --R 4 --R cos(x) + 1 --R Type: Expression Integer ---R --E 368 --S 369 of 504 ---Rr0171:= 1/2*atan(tan(x)/(1-%i)^(1/2))/(1-%i)^(1/2)+1/2*atan(tan(x)/(1+%i)^(1/2))/(1+%i)^(1/2) +r0171:= 1/2*atan(tan(x)/(1-%i)^(1/2))/(1-%i)^(1/2)+_ + 1/2*atan(tan(x)/(1+%i)^(1/2))/(1+%i)^(1/2) --R --R --R +------+ tan(x) +------+ tan(x) --R \|1 + %i atan(---------) + \|1 - %i atan(---------) --R +------+ +------+ --R \|1 - %i \|1 + %i ---R (321) --------------------------------------------------- +--R (235) --------------------------------------------------- --R +------+ +------+ --R 2\|1 - %i \|1 + %i --R Type: Expression Complex Integer ---R --E 369 --S 370 of 504 ---Ra0171:= integrate(t0171,x) +a0171:= integrate(t0171,x) --R --R ---R (322) +--R (236) --R 4+-+ %pi --R \|2 cos(---) --R 8 @@ -12714,14 +10030,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +-+ --R 4\|2 --R Type: Union(Expression Integer,...) ---R --E 370 --S 371 of 504 ---Rm0171:= a0171-r0171 +m0171:= a0171-r0171 --R --R ---R (323) +--R (237) --R +------+ +------+4+-+ %pi --R \|1 - %i \|1 + %i \|2 cos(---) --R 8 @@ -12803,898 +10118,31 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +------+ +------+ +-+ --R 4\|1 - %i \|1 + %i \|2 --R Type: Expression Complex Integer ---R --E 371 --S 372 of 504 ---Rd0171:= D(m0171,x) ---R ---R ---R (324) ---R 4+-+2 %pi 2 4+-+2 %pi 2 x 16 ---R (\|2 sin(---) - \|2 cos(---) - 2)sin(-) ---R 8 8 2 ---R + ---R x 2 %pi 4 %pi 2 4+-+2 x 2 %pi 2 ---R 12cos(-) sin(---) + (- 8cos(---) - 20\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 2 ---R (12cos(---) + 20\|2 cos(---) + 16)cos(-) ---R 8 8 2 ---R * ---R x 14 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 4 %pi 6 ---R 24\|2 cos(-) sin(---) ---R 2 8 ---R + ---R 4+-+2 %pi 2 x 4 %pi 4 ---R (24\|2 cos(---) - 120)cos(-) sin(---) ---R 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 4 %pi 2 ---R (- 24\|2 cos(---) + 80cos(---) + 100\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 4 ---R (- 24\|2 cos(---) - 120cos(---) - 100\|2 cos(---) - 56)cos(-) ---R 8 8 8 2 ---R * ---R x 12 ---R sin(-) ---R 2 ---R + ---R x 6 %pi 8 %pi 2 4+-+2 x 6 %pi 6 ---R 32cos(-) sin(---) + (128cos(---) - 128\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 6 %pi 4 ---R (192cos(---) - 128\|2 cos(---) + 372)cos(-) sin(---) ---R 8 8 2 8 ---R + ---R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 ---R (128cos(---) + 128\|2 cos(---) - 248cos(---) - 236\|2 ) ---R 8 8 8 ---R * ---R x 6 %pi 2 ---R cos(-) sin(---) ---R 2 8 ---R + ---R %pi 8 4+-+2 %pi 6 %pi 4 ---R 32cos(---) + 128\|2 cos(---) + 372cos(---) ---R 8 8 8 ---R + ---R 4+-+2 %pi 2 ---R 236\|2 cos(---) + 112 ---R 8 ---R * ---R x 6 ---R cos(-) ---R 2 ---R * ---R x 10 ---R sin(-) ---R 2 ---R + ---R x 8 %pi 8 ---R - 64cos(-) sin(---) ---R 2 8 ---R + ---R %pi 2 4+-+2 x 8 %pi 6 ---R (- 256cos(---) + 208\|2 )cos(-) sin(---) ---R 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 8 %pi 4 ---R (- 384cos(---) + 208\|2 cos(---) - 528)cos(-) sin(---) ---R 8 8 2 8 ---R + ---R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 ---R (- 256cos(---) - 208\|2 cos(---) + 352cos(---) + 310\|2 ) ---R 8 8 8 ---R * ---R x 8 %pi 2 ---R cos(-) sin(---) ---R 2 8 ---R + ---R %pi 8 4+-+2 %pi 6 %pi 4 ---R - 64cos(---) - 208\|2 cos(---) - 528cos(---) ---R 8 8 8 ---R + ---R 4+-+2 %pi 2 ---R - 310\|2 cos(---) - 140 ---R 8 ---R * ---R x 8 ---R cos(-) ---R 2 ---R * ---R x 8 ---R sin(-) ---R 2 ---R + ---R x 10 %pi 8 %pi 2 4+-+2 x 10 %pi 6 ---R 32cos(-) sin(---) + (128cos(---) - 128\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 10 %pi 4 ---R (192cos(---) - 128\|2 cos(---) + 372)cos(-) sin(---) ---R 8 8 2 8 ---R + ---R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 ---R (128cos(---) + 128\|2 cos(---) - 248cos(---) - 236\|2 ) ---R 8 8 8 ---R * ---R x 10 %pi 2 ---R cos(-) sin(---) ---R 2 8 ---R + ---R %pi 8 4+-+2 %pi 6 %pi 4 ---R 32cos(---) + 128\|2 cos(---) + 372cos(---) ---R 8 8 8 ---R + ---R 4+-+2 %pi 2 ---R 236\|2 cos(---) + 112 ---R 8 ---R * ---R x 10 ---R cos(-) ---R 2 ---R * ---R x 6 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 12 %pi 6 ---R 24\|2 cos(-) sin(---) ---R 2 8 ---R + ---R 4+-+2 %pi 2 x 12 %pi 4 ---R (24\|2 cos(---) - 120)cos(-) sin(---) ---R 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 12 %pi 2 ---R (- 24\|2 cos(---) + 80cos(---) + 100\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 ---R (- 24\|2 cos(---) - 120cos(---) - 100\|2 cos(---) - 56) ---R 8 8 8 ---R * ---R x 12 ---R cos(-) ---R 2 ---R * ---R x 4 ---R sin(-) ---R 2 ---R + ---R x 14 %pi 4 %pi 2 4+-+2 x 14 %pi 2 ---R 12cos(-) sin(---) + (- 8cos(---) - 20\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 14 ---R (12cos(---) + 20\|2 cos(---) + 16)cos(-) ---R 8 8 2 ---R * ---R x 2 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 16 %pi 2 4+-+2 %pi 2 x 16 ---R \|2 cos(-) sin(---) + (- \|2 cos(---) - 2)cos(-) ---R 2 8 8 2 ---R * ---R 4 ---R tan(x) ---R + ---R 4+-+2 %pi 2 4+-+2 %pi 2 x 16 ---R (2\|2 sin(---) - 2\|2 cos(---) - 4)sin(-) ---R 8 8 2 ---R + ---R x 2 %pi 4 %pi 2 4+-+2 x 2 %pi 2 ---R 24cos(-) sin(---) + (- 16cos(---) - 40\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 2 ---R (24cos(---) + 40\|2 cos(---) + 32)cos(-) ---R 8 8 2 ---R * ---R x 14 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 4 %pi 6 ---R 48\|2 cos(-) sin(---) ---R 2 8 ---R + ---R 4+-+2 %pi 2 x 4 %pi 4 ---R (48\|2 cos(---) - 240)cos(-) sin(---) ---R 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 4 %pi 2 ---R (- 48\|2 cos(---) + 160cos(---) + 200\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 ---R (- 48\|2 cos(---) - 240cos(---) - 200\|2 cos(---) - 112) ---R 8 8 8 ---R * ---R x 4 ---R cos(-) ---R 2 ---R * ---R x 12 ---R sin(-) ---R 2 ---R + ---R x 6 %pi 8 %pi 2 4+-+2 x 6 %pi 6 ---R 64cos(-) sin(---) + (256cos(---) - 256\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 6 %pi 4 ---R (384cos(---) - 256\|2 cos(---) + 744)cos(-) sin(---) ---R 8 8 2 8 ---R + ---R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 ---R (256cos(---) + 256\|2 cos(---) - 496cos(---) - 472\|2 ) ---R 8 8 8 ---R * ---R x 6 %pi 2 ---R cos(-) sin(---) ---R 2 8 ---R + ---R %pi 8 4+-+2 %pi 6 %pi 4 ---R 64cos(---) + 256\|2 cos(---) + 744cos(---) ---R 8 8 8 ---R + ---R 4+-+2 %pi 2 ---R 472\|2 cos(---) + 224 ---R 8 ---R * ---R x 6 ---R cos(-) ---R 2 ---R * ---R x 10 ---R sin(-) ---R 2 ---R + ---R x 8 %pi 8 ---R - 128cos(-) sin(---) ---R 2 8 ---R + ---R %pi 2 4+-+2 x 8 %pi 6 ---R (- 512cos(---) + 416\|2 )cos(-) sin(---) ---R 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 8 %pi 4 ---R (- 768cos(---) + 416\|2 cos(---) - 1056)cos(-) sin(---) ---R 8 8 2 8 ---R + ---R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 ---R (- 512cos(---) - 416\|2 cos(---) + 704cos(---) + 620\|2 ) ---R 8 8 8 ---R * ---R x 8 %pi 2 ---R cos(-) sin(---) ---R 2 8 ---R + ---R %pi 8 4+-+2 %pi 6 %pi 4 ---R - 128cos(---) - 416\|2 cos(---) - 1056cos(---) ---R 8 8 8 ---R + ---R 4+-+2 %pi 2 ---R - 620\|2 cos(---) - 280 ---R 8 ---R * ---R x 8 ---R cos(-) ---R 2 ---R * ---R x 8 ---R sin(-) ---R 2 ---R + ---R x 10 %pi 8 %pi 2 4+-+2 x 10 %pi 6 ---R 64cos(-) sin(---) + (256cos(---) - 256\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 10 %pi 4 ---R (384cos(---) - 256\|2 cos(---) + 744)cos(-) sin(---) ---R 8 8 2 8 ---R + ---R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 ---R (256cos(---) + 256\|2 cos(---) - 496cos(---) - 472\|2 ) ---R 8 8 8 ---R * ---R x 10 %pi 2 ---R cos(-) sin(---) ---R 2 8 ---R + ---R %pi 8 4+-+2 %pi 6 %pi 4 ---R 64cos(---) + 256\|2 cos(---) + 744cos(---) ---R 8 8 8 ---R + ---R 4+-+2 %pi 2 ---R 472\|2 cos(---) + 224 ---R 8 ---R * ---R x 10 ---R cos(-) ---R 2 ---R * ---R x 6 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 12 %pi 6 ---R 48\|2 cos(-) sin(---) ---R 2 8 ---R + ---R 4+-+2 %pi 2 x 12 %pi 4 ---R (48\|2 cos(---) - 240)cos(-) sin(---) ---R 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 12 %pi 2 ---R (- 48\|2 cos(---) + 160cos(---) + 200\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 ---R (- 48\|2 cos(---) - 240cos(---) - 200\|2 cos(---) - 112) ---R 8 8 8 ---R * ---R x 12 ---R cos(-) ---R 2 ---R * ---R x 4 ---R sin(-) ---R 2 ---R + ---R x 14 %pi 4 %pi 2 4+-+2 x 14 %pi 2 ---R 24cos(-) sin(---) + (- 16cos(---) - 40\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 14 ---R (24cos(---) + 40\|2 cos(---) + 32)cos(-) ---R 8 8 2 ---R * ---R x 2 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 16 %pi 2 4+-+2 %pi 2 x 16 ---R 2\|2 cos(-) sin(---) + (- 2\|2 cos(---) - 4)cos(-) ---R 2 8 8 2 ---R * ---R 2 ---R tan(x) ---R + ---R 4+-+2 %pi 2 4+-+2 %pi 2 x 16 ---R (2\|2 sin(---) - 2\|2 cos(---) - 2)sin(-) ---R 8 8 2 ---R + ---R x 2 %pi 4 %pi 2 4+-+2 x 2 %pi 2 ---R 24cos(-) sin(---) + (- 16cos(---) - 24\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 2 ---R (24cos(---) + 24\|2 cos(---) + 16)cos(-) ---R 8 8 2 ---R * ---R x 14 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 4 %pi 6 4+-+2 %pi 2 x 4 %pi 4 ---R 48\|2 cos(-) sin(---) + (48\|2 cos(---) - 144)cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 4 %pi 2 ---R (- 48\|2 cos(---) + 96cos(---) + 104\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 4 ---R (- 48\|2 cos(---) - 144cos(---) - 104\|2 cos(---) - 56)cos(-) ---R 8 8 8 2 ---R * ---R x 12 ---R sin(-) ---R 2 ---R + ---R x 6 %pi 8 %pi 2 4+-+2 x 6 %pi 6 ---R 64cos(-) sin(---) + (256cos(---) - 128\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 6 %pi 4 ---R (384cos(---) - 128\|2 cos(---) + 360)cos(-) sin(---) ---R 8 8 2 8 ---R + ---R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 x 6 ---R (256cos(---) + 128\|2 cos(---) - 240cos(---) - 232\|2 )cos(-) ---R 8 8 8 2 ---R * ---R %pi 2 ---R sin(---) ---R 8 ---R + ---R %pi 8 4+-+2 %pi 6 %pi 4 ---R 64cos(---) + 128\|2 cos(---) + 360cos(---) ---R 8 8 8 ---R + ---R 4+-+2 %pi 2 ---R 232\|2 cos(---) + 112 ---R 8 ---R * ---R x 6 ---R cos(-) ---R 2 ---R * ---R x 10 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 8 %pi 6 4+-+2 %pi 2 x 8 %pi 4 ---R 160\|2 cos(-) sin(---) + (160\|2 cos(---) - 480)cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 8 %pi 2 ---R (- 160\|2 cos(---) + 320cos(---) + 300\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 8 ---R (- 160\|2 cos(---) - 480cos(---) - 300\|2 cos(---) - 140)cos(-) ---R 8 8 8 2 ---R * ---R x 8 ---R sin(-) ---R 2 ---R + ---R x 10 %pi 8 %pi 2 4+-+2 x 10 %pi 6 ---R 64cos(-) sin(---) + (256cos(---) - 128\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 10 %pi 4 ---R (384cos(---) - 128\|2 cos(---) + 360)cos(-) sin(---) ---R 8 8 2 8 ---R + ---R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 ---R (256cos(---) + 128\|2 cos(---) - 240cos(---) - 232\|2 ) ---R 8 8 8 ---R * ---R x 10 %pi 2 ---R cos(-) sin(---) ---R 2 8 ---R + ---R %pi 8 4+-+2 %pi 6 %pi 4 ---R 64cos(---) + 128\|2 cos(---) + 360cos(---) ---R 8 8 8 ---R + ---R 4+-+2 %pi 2 ---R 232\|2 cos(---) + 112 ---R 8 ---R * ---R x 10 ---R cos(-) ---R 2 ---R * ---R x 6 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 12 %pi 6 4+-+2 %pi 2 x 12 %pi 4 ---R 48\|2 cos(-) sin(---) + (48\|2 cos(---) - 144)cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 12 %pi 2 ---R (- 48\|2 cos(---) + 96cos(---) + 104\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 12 ---R (- 48\|2 cos(---) - 144cos(---) - 104\|2 cos(---) - 56)cos(-) ---R 8 8 8 2 ---R * ---R x 4 ---R sin(-) ---R 2 ---R + ---R x 14 %pi 4 %pi 2 4+-+2 x 14 %pi 2 ---R 24cos(-) sin(---) + (- 16cos(---) - 24\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 14 ---R (24cos(---) + 24\|2 cos(---) + 16)cos(-) ---R 8 8 2 ---R * ---R x 2 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 16 %pi 2 4+-+2 %pi 2 x 16 ---R 2\|2 cos(-) sin(---) + (- 2\|2 cos(---) - 2)cos(-) ---R 2 8 8 2 ---R / ---R x 16 ---R 2sin(-) ---R 2 ---R + ---R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 14 ---R (16\|2 cos(-) sin(---) + (- 16\|2 cos(---) - 16)cos(-) )sin(-) ---R 2 8 8 2 2 ---R + ---R x 4 %pi 4 %pi 2 4+-+2 x 4 %pi 2 ---R 96cos(-) sin(---) + (- 64cos(---) - 96\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 4 ---R (96cos(---) + 96\|2 cos(---) + 56)cos(-) ---R 8 8 2 ---R * ---R x 12 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 6 %pi 6 ---R 128\|2 cos(-) sin(---) ---R 2 8 ---R + ---R 4+-+2 %pi 2 x 6 %pi 4 ---R (128\|2 cos(---) - 384)cos(-) sin(---) ---R 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 6 %pi 2 ---R (- 128\|2 cos(---) + 256cos(---) + 240\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 ---R (- 128\|2 cos(---) - 384cos(---) - 240\|2 cos(---) - 112) ---R 8 8 8 ---R * ---R x 6 ---R cos(-) ---R 2 ---R * ---R x 10 ---R sin(-) ---R 2 ---R + ---R x 8 %pi 8 %pi 2 4+-+2 x 8 %pi 6 ---R 128cos(-) sin(---) + (512cos(---) - 256\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 8 %pi 4 ---R (768cos(---) - 256\|2 cos(---) + 576)cos(-) sin(---) ---R 8 8 2 8 ---R + ---R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 ---R (512cos(---) + 256\|2 cos(---) - 384cos(---) - 320\|2 ) ---R 8 8 8 ---R * ---R x 8 %pi 2 ---R cos(-) sin(---) ---R 2 8 ---R + ---R %pi 8 4+-+2 %pi 6 %pi 4 ---R 128cos(---) + 256\|2 cos(---) + 576cos(---) ---R 8 8 8 ---R + ---R 4+-+2 %pi 2 ---R 320\|2 cos(---) + 140 ---R 8 ---R * ---R x 8 ---R cos(-) ---R 2 ---R * ---R x 8 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 10 %pi 6 ---R 128\|2 cos(-) sin(---) ---R 2 8 ---R + ---R 4+-+2 %pi 2 x 10 %pi 4 ---R (128\|2 cos(---) - 384)cos(-) sin(---) ---R 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 10 %pi 2 ---R (- 128\|2 cos(---) + 256cos(---) + 240\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 ---R (- 128\|2 cos(---) - 384cos(---) - 240\|2 cos(---) - 112) ---R 8 8 8 ---R * ---R x 10 ---R cos(-) ---R 2 ---R * ---R x 6 ---R sin(-) ---R 2 ---R + ---R x 12 %pi 4 %pi 2 4+-+2 x 12 %pi 2 ---R 96cos(-) sin(---) + (- 64cos(---) - 96\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 12 ---R (96cos(---) + 96\|2 cos(---) + 56)cos(-) ---R 8 8 2 ---R * ---R x 4 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 14 %pi 2 4+-+2 %pi 2 x 14 x 2 ---R (16\|2 cos(-) sin(---) + (- 16\|2 cos(---) - 16)cos(-) )sin(-) ---R 2 8 8 2 2 ---R + ---R x 16 ---R 2cos(-) ---R 2 ---R * ---R 4 ---R tan(x) ---R + ---R x 16 ---R 4sin(-) ---R 2 ---R + ---R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 14 ---R (32\|2 cos(-) sin(---) + (- 32\|2 cos(---) - 32)cos(-) )sin(-) ---R 2 8 8 2 2 ---R + ---R x 4 %pi 4 %pi 2 4+-+2 x 4 %pi 2 ---R 192cos(-) sin(---) + (- 128cos(---) - 192\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 4 ---R (192cos(---) + 192\|2 cos(---) + 112)cos(-) ---R 8 8 2 ---R * ---R x 12 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 6 %pi 6 ---R 256\|2 cos(-) sin(---) ---R 2 8 ---R + ---R 4+-+2 %pi 2 x 6 %pi 4 ---R (256\|2 cos(---) - 768)cos(-) sin(---) ---R 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 6 %pi 2 ---R (- 256\|2 cos(---) + 512cos(---) + 480\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 ---R (- 256\|2 cos(---) - 768cos(---) - 480\|2 cos(---) - 224) ---R 8 8 8 ---R * ---R x 6 ---R cos(-) ---R 2 ---R * ---R x 10 ---R sin(-) ---R 2 ---R + ---R x 8 %pi 8 %pi 2 4+-+2 x 8 %pi 6 ---R 256cos(-) sin(---) + (1024cos(---) - 512\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 8 %pi 4 ---R (1536cos(---) - 512\|2 cos(---) + 1152)cos(-) sin(---) ---R 8 8 2 8 ---R + ---R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 ---R (1024cos(---) + 512\|2 cos(---) - 768cos(---) - 640\|2 ) ---R 8 8 8 ---R * ---R x 8 %pi 2 ---R cos(-) sin(---) ---R 2 8 ---R + ---R %pi 8 4+-+2 %pi 6 %pi 4 ---R 256cos(---) + 512\|2 cos(---) + 1152cos(---) ---R 8 8 8 ---R + ---R 4+-+2 %pi 2 ---R 640\|2 cos(---) + 280 ---R 8 ---R * ---R x 8 ---R cos(-) ---R 2 ---R * ---R x 8 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 10 %pi 6 ---R 256\|2 cos(-) sin(---) ---R 2 8 ---R + ---R 4+-+2 %pi 2 x 10 %pi 4 ---R (256\|2 cos(---) - 768)cos(-) sin(---) ---R 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 10 %pi 2 ---R (- 256\|2 cos(---) + 512cos(---) + 480\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 ---R (- 256\|2 cos(---) - 768cos(---) - 480\|2 cos(---) - 224) ---R 8 8 8 ---R * ---R x 10 ---R cos(-) ---R 2 ---R * ---R x 6 ---R sin(-) ---R 2 ---R + ---R x 12 %pi 4 ---R 192cos(-) sin(---) ---R 2 8 ---R + ---R %pi 2 4+-+2 x 12 %pi 2 ---R (- 128cos(---) - 192\|2 )cos(-) sin(---) ---R 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 12 ---R (192cos(---) + 192\|2 cos(---) + 112)cos(-) ---R 8 8 2 ---R * ---R x 4 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 14 %pi 2 4+-+2 %pi 2 x 14 x 2 ---R (32\|2 cos(-) sin(---) + (- 32\|2 cos(---) - 32)cos(-) )sin(-) ---R 2 8 8 2 2 ---R + ---R x 16 ---R 4cos(-) ---R 2 ---R * ---R 2 ---R tan(x) ---R + ---R x 16 ---R 4sin(-) ---R 2 ---R + ---R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 14 ---R (32\|2 cos(-) sin(---) + (- 32\|2 cos(---) - 32)cos(-) )sin(-) ---R 2 8 8 2 2 ---R + ---R x 4 %pi 4 %pi 2 4+-+2 x 4 %pi 2 ---R 192cos(-) sin(---) + (- 128cos(---) - 192\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 4 ---R (192cos(---) + 192\|2 cos(---) + 112)cos(-) ---R 8 8 2 ---R * ---R x 12 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 6 %pi 6 4+-+2 %pi 2 x 6 %pi 4 ---R 256\|2 cos(-) sin(---) + (256\|2 cos(---) - 768)cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 6 %pi 2 ---R (- 256\|2 cos(---) + 512cos(---) + 480\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 6 ---R (- 256\|2 cos(---) - 768cos(---) - 480\|2 cos(---) - 224)cos(-) ---R 8 8 8 2 ---R * ---R x 10 ---R sin(-) ---R 2 ---R + ---R x 8 %pi 8 %pi 2 4+-+2 x 8 %pi 6 ---R 256cos(-) sin(---) + (1024cos(---) - 512\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 8 %pi 4 ---R (1536cos(---) - 512\|2 cos(---) + 1152)cos(-) sin(---) ---R 8 8 2 8 ---R + ---R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 ---R (1024cos(---) + 512\|2 cos(---) - 768cos(---) - 640\|2 ) ---R 8 8 8 ---R * ---R x 8 %pi 2 ---R cos(-) sin(---) ---R 2 8 ---R + ---R %pi 8 4+-+2 %pi 6 %pi 4 ---R 256cos(---) + 512\|2 cos(---) + 1152cos(---) ---R 8 8 8 ---R + ---R 4+-+2 %pi 2 ---R 640\|2 cos(---) + 280 ---R 8 ---R * ---R x 8 ---R cos(-) ---R 2 ---R * ---R x 8 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 10 %pi 6 ---R 256\|2 cos(-) sin(---) ---R 2 8 ---R + ---R 4+-+2 %pi 2 x 10 %pi 4 ---R (256\|2 cos(---) - 768)cos(-) sin(---) ---R 8 2 8 ---R + ---R 4+-+2 %pi 4 %pi 2 4+-+2 x 10 %pi 2 ---R (- 256\|2 cos(---) + 512cos(---) + 480\|2 )cos(-) sin(---) ---R 8 8 2 8 ---R + ---R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 10 ---R (- 256\|2 cos(---) - 768cos(---) - 480\|2 cos(---) - 224)cos(-) ---R 8 8 8 2 ---R * ---R x 6 ---R sin(-) ---R 2 ---R + ---R x 12 %pi 4 %pi 2 4+-+2 x 12 %pi 2 ---R 192cos(-) sin(---) + (- 128cos(---) - 192\|2 )cos(-) sin(---) ---R 2 8 8 2 8 ---R + ---R %pi 4 4+-+2 %pi 2 x 12 ---R (192cos(---) + 192\|2 cos(---) + 112)cos(-) ---R 8 8 2 ---R * ---R x 4 ---R sin(-) ---R 2 ---R + ---R 4+-+2 x 14 %pi 2 4+-+2 %pi 2 x 14 x 2 ---R (32\|2 cos(-) sin(---) + (- 32\|2 cos(---) - 32)cos(-) )sin(-) ---R 2 8 8 2 2 ---R + ---R x 16 ---R 4cos(-) ---R 2 ---R Type: Expression Complex Integer ---R +--d0171:= D(m0171,x) --E 372 --S 373 of 504 ---Rt0172:= 1/(1+cos(x)^8) +t0172:= 1/(1+cos(x)^8) --R --R --R 1 ---R (325) ----------- +--R (238) ----------- --R 8 --R cos(x) + 1 --R Type: Expression Integer ---R --E 373 --S 374 of 504 ---Rr0172:= 1/4*atan(tan(x)/(1-(-1)^(1/4))^(1/2))/(1-(-1)^(1/4))^(1/2)+1/4*atan(tan(x)/(1+(-1)^(1/4))^(1/2))/(1+(-1)^(1/4))^(1/2)+1/4*atan(tan(x)/(1-(-1)^(3/4))^(1/2))/(1-(-1)^(3/4))^(1/2)+1/4*atan(tan(x)/(1+(-1)^(3/4))^(1/2))/(1+(-1)^(3/4))^(1/2) +r0172:= 1/4*atan(tan(x)/(1-(-1)^(1/4))^(1/2))/(1-(-1)^(1/4))^(1/2)+_ + 1/4*atan(tan(x)/(1+(-1)^(1/4))^(1/2))/(1+(-1)^(1/4))^(1/2)+_ + 1/4*atan(tan(x)/(1-(-1)^(3/4))^(1/2))/(1-(-1)^(3/4))^(1/2)+_ + 1/4*atan(tan(x)/(1+(-1)^(3/4))^(1/2))/(1+(-1)^(3/4))^(1/2) --R --R ---R (326) +--R (239) --R +-----------------+ +-----------------+ +-----------------+ --R | +-+ +---+ | +-+ +---+ | +-+ +---+ --R |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 @@ -13773,14 +10221,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R | +-+ --R \| \|2 --R Type: Expression Integer ---R --E 374 --S 375 of 504 ---Ra0172:= integrate(t0172,x) +a0172:= integrate(t0172,x) --R --R ---R (327) +--R (240) --R +---------+ --R | +-+ --R |3\|2 + 4 @@ -15616,28 +12063,26 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +-+ --R 16\|2 --R Type: Union(Expression Integer,...) ---R ---R ---R --E 375 --S 376 of 504 ---Rt0173:= 1/(1-cos(x)^3) +t0173:= 1/(1-cos(x)^3) --R --R --R 1 ---R (328) - ----------- +--R (241) - ----------- --R 3 --R cos(x) - 1 --R Type: Expression Integer ---R --E 376 --S 377 of 504 ---Rr0173:= 2/3*atan((1-(-1)^(1/3))*tan(1/2*x)/(1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^(1/2)+2/3*atan((1+(-1)^(2/3))*tan(1/2*x)/(1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)-sin(x)/(3-3*cos(x)) +r0173:= 2/3*atan((1-(-1)^(1/3))*tan(1/2*x)/(1-(-1)^(2/3))^(1/2))/_ + (1-(-1)^(2/3))^(1/2)+2/3*atan((1+(-1)^(2/3))*tan(1/2*x)/_ + (1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)-sin(x)/(3-3*cos(x)) --R --R ---R (329) +--R (242) --R 3+---+ x --R +----------+ (\|- 1 - 1)tan(-) --R |3+---+ 2 @@ -15662,14 +12107,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R | 3+---+2 |3+---+ --R (3cos(x) - 3)\|- \|- 1 + 1 \|\|- 1 + 1 --R Type: Expression Integer ---R --E 377 --S 378 of 504 ---Ra0173:= integrate(t0173,x) +a0173:= integrate(t0173,x) --R --R ---R (330) +--R (243) --R %pi x 4 %pi x 2 %pi x 2 --R - cos(---)sin(-) + (- 2cos(---)cos(-) - 2cos(---))sin(-) --R 12 2 12 2 12 2 @@ -16186,28 +12630,25 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R - 12\|3 cos(-) + 6\|3 --R 2 --R Type: Union(Expression Integer,...) ---R ---R ---R --E 378 --S 379 of 504 ---Rt0174:= 1/(1-cos(x)^6) +t0174:= 1/(1-cos(x)^6) --R --R --R 1 ---R (331) - ----------- +--R (244) - ----------- --R 6 --R cos(x) - 1 --R Type: Expression Integer ---R --E 379 --S 380 of 504 ---Rr0174:= 1/3*atan(tan(x)/(1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)+1/3*atan(tan(x)/(1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^(1/2)-1/3*cot(x) +r0174:= 1/3*atan(tan(x)/(1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)+_ + 1/3*atan(tan(x)/(1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^(1/2)-1/3*cot(x) --R --R ---R (332) +--R (245) --R +----------+ +-------------+ --R |3+---+ tan(x) | 3+---+2 tan(x) --R \|\|- 1 + 1 atan(----------------) + \|- \|- 1 + 1 atan(-------------) @@ -16223,14 +12664,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R | 3+---+2 |3+---+ --R 3\|- \|- 1 + 1 \|\|- 1 + 1 --R Type: Expression Integer ---R --E 380 --S 381 of 504 ---Ra0174:= integrate(t0174,x) +a0174:= integrate(t0174,x) --R --R ---R (333) +--R (246) --R %pi x 8 %pi x 2 x 6 --R cos(---)sin(-) + 4cos(---)cos(-) sin(-) --R 12 2 12 2 2 @@ -17026,28 +13466,26 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 4+-+ --R 12\|3 --R Type: Union(Expression Integer,...) ---R ---R ---R --E 381 --S 382 of 504 ---Rt0175:= 1/(1-cos(x)^8) +t0175:= 1/(1-cos(x)^8) --R --R --R 1 ---R (334) - ----------- +--R (247) - ----------- --R 8 --R cos(x) - 1 --R Type: Expression Integer ---R --E 382 --S 383 of 504 ---Rr0175:= 1/4*atan(tan(x)/(1-%i)^(1/2))/(1-%i)^(1/2)+1/4*atan(tan(x)/(1+%i)^(1/2))/(1+%i)^(1/2)+1/8*atan(1/2*2^(1/2)*tan(x))*2^(1/2)-1/4*cot(x) +r0175:= 1/4*atan(tan(x)/(1-%i)^(1/2))/(1-%i)^(1/2)+_ + 1/4*atan(tan(x)/(1+%i)^(1/2))/(1+%i)^(1/2)+_ + 1/8*atan(1/2*2^(1/2)*tan(x))*2^(1/2)-1/4*cot(x) --R --R ---R (335) +--R (248) --R +-+ --R +------+ +------+ +-+ \|2 tan(x) +------+ tan(x) --R \|1 - %i \|1 + %i \|2 atan(----------) + 2\|1 + %i atan(---------) @@ -17062,14 +13500,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R +------+ +------+ --R 8\|1 - %i \|1 + %i --R Type: Expression Complex Integer ---R --E 383 --S 384 of 504 ---Ra0175:= integrate(t0175,x) +a0175:= integrate(t0175,x) --R --R ---R (336) +--R (249) --R +-+4+-+ %pi x 8 +-+4+-+ %pi x 2 x 6 --R \|2 \|2 cos(---)sin(-) + 4\|2 \|2 cos(---)cos(-) sin(-) --R 8 2 8 2 2 @@ -17239,26 +13676,26 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R (64cos(-) + 192cos(-) )sin(-) + 16cos(-) - 32cos(-) + 16 --R 2 2 2 2 2 --R Type: Union(Expression Integer,...) ---R ---R ---R --E 384 --S 385 of 504 ---Rt0176:= cos(a+b*x+c*x^2)/x^2+b*sin(a+b*x+c*x^2)/x +t0176:= cos(a+b*x+c*x^2)/x^2+b*sin(a+b*x+c*x^2)/x --R --R --R 2 2 --R b x sin(c x + b x + a) + cos(c x + b x + a) ---R (337) --------------------------------------------- +--R (250) --------------------------------------------- --R 2 --R x --R Type: Expression Integer ---R --E 385 --S 386 of 504 ---Rr0176:= -cos(a+b*x+c*x^2)/x-c^(1/2)*2^(1/2)*%pi^(1/2)*cos(1/4*(b^2-4*a*c)/c)*FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))+c^(1/2)*2^(1/2)*%pi^(1/2)*FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*sin(1/4*(b^2-4*a*c)/c) +r0176:= -cos(a+b*x+c*x^2)/x-c^(1/2)*2^(1/2)*%pi^(1/2)*_ + cos(1/4*(b^2-4*a*c)/c)*FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/_ + %pi^(1/2))+c^(1/2)*2^(1/2)*%pi^(1/2)*_ + FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + sin(1/4*(b^2-4*a*c)/c) --R --R There are no library operations named FresnelS --R Use HyperDoc Browse or issue @@ -17266,69 +13703,54 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " FresnelS " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R FresnelS with argument type(s) --R Expression Integer --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 386 --S 387 of 504 ---Ra0176:= integrate(t0176,x) +a0176:= integrate(t0176,x) --R --R --R x 2 2 --R ++ %H b sin(%H c + %H b + a) + cos(%H c + %H b + a) ---R (338) | ------------------------------------------------ d%H +--R (251) | ------------------------------------------------ d%H --R ++ 2 --R %H --R Type: Union(Expression Integer,...) ---R --E 387 --S 388 of 504 ---Rm0176:= a0176-r0176 ---R ---R ---R x 2 2 ---R ++ %H b sin(%H c + %H b + a) + cos(%H c + %H b + a) ---R (339) | ------------------------------------------------ d%H - r0176 ---R ++ 2 ---R %H ---R Type: Expression Integer ---R +--m0176:= a0176-r0176 --E 388 --S 389 of 504 ---Rd0176:= D(m0176,x) ---R ---R ---R 2 2 ---R b x sin(c x + b x + a) + cos(c x + b x + a) ---R (340) --------------------------------------------- ---R 2 ---R x ---R Type: Expression Integer ---R +--d0176:= D(m0176,x) --E 389 --S 390 of 504 ---Rt0177:= cos(a+b*x-c*x^2)/x^2+b*sin(a+b*x-c*x^2)/x +t0177:= cos(a+b*x-c*x^2)/x^2+b*sin(a+b*x-c*x^2)/x --R --R --R 2 2 --R - b x sin(c x - b x - a) + cos(c x - b x - a) ---R (341) ----------------------------------------------- +--R (252) ----------------------------------------------- --R 2 --R x --R Type: Expression Integer ---R --E 390 --S 391 of 504 ---Rr0177:= -cos(a+b*x-c*x^2)/x+c^(1/2)*2^(1/2)*%pi^(1/2)*cos(1/4*(b^2+4*a*c)/c)*FresnelS(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))-c^(1/2)*2^(1/2)*%pi^(1/2)*FresnelC(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*sin(1/4*(b^2+4*a*c)/c) +r0177:= -cos(a+b*x-c*x^2)/x+c^(1/2)*2^(1/2)*%pi^(1/2)*_ + cos(1/4*(b^2+4*a*c)/c)*_ + FresnelS(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))-_ + c^(1/2)*2^(1/2)*%pi^(1/2)*_ + FresnelC(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + sin(1/4*(b^2+4*a*c)/c) --R --R There are no library operations named FresnelS --R Use HyperDoc Browse or issue @@ -17336,66 +13758,51 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " FresnelS " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R FresnelS with argument type(s) --R Expression Integer --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 391 --S 392 of 504 ---Ra0177:= integrate(t0177,x) +a0177:= integrate(t0177,x) --R --R --R x 2 2 --R ++ - %H b sin(%H c - %H b - a) + cos(%H c - %H b - a) ---R (342) | -------------------------------------------------- d%H +--R (253) | -------------------------------------------------- d%H --R ++ 2 --R %H --R Type: Union(Expression Integer,...) ---R --E 392 --S 393 of 504 ---Rm0177:= a0177-r0177 ---R ---R ---R x 2 2 ---R ++ - %H b sin(%H c - %H b - a) + cos(%H c - %H b - a) ---R (343) | -------------------------------------------------- d%H - r0177 ---R ++ 2 ---R %H ---R Type: Expression Integer ---R +--m0177:= a0177-r0177 --E 393 --S 394 of 504 ---Rd0177:= D(m0177,x) ---R ---R ---R 2 2 ---R - b x sin(c x - b x - a) + cos(c x - b x - a) ---R (344) ----------------------------------------------- ---R 2 ---R x ---R Type: Expression Integer ---R +--d0177:= D(m0177,x) --E 394 --S 395 of 504 ---Rt0178:= (d+e*x)^2*cos(a+b*x+c*x^2) +t0178:= (d+e*x)^2*cos(a+b*x+c*x^2) --R --R --R 2 2 2 2 ---R (345) (e x + 2d e x + d )cos(c x + b x + a) +--R (254) (e x + 2d e x + d )cos(c x + b x + a) --R Type: Expression Integer ---R --E 395 --S 396 of 504 ---Rr0178:= 1/8*2^(1/2)*%pi^(1/2)*FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*((2*c*d-b*e)^2*cos(a-1/4*b^2/c)-2*c*e^2*sin(a-1/4*b^2/c))/c^(5/2)-1/8*2^(1/2)*%pi^(1/2)*FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*(2*c*e^2*cos(a-1/4*b^2/c)+(2*c*d-b*e)^2*sin(a-1/4*b^2/c))/c^(5/2)+1/4*e*(4*c*d-b*e)*sin(a+b*x+c*x^2)/c^2+1/2*e^2*x*sin(a+b*x+c*x^2)/c +r0178:= 1/8*2^(1/2)*%pi^(1/2)*FresnelC(1/2*(b+2*c*x)/c^(1/2)*_ + 2^(1/2)/%pi^(1/2))*((2*c*d-b*e)^2*cos(a-1/4*b^2/c)-_ + 2*c*e^2*sin(a-1/4*b^2/c))/c^(5/2)-1/8*2^(1/2)*%pi^(1/2)*_ + FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + (2*c*e^2*cos(a-1/4*b^2/c)+(2*c*d-b*e)^2*sin(a-1/4*b^2/c))/c^(5/2)+_ + 1/4*e*(4*c*d-b*e)*sin(a+b*x+c*x^2)/c^2+1/2*e^2*x*sin(a+b*x+c*x^2)/c --R --R There are no library operations named FresnelC --R Use HyperDoc Browse or issue @@ -17403,65 +13810,51 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " FresnelC " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R FresnelC with argument type(s) --R Expression Integer --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 396 --S 397 of 504 ---Ra0178:= integrate(t0178,x) +a0178:= integrate(t0178,x) --R --R --R x --R ++ 2 2 2 2 ---R (346) | (%H e + 2%H d e + d )cos(%H c + %H b + a)d%H +--R (255) | (%H e + 2%H d e + d )cos(%H c + %H b + a)d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 397 --S 398 of 504 ---Rm0178:= a0178-r0178 ---R ---R ---R x ---R ++ 2 2 2 2 ---R (347) | (%H e + 2%H d e + d )cos(%H c + %H b + a)d%H - r0178 ---R ++ ---R Type: Expression Integer ---R +--m0178:= a0178-r0178 --E 398 --S 399 of 504 ---Rd0178:= D(m0178,x) ---R ---R ---R 2 2 2 2 ---R (348) (e x + 2d e x + d )cos(c x + b x + a) ---R Type: Expression Integer ---R +--d0178:= D(m0178,x) --E 399 --S 400 of 504 ---Rt0179:= cos((a+b*x)/(c+d*x))^2 +t0179:= cos((a+b*x)/(c+d*x))^2 --R --R --R b x + a 2 ---R (349) cos(-------) +--R (256) cos(-------) --R d x + c --R Type: Expression Integer ---R --E 400 --S 401 of 504 ---Rr0179:= 1/2*x+1/2*(c+d*x)*cos(2*(a+b*x)/(c+d*x))/d-(b*c-a*d)*Ci(-2*(b*c-a*d)/d/(c+d*x))*sin(2*b/d)/d^2-(b*c-a*d)*cos(2*b/d)*Si(2*a/(c+d*x)-2*b*c/d/(c+d*x))/d^2 +r0179:= 1/2*x+1/2*(c+d*x)*cos(2*(a+b*x)/(c+d*x))/d-(b*c-a*d)*_ + Ci(-2*(b*c-a*d)/d/(c+d*x))*sin(2*b/d)/d^2-(b*c-a*d)*_ + cos(2*b/d)*Si(2*a/(c+d*x)-2*b*c/d/(c+d*x))/d^2 --R --R ---R (350) +--R (257) --R 2a d - 2b c 2b 2 2b x + 2a --R (2a d - 2b c)Ci(-----------)sin(--) + (d x + c d)cos(---------) --R 2 d d x + c @@ -17475,234 +13868,135 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 --R 2d --R Type: Expression Integer ---R --E 401 --S 402 of 504 ---Ra0179:= integrate(t0179,x) +a0179:= integrate(t0179,x) --R --R --R x --R ++ %H b + a 2 ---R (351) | cos(--------) d%H +--R (258) | cos(--------) d%H --R ++ %H d + c --R Type: Union(Expression Integer,...) ---R --E 402 --S 403 of 504 ---Rm0179:= a0179-r0179 ---R ---R ---R (352) ---R x ---R 2 ++ %H b + a 2 2a d - 2b c 2b ---R 2d | cos(--------) d%H + (- 2a d + 2b c)Ci(-----------)sin(--) ---R ++ %H d + c 2 d ---R d x + c d ---R + ---R 2 2b x + 2a 2a d - 2b c 2b 2 ---R (- d x - c d)cos(---------) + (- 2a d + 2b c)Si(-----------)cos(--) - d x ---R d x + c 2 d ---R d x + c d ---R / ---R 2 ---R 2d ---R Type: Expression Integer ---R +--m0179:= a0179-r0179 --E 403 --S 404 of 504 ---Rd0179:= D(m0179,x) ---R ---R ---R (353) ---R 2b x + 2a 2a d - 2b c 2b ---R (- 2a d + 2b c)sin(---------) + (2a d - 2b c)cos(-----------)sin(--) ---R d x + c 2 d ---R d x + c d ---R + ---R 2b 2a d - 2b c 2 2b x + 2a ---R (2a d - 2b c)cos(--)sin(-----------) + (- d x - c d)cos(---------) ---R d 2 d x + c ---R d x + c d ---R + ---R 2 b x + a 2 2 ---R (2d x + 2c d)cos(-------) - d x - c d ---R d x + c ---R / ---R 2 ---R 2d x + 2c d ---R Type: Expression Integer ---R +--d0179:= D(m0179,x) --E 404 --S 405 of 504 ---Rt0180:= cos(a+b*x^2)^2/x^3 +t0180:= cos(a+b*x^2)^2/x^3 --R --R --R 2 2 --R cos(b x + a) ---R (354) -------------- +--R (259) -------------- --R 3 --R x --R Type: Expression Integer ---R --E 405 --S 406 of 504 ---Rr0180:= -1/4*(1+cos(2*a+2*b*x^2)+2*b*Ci(2*b*x^2)*sin(2*a)*x^2+2*b*cos(2*a)*Si(2*b*x^2)*x^2)/x^2 +r0180:= -1/4*(1+cos(2*a+2*b*x^2)+2*b*Ci(2*b*x^2)*sin(2*a)*x^2+_ + 2*b*cos(2*a)*Si(2*b*x^2)*x^2)/x^2 --R --R ---R (355) +--R (260) --R 2 2 2 2 2 --R - 2b x Ci(2b x )sin(2a) - cos(2b x + 2a) - 2b x Si(2b x )cos(2a) - 1 --R --------------------------------------------------------------------- --R 2 --R 4x --R Type: Expression Integer ---R --E 406 --S 407 of 504 ---Ra0180:= integrate(t0180,x) +a0180:= integrate(t0180,x) --R --R --R x 2 2 --R ++ cos(%H b + a) ---R (356) | -------------- d%H +--R (261) | -------------- d%H --R ++ 3 --R %H --R Type: Union(Expression Integer,...) ---R --E 407 --S 408 of 504 ---Rm0180:= a0180-r0180 ---R ---R ---R (357) ---R x 2 2 ---R 2 ++ cos(%H b + a) 2 2 2 ---R 4x | -------------- d%H + 2b x Ci(2b x )sin(2a) + cos(2b x + 2a) ---R ++ 3 ---R %H ---R + ---R 2 2 ---R 2b x Si(2b x )cos(2a) + 1 ---R / ---R 2 ---R 4x ---R Type: Expression Integer ---R +--m0180:= a0180-r0180 --E 408 --S 409 of 504 ---Rd0180:= D(m0180,x) ---R ---R ---R (358) ---R 2 2 2 2 2 2 ---R - 2b x sin(2b x + 2a) + 2b x cos(2a)sin(2b x ) + 2b x cos(2b x )sin(2a) ---R + ---R 2 2 2 ---R - cos(2b x + 2a) + 2cos(b x + a) - 1 ---R / ---R 3 ---R 2x ---R Type: Expression Integer ---R +--d0180:= D(m0180,x) --E 409 --S 410 of 504 ---Rt0181:= cos(a+b*x^2)^3/x +t0181:= cos(a+b*x^2)^3/x --R --R --R 2 3 --R cos(b x + a) ---R (359) -------------- +--R (262) -------------- --R x --R Type: Expression Integer ---R --E 410 --S 411 of 504 ---Rr0181:= 3/8*cos(a)*Ci(b*x^2)+1/8*cos(3*a)*Ci(3*b*x^2)-3/8*sin(a)*Si(b*x^2)-1/8*sin(3*a)*Si(3*b*x^2) +r0181:= 3/8*cos(a)*Ci(b*x^2)+1/8*cos(3*a)*Ci(3*b*x^2)-_ + 3/8*sin(a)*Si(b*x^2)-1/8*sin(3*a)*Si(3*b*x^2) --R --R ---R (360) +--R (263) --R 2 2 2 2 --R - Si(3b x )sin(3a) - 3Si(b x )sin(a) + Ci(3b x )cos(3a) + 3Ci(b x )cos(a) --R ------------------------------------------------------------------------- --R 8 --R Type: Expression Integer ---R --E 411 --S 412 of 504 ---Ra0181:= integrate(t0181,x) +a0181:= integrate(t0181,x) --R --R --R x 2 3 --R ++ cos(%H b + a) ---R (361) | -------------- d%H +--R (264) | -------------- d%H --R ++ %H --R Type: Union(Expression Integer,...) ---R --E 412 --S 413 of 504 ---Rm0181:= a0181-r0181 ---R ---R ---R (362) ---R x 2 3 ---R ++ cos(%H b + a) 2 2 ---R 8 | -------------- d%H + Si(3b x )sin(3a) + 3Si(b x )sin(a) ---R ++ %H ---R + ---R 2 2 ---R - Ci(3b x )cos(3a) - 3Ci(b x )cos(a) ---R / ---R 8 ---R Type: Expression Integer ---R +--m0181:= a0181-r0181 --E 413 --S 414 of 504 ---Rd0181:= D(m0181,x) ---R ---R ---R (363) ---R 2 2 2 ---R sin(3a)sin(3b x ) + 3sin(a)sin(b x ) - cos(3a)cos(3b x ) ---R + ---R 2 3 2 ---R 4cos(b x + a) - 3cos(a)cos(b x ) ---R / ---R 4x ---R Type: Expression Integer ---R +--d0181:= D(m0181,x) --E 414 --S 415 of 504 ---Rt0182:= cos(a+b*x^2)^3/x^3 +t0182:= cos(a+b*x^2)^3/x^3 --R --R --R 2 3 --R cos(b x + a) ---R (364) -------------- +--R (265) -------------- --R 3 --R x --R Type: Expression Integer ---R --E 415 --S 416 of 504 ---Rr0182:= -1/8*(3*cos(a+b*x^2)+cos(3*a+3*b*x^2)+3*b*Ci(b*x^2)*sin(a)*x^2+3*b*Ci(3*b*x^2)*sin(3*a)*x^2+3*b*cos(a)*Si(b*x^2)*x^2+3*b*cos(3*a)*Si(3*b*x^2)*x^2)/x^2 +r0182:= -1/8*(3*cos(a+b*x^2)+cos(3*a+3*b*x^2)+3*b*Ci(b*x^2)*sin(a)*x^2+_ + 3*b*Ci(3*b*x^2)*sin(3*a)*x^2+3*b*cos(a)*Si(b*x^2)*x^2+_ + 3*b*cos(3*a)*Si(3*b*x^2)*x^2)/x^2 --R --R ---R (365) +--R (266) --R 2 2 2 2 2 --R - 3b x Ci(3b x )sin(3a) - 3b x Ci(b x )sin(a) - cos(3b x + 3a) --R + @@ -17712,80 +14006,44 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 --R 8x --R Type: Expression Integer ---R --E 416 --S 417 of 504 ---Ra0182:= integrate(t0182,x) +a0182:= integrate(t0182,x) --R --R --R x 2 3 --R ++ cos(%H b + a) ---R (366) | -------------- d%H +--R (267) | -------------- d%H --R ++ 3 --R %H --R Type: Union(Expression Integer,...) ---R --E 417 --S 418 of 504 ---Rm0182:= a0182-r0182 ---R ---R ---R (367) ---R x 2 3 ---R 2 ++ cos(%H b + a) 2 2 2 2 ---R 8x | -------------- d%H + 3b x Ci(3b x )sin(3a) + 3b x Ci(b x )sin(a) ---R ++ 3 ---R %H ---R + ---R 2 2 2 2 ---R cos(3b x + 3a) + 3cos(b x + a) + 3b x Si(3b x )cos(3a) ---R + ---R 2 2 ---R 3b x Si(b x )cos(a) ---R / ---R 2 ---R 8x ---R Type: Expression Integer ---R +--m0182:= a0182-r0182 --E 418 --S 419 of 504 ---Rd0182:= D(m0182,x) ---R ---R ---R (368) ---R 2 2 2 2 2 2 ---R - 3b x sin(3b x + 3a) + 3b x cos(3a)sin(3b x ) - 3b x sin(b x + a) ---R + ---R 2 2 2 2 2 2 ---R 3b x cos(a)sin(b x ) + 3b x cos(3b x )sin(3a) + 3b x cos(b x )sin(a) ---R + ---R 2 2 3 2 ---R - cos(3b x + 3a) + 4cos(b x + a) - 3cos(b x + a) ---R / ---R 3 ---R 4x ---R Type: Expression Integer ---R +--d0182:= D(m0182,x) --E 419 --S 420 of 504 ---Rt0183:= cos(a+b*x^n) +t0183:= cos(a+b*x^n) --R --R --R n ---R (369) cos(b x + a) +--R (268) cos(b x + a) --R Type: Expression Integer ---R --E 420 --S 421 of 504 ---Rr0183:= -1/2*x/n*(exp(%i*a)*(-%i*b*x^n)^(-1/n)*Gamma(1/n,-%i*b*x^n)+(%i*b*x^n)^(-1/n)*exp(-%i*a)*Gamma(1/n,%i*b*x^n)) +r0183:= -1/2*x/n*(exp(%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-%i*b*x^n)+(%i*b*x^n)^(-1/n)*exp(-%i*a)*_ + Gamma(1/n,%i*b*x^n)) --R --R ---R (370) +--R (269) --R 1 1 --R - - - - --R - %i a n n _ 1 n %i a n n _ 1 n @@ -17794,99 +14052,43 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R ----------------------------------------------------------------------------- --R 2n --R Type: Expression Complex Integer ---R --E 421 --S 422 of 504 ---Ra0183:= integrate(t0183,x) +a0183:= integrate(t0183,x) --R --R --R x --R ++ n ---R (371) | cos(b %H + a)d%H +--R (270) | cos(b %H + a)d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 422 --S 423 of 504 ---Rm0183:= a0183-r0183 ---R ---R ---R (372) ---R 1 ---R x - - ---R ++ n - %i a n n _ 1 n ---R 2n | cos(b %H + a)d%H + x %e (%i b x ) | (-,%i b x ) ---R ++ n ---R + ---R 1 ---R - - ---R %i a n n _ 1 n ---R x %e (- %i b x ) | (-,- %i b x ) ---R n ---R / ---R 2n ---R Type: Expression Complex Integer ---R +--m0183:= a0183-r0183 --E 423 --S 424 of 504 ---Rd0183:= D(m0183,x) ---R ---R ---R (373) ---R 1 - n - 1 ---R - - ------- ---R - %i a n n - %i a n - 1 n n ---R (%e (%i b x ) - %i b x %e x (%i b x ) ) ---R * ---R _ 1 n ---R | (-,%i b x ) ---R n ---R + ---R 1 - n - 1 ---R - - ------- ---R %i a n n %i a n - 1 n n ---R (%e (- %i b x ) + %i b x %e x (- %i b x ) ) ---R * ---R _ 1 n ---R | (-,- %i b x ) ---R n ---R + ---R - n + 1 1 ---R n ------- - - ---R - %i a n - 1 - %i b x n n n n ---R - %i b n x %e x %e (%i b x ) (%i b x ) ---R + ---R - n + 1 1 ---R n ------- - - ---R %i a n - 1 %i b x n n n n ---R %i b n x %e x %e (- %i b x ) (- %i b x ) ---R + ---R n ---R 2n cos(b x + a) ---R / ---R 2n ---R Type: Expression Complex Integer ---R +--d0183:= D(m0183,x) --E 424 --S 425 of 504 ---Rt0184:= cos(a+b*x^n)^2 +t0184:= cos(a+b*x^n)^2 --R --R --R n 2 ---R (374) cos(b x + a) +--R (271) cos(b x + a) --R Type: Expression Integer ---R --E 425 --S 426 of 504 ---Rr0184:= -1/2*x/n*(2^(-(1+n)/n)*exp(2*%i*a)*(-%i*b*x^n)^(-1/n)*Gamma(1/n,-2*%i*b*x^n)+2^(-(1+n)/n)*exp(-2*%i*a)*(%i*b*x^n)^(-1/n)*Gamma(1/n,2*%i*b*x^n)-n) +r0184:= -1/2*x/n*(2^(-(1+n)/n)*exp(2*%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-2*%i*b*x^n)+2^(-(1+n)/n)*exp(-2*%i*a)*(%i*b*x^n)^(-1/n)*_ + Gamma(1/n,2*%i*b*x^n)-n) --R --R ---R (375) +--R (272) --R - n - 1 1 --R ------- - - --R - 2%i a n n n _ 1 n @@ -17901,125 +14103,45 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 2n --R Type: Expression Complex Integer ---R --E 426 --S 427 of 504 ---Ra0184:= integrate(t0184,x) +a0184:= integrate(t0184,x) --R --R --R x --R ++ n 2 ---R (376) | cos(b %H + a) d%H +--R (273) | cos(b %H + a) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 427 --S 428 of 504 ---Rm0184:= a0184-r0184 ---R ---R ---R (377) ---R x ---R ++ n 2 ---R 2n | cos(b %H + a) d%H ---R ++ ---R + ---R - n - 1 1 ---R ------- - - ---R - 2%i a n n n _ 1 n ---R x %e 2 (%i b x ) | (-,2%i b x ) ---R n ---R + ---R - n - 1 1 ---R ------- - - ---R 2%i a n n n _ 1 n ---R x %e 2 (- %i b x ) | (-,- 2%i b x ) - n x ---R n ---R / ---R 2n ---R Type: Expression Complex Integer ---R +--m0184:= a0184-r0184 --E 428 --S 429 of 504 ---Rd0184:= D(m0184,x) ---R ---R ---R (378) ---R - n - 1 1 ---R ------- - - ---R - 2%i a n n n ---R %e 2 (%i b x ) ---R + ---R - n - 1 - n - 1 ---R ------- ------- ---R - 2%i a n n - 1 n n ---R - %i b x %e 2 x (%i b x ) ---R * ---R _ 1 n ---R | (-,2%i b x ) ---R n ---R + ---R - n - 1 1 ---R ------- - - ---R 2%i a n n n ---R %e 2 (- %i b x ) ---R + ---R - n - 1 - n - 1 ---R ------- ------- ---R 2%i a n n - 1 n n ---R %i b x %e 2 x (- %i b x ) ---R * ---R _ 1 n ---R | (-,- 2%i b x ) ---R n ---R + ---R - ---R - n - 1 1 ---R ------- n - - ---R - 2%i a n n - 1 - 2%i b x n n ---R 2%i b n x %e 2 x %e (%i b x ) ---R * ---R - n + 1 ---R ------- ---R n n ---R (2%i b x ) ---R + ---R - n - 1 - n + 1 ---R ------- n ------- ---R 2%i a n n - 1 2%i b x n n ---R 2%i b n x %e 2 x %e (- 2%i b x ) ---R * ---R 1 ---R - - ---R n n ---R (- %i b x ) ---R + ---R n 2 ---R 2n cos(b x + a) - n ---R / ---R 2n ---R Type: Expression Complex Integer ---R +--d0184:= D(m0184,x) --E 429 --S 430 of 504 ---Rt0185:= cos(a+b*x^n)^3 +t0185:= cos(a+b*x^n)^3 --R --R --R n 3 ---R (379) cos(b x + a) +--R (274) cos(b x + a) --R Type: Expression Integer ---R --E 430 --S 431 of 504 ---Rr0185:= -1/8*x/n*(3*exp(%i*a)*(-%i*b*x^n)^(-1/n)*Gamma(1/n,-%i*b*x^n)+3*(%i*b*x^n)^(-1/n)*exp(-%i*a)*Gamma(1/n,%i*b*x^n)+exp(3*%i*a)*(-%i*b*x^n)^(-1/n)*3^(-1/n)*Gamma(1/n,-3*%i*b*x^n)+(%i*b*x^n)^(-1/n)*3^(-1/n)*exp(-3*%i*a)*Gamma(1/n,3*%i*b*x^n)) +r0185:= -1/8*x/n*(3*exp(%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-%i*b*x^n)+3*(%i*b*x^n)^(-1/n)*exp(-%i*a)*_ + Gamma(1/n,%i*b*x^n)+exp(3*%i*a)*(-%i*b*x^n)^(-1/n)*3^(-1/n)*_ + Gamma(1/n,-3*%i*b*x^n)+(%i*b*x^n)^(-1/n)*3^(-1/n)*exp(-3*%i*a)*_ + Gamma(1/n,3*%i*b*x^n)) --R --R ---R (380) +--R (275) --R 1 1 --R - - - - --R - 3%i a n n n _ 1 n @@ -18046,154 +14168,43 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 8n --R Type: Expression Complex Integer ---R --E 431 --S 432 of 504 ---Ra0185:= integrate(t0185,x) +a0185:= integrate(t0185,x) --R --R --R x --R ++ n 3 ---R (381) | cos(b %H + a) d%H +--R (276) | cos(b %H + a) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 432 --S 433 of 504 ---Rm0185:= a0185-r0185 ---R ---R ---R (382) ---R 1 1 ---R x - - - - ---R ++ n 3 - 3%i a n n n _ 1 n ---R 8n | cos(b %H + a) d%H + x %e 3 (%i b x ) | (-,3%i b x ) ---R ++ n ---R + ---R 1 ---R - - ---R - %i a n n _ 1 n ---R 3x %e (%i b x ) | (-,%i b x ) ---R n ---R + ---R 1 ---R - - ---R %i a n n _ 1 n ---R 3x %e (- %i b x ) | (-,- %i b x ) ---R n ---R + ---R 1 1 ---R - - - - ---R 3%i a n n n _ 1 n ---R x %e 3 (- %i b x ) | (-,- 3%i b x ) ---R n ---R / ---R 8n ---R Type: Expression Complex Integer ---R +--m0185:= a0185-r0185 --E 433 --S 434 of 504 ---Rd0185:= D(m0185,x) ---R ---R ---R (383) ---R 1 1 ---R - - - - ---R - 3%i a n n n ---R %e 3 (%i b x ) ---R + ---R 1 - n - 1 ---R - - ------- ---R - 3%i a n n - 1 n n ---R - %i b x %e 3 x (%i b x ) ---R * ---R _ 1 n ---R | (-,3%i b x ) ---R n ---R + ---R 1 - n - 1 ---R - - ------- ---R - %i a n n - %i a n - 1 n n ---R (3%e (%i b x ) - 3%i b x %e x (%i b x ) ) ---R * ---R _ 1 n ---R | (-,%i b x ) ---R n ---R + ---R 1 - n - 1 ---R - - ------- ---R %i a n n %i a n - 1 n n ---R (3%e (- %i b x ) + 3%i b x %e x (- %i b x ) ) ---R * ---R _ 1 n ---R | (-,- %i b x ) ---R n ---R + ---R 1 1 ---R - - - - ---R 3%i a n n n ---R %e 3 (- %i b x ) ---R + ---R 1 - n - 1 ---R - - ------- ---R 3%i a n n - 1 n n ---R %i b x %e 3 x (- %i b x ) ---R * ---R _ 1 n ---R | (-,- 3%i b x ) ---R n ---R + ---R 1 1 - n + 1 ---R - - n - - ------- ---R - 3%i a n n - 1 - 3%i b x n n n n ---R - 3%i b n x %e 3 x %e (%i b x ) (3%i b x ) ---R + ---R - n + 1 1 ---R n ------- - - ---R - %i a n - 1 - %i b x n n n n ---R - 3%i b n x %e x %e (%i b x ) (%i b x ) ---R + ---R - n + 1 ---R n ------- ---R %i a n - 1 %i b x n n ---R 3%i b n x %e x %e (- %i b x ) ---R + ---R 1 - n + 1 ---R - - n ------- ---R 3%i a n n - 1 3%i b x n n ---R 3%i b n x %e 3 x %e (- 3%i b x ) ---R * ---R 1 ---R - - ---R n n ---R (- %i b x ) ---R + ---R n 3 ---R 8n cos(b x + a) ---R / ---R 8n ---R Type: Expression Complex Integer ---R +--d0185:= D(m0185,x) --E 434 --S 435 of 504 ---Rt0186:= x^m*cos(a+b*x^n) +t0186:= x^m*cos(a+b*x^n) --R --R --R m n ---R (384) x cos(b x + a) +--R (277) x cos(b x + a) --R Type: Expression Integer ---R --E 435 --S 436 of 504 ---Rr0186:= -1/2*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)+exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,%i*b*x^n))/n +r0186:= -1/2*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)+exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,%i*b*x^n))/n --R --R ---R (385) +--R (278) --R - m - 1 --R ------- --R - %i a m n n _ m + 1 n @@ -18208,120 +14219,44 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 2n --R Type: Expression Complex Integer ---R --E 436 --S 437 of 504 ---Ra0186:= integrate(t0186,x) +a0186:= integrate(t0186,x) --R --R --R x --R ++ m n ---R (386) | %H cos(b %H + a)d%H +--R (279) | %H cos(b %H + a)d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 437 --S 438 of 504 ---Rm0186:= a0186-r0186 ---R ---R ---R (387) ---R x ---R ++ m n ---R 2n | %H cos(b %H + a)d%H ---R ++ ---R + ---R - m - 1 ---R ------- ---R - %i a m n n _ m + 1 n ---R x %e x (%i b x ) | (-----,%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R %i a m n n _ m + 1 n ---R x %e x (- %i b x ) | (-----,- %i b x ) ---R n ---R / ---R 2n ---R Type: Expression Complex Integer ---R +--m0186:= a0186-r0186 --E 438 --S 439 of 504 ---Rd0186:= D(m0186,x) ---R ---R ---R (388) ---R - m - 1 ---R ------- ---R - %i a m - %i a m - 1 n n ---R (%e x + m x %e x )(%i b x ) ---R + ---R - n - m - 1 ---R ----------- ---R - %i a m n - 1 n n ---R (- %i b m - %i b)x %e x x (%i b x ) ---R * ---R _ m + 1 n ---R | (-----,%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R %i a m %i a m - 1 n n ---R (%e x + m x %e x )(- %i b x ) ---R + ---R - n - m - 1 ---R ----------- ---R %i a m n - 1 n n ---R (%i b m + %i b)x %e x x (- %i b x ) ---R * ---R _ m + 1 n ---R | (-----,- %i b x ) ---R n ---R + ---R - ---R - n + m + 1 ---R n ----------- ---R - %i a m n - 1 - %i b x n n ---R %i b n x %e x x %e (%i b x ) ---R * ---R - m - 1 ---R ------- ---R n n ---R (%i b x ) ---R + ---R - n + m + 1 - m - 1 ---R n ----------- ------- ---R %i a m n - 1 %i b x n n n n ---R %i b n x %e x x %e (- %i b x ) (- %i b x ) ---R + ---R m n ---R 2n x cos(b x + a) ---R / ---R 2n ---R Type: Expression Complex Integer ---R +--d0186:= D(m0186,x) --E 439 --S 440 of 504 ---Rt0187:= x^m*cos(a+b*x^n)^2 +t0187:= x^m*cos(a+b*x^n)^2 --R --R --R m n 2 ---R (389) x cos(b x + a) +--R (280) x cos(b x + a) --R Type: Expression Integer ---R --E 440 --S 441 of 504 ---Rr0187:= x^(1+m)/(2+2*m)-2^(-2-(1+m)/n)*exp(1)^(2*%i*a)*x^(1+m)*Gamma((1+m)/n,-2*%i*b*x^n)/((-%i*b*x^n)^((1+m)/n))/n-2^(-2-(1+m)/n)*x^(1+m)*Gamma((1+m)/n,2*%i*b*x^n)/(exp(1)^(2*%i*a))/((%i*b*x^n)^((1+m)/n))/n +r0187:= x^(1+m)/(2+2*m)-2^(-2-(1+m)/n)*exp(1)^(2*%i*a)*x^(1+m)*_ + Gamma((1+m)/n,-2*%i*b*x^n)/((-%i*b*x^n)^((1+m)/n))/n-_ + 2^(-2-(1+m)/n)*x^(1+m)*_ + Gamma((1+m)/n,2*%i*b*x^n)/(exp(1)^(2*%i*a))/((%i*b*x^n)^((1+m)/n))/n --R --R ---R (390) +--R (281) --R - 2n - m - 1 m + 1 --R ------------ ----- --R n m + 1 n n _ m + 1 n @@ -18344,160 +14279,46 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2%i a n n n n --R (2m + 2)n %e (- %i b x ) (%i b x ) --R Type: Expression Complex Integer ---R --E 441 --S 442 of 504 ---Ra0187:= integrate(t0187,x) +a0187:= integrate(t0187,x) --R --R --R x --R ++ m n 2 ---R (391) | %H cos(b %H + a) d%H +--R (282) | %H cos(b %H + a) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 442 --S 443 of 504 ---Rm0187:= a0187-r0187 ---R ---R ---R (392) ---R m + 1 m + 1 ---R ----- ----- ---R 2%i a n n n n ---R (2m + 2)n %e (- %i b x ) (%i b x ) ---R * ---R x ---R ++ m n 2 ---R | %H cos(b %H + a) d%H ---R ++ ---R + ---R - 2n - m - 1 m + 1 ---R ------------ ----- ---R n m + 1 n n _ m + 1 n ---R (2m + 2)2 x (- %i b x ) | (-----,2%i b x ) ---R n ---R + ---R - 2n - m - 1 m + 1 ---R ------------ ----- ---R 2%i a 2 n m + 1 n n _ m + 1 n ---R (2m + 2)(%e ) 2 x (%i b x ) | (-----,- 2%i b x ) ---R n ---R + ---R m + 1 m + 1 ---R ----- ----- ---R 2%i a m + 1 n n n n ---R - n %e x (- %i b x ) (%i b x ) ---R / ---R m + 1 m + 1 ---R ----- ----- ---R 2%i a n n n n ---R (2m + 2)n %e (- %i b x ) (%i b x ) ---R Type: Expression Complex Integer ---R +--m0187:= a0187-r0187 --E 443 --S 444 of 504 ---Rd0187:= D(m0187,x) ---R ---R ---R (393) ---R - 2n - m - 1 m + 1 2 m + 1 ---R ------------ ----- ----- ---R n m n n n n ---R (2m + 2)2 x ((- %i b x ) ) (%i b x ) ---R + ---R - 2n - m - 1 m + 1 2 ---R ------------ ----- ---R n m + 1 n - 1 n n ---R (- 2%i b m - 2%i b)2 x x ((- %i b x ) ) ---R * ---R - n + m + 1 ---R ----------- ---R n n ---R (%i b x ) ---R * ---R _ m + 1 n ---R | (-----,2%i b x ) ---R n ---R + ---R - 2n - m - 1 m + 1 ---R ------------ ----- ---R 2%i a 2 n m n n ---R (2m + 2)(%e ) 2 x (- %i b x ) ---R + ---R - 2n - m - 1 ---R ------------ ---R 2%i a 2 n m + 1 n - 1 ---R (2%i b m + 2%i b)(%e ) 2 x x ---R * ---R - n + m + 1 ---R ----------- ---R n n ---R (- %i b x ) ---R * ---R m + 1 2 ---R ----- ---R n n _ m + 1 n ---R ((%i b x ) ) | (-----,- 2%i b x ) ---R n ---R + ---R - ---R - 2n - m - 1 m + 1 2 ---R ------------ n ----- ---R n m + 1 n - 1 - 2%i b x n n ---R 4%i b n 2 x x %e ((- %i b x ) ) ---R * ---R m + 1 - n + m + 1 ---R ----- ----------- ---R n n n n ---R (%i b x ) (2%i b x ) ---R + ---R m + 1 2 ---R ----- ---R 2%i a m n 2 2%i a m n n ---R (2n %e x cos(b x + a) - n %e x )((- %i b x ) ) ---R + ---R - 2n - m - 1 ---R ------------ n ---R 2%i a 2 n m + 1 n - 1 2%i b x ---R 4%i b n (%e ) 2 x x %e ---R * ---R - n + m + 1 m + 1 ---R ----------- ----- ---R n n n n ---R (- 2%i b x ) (- %i b x ) ---R * ---R m + 1 2 ---R ----- ---R n n ---R ((%i b x ) ) ---R / ---R m + 1 2 m + 1 2 ---R ----- ----- ---R 2%i a n n n n ---R 2n %e ((- %i b x ) ) ((%i b x ) ) ---R Type: Expression Complex Integer ---R +--d0187:= D(m0187,x) --E 444 --S 445 of 504 ---Rt0188:= x^m*cos(a+b*x^n)^3 +t0188:= x^m*cos(a+b*x^n)^3 --R --R --R m n 3 ---R (394) x cos(b x + a) +--R (283) x cos(b x + a) --R Type: Expression Integer ---R --E 445 --S 446 of 504 ---Rr0188:= -1/8*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*Gamma((1+m)/n,-3*%i*b*x^n)*exp(3*%i*a)+3*(-%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)+3*exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*Gamma((1+m)/n,%i*b*x^n)+(%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*Gamma((1+m)/n,3*%i*b*x^n)*exp(-3*%i*a))/n +r0188:= -1/8*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*_ + Gamma((1+m)/n,-3*%i*b*x^n)*exp(3*%i*a)+3*(-%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)+3*exp(-%i*a)*_ + (%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,%i*b*x^n)+(%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*_ + Gamma((1+m)/n,3*%i*b*x^n)*exp(-3*%i*a))/n --R --R ---R (395) +--R (284) --R - m - 1 - m - 1 --R ------- ------- --R - 3%i a n m n n _ m + 1 n @@ -18524,365 +14345,180 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R / --R 8n --R Type: Expression Complex Integer ---R --E 446 --S 447 of 504 ---Ra0188:= integrate(t0188,x) +a0188:= integrate(t0188,x) --R --R --R x --R ++ m n 3 ---R (396) | %H cos(b %H + a) d%H +--R (285) | %H cos(b %H + a) d%H --R ++ --R Type: Union(Expression Integer,...) ---R --E 447 --S 448 of 504 ---Rm0188:= a0188-r0188 ---R ---R ---R (397) ---R x ---R ++ m n 3 ---R 8n | %H cos(b %H + a) d%H ---R ++ ---R + ---R - m - 1 - m - 1 ---R ------- ------- ---R - 3%i a n m n n _ m + 1 n ---R x %e 3 x (%i b x ) | (-----,3%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R - %i a m n n _ m + 1 n ---R 3x %e x (%i b x ) | (-----,%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R %i a m n n _ m + 1 n ---R 3x %e x (- %i b x ) | (-----,- %i b x ) ---R n ---R + ---R - m - 1 - m - 1 ---R ------- ------- ---R 3%i a n m n n _ m + 1 n ---R x %e 3 x (- %i b x ) | (-----,- 3%i b x ) ---R n ---R / ---R 8n ---R Type: Expression Complex Integer ---R +--m0188:= a0188-r0188 --E 448 --S 449 of 504 ---Rd0188:= D(m0188,x) ---R ---R ---R (398) ---R - m - 1 - m - 1 - m - 1 ---R ------- ------- ------- ---R - 3%i a n m - 3%i a n m - 1 n n ---R (%e 3 x + m x %e 3 x )(%i b x ) ---R + ---R - m - 1 - n - m - 1 ---R ------- ----------- ---R - 3%i a n m n - 1 n n ---R (- %i b m - %i b)x %e 3 x x (%i b x ) ---R * ---R _ m + 1 n ---R | (-----,3%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R - %i a m - %i a m - 1 n n ---R (3%e x + 3m x %e x )(%i b x ) ---R + ---R - n - m - 1 ---R ----------- ---R - %i a m n - 1 n n ---R (- 3%i b m - 3%i b)x %e x x (%i b x ) ---R * ---R _ m + 1 n ---R | (-----,%i b x ) ---R n ---R + ---R - m - 1 ---R ------- ---R %i a m %i a m - 1 n n ---R (3%e x + 3m x %e x )(- %i b x ) ---R + ---R - n - m - 1 ---R ----------- ---R %i a m n - 1 n n ---R (3%i b m + 3%i b)x %e x x (- %i b x ) ---R * ---R _ m + 1 n ---R | (-----,- %i b x ) ---R n ---R + ---R - m - 1 - m - 1 - m - 1 ---R ------- ------- ------- ---R 3%i a n m 3%i a n m - 1 n n ---R (%e 3 x + m x %e 3 x )(- %i b x ) ---R + ---R - m - 1 - n - m - 1 ---R ------- ----------- ---R 3%i a n m n - 1 n n ---R (%i b m + %i b)x %e 3 x x (- %i b x ) ---R * ---R _ m + 1 n ---R | (-----,- 3%i b x ) ---R n ---R + ---R - ---R - m - 1 - m - 1 ---R ------- n ------- ---R - 3%i a n m n - 1 - 3%i b x n n ---R 3%i b n x %e 3 x x %e (%i b x ) ---R * ---R - n + m + 1 ---R ----------- ---R n n ---R (3%i b x ) ---R + ---R - ---R - n + m + 1 ---R n ----------- ---R - %i a m n - 1 - %i b x n n ---R 3%i b n x %e x x %e (%i b x ) ---R * ---R - m - 1 ---R ------- ---R n n ---R (%i b x ) ---R + ---R - n + m + 1 ---R n ----------- ---R %i a m n - 1 %i b x n n ---R 3%i b n x %e x x %e (- %i b x ) ---R + ---R - m - 1 - n + m + 1 ---R ------- n ----------- ---R 3%i a n m n - 1 3%i b x n n ---R 3%i b n x %e 3 x x %e (- 3%i b x ) ---R * ---R - m - 1 ---R ------- ---R n n ---R (- %i b x ) ---R + ---R m n 3 ---R 8n x cos(b x + a) ---R / ---R 8n ---R Type: Expression Complex Integer ---R +--d0188:= D(m0188,x) --E 449 --S 450 of 504 ---Rt0189:= x/cos(x)^(3/2)+x*cos(x)^(1/2) +t0189:= x/cos(x)^(3/2)+x*cos(x)^(1/2) --R --R --R 2 --R x cos(x) + x ---R (399) --------------- +--R (286) --------------- --R +------+ --R cos(x)\|cos(x) --R Type: Expression Integer ---R --E 450 --S 451 of 504 ---Rr0189:= 2*(2*cos(x)+x*sin(x))/cos(x)^(1/2) +r0189:= 2*(2*cos(x)+x*sin(x))/cos(x)^(1/2) --R --R --R 2x sin(x) + 4cos(x) ---R (400) ------------------- +--R (287) ------------------- --R +------+ --R \|cos(x) --R Type: Expression Integer ---R --E 451 --S 452 of 504 ---Ra0189:= integrate(t0189,x) +a0189:= integrate(t0189,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 452 --S 453 of 504 ---Rm0189:= a0189-r0189 ---R ---R ---R +------+ ---R a0189\|cos(x) - 2x sin(x) - 4cos(x) ---R (401) ------------------------------------ ---R +------+ ---R \|cos(x) ---R Type: Expression Integer ---R +--m0189:= a0189-r0189 --E 453 --S 454 of 504 ---Rd0189:= D(m0189,x) ---R ---R ---R 2 2 ---R - x sin(x) - 2x cos(x) ---R (402) ------------------------ ---R +------+ ---R cos(x)\|cos(x) ---R Type: Expression Integer ---R +--d0189:= D(m0189,x) --E 454 --S 455 of 504 ---Rt0190:= x/cos(x)^(5/2)-1/3*x/cos(x)^(1/2) +t0190:= x/cos(x)^(5/2)-1/3*x/cos(x)^(1/2) --R --R --R 2 --R - x cos(x) + 3x ---R (403) ----------------- +--R (288) ----------------- --R 2 +------+ --R 3cos(x) \|cos(x) --R Type: Expression Integer ---R --E 455 --S 456 of 504 ---Rr0190:= -2/3*(2*cos(x)-x*sin(x))/cos(x)^(3/2) +r0190:= -2/3*(2*cos(x)-x*sin(x))/cos(x)^(3/2) --R --R --R 2x sin(x) - 4cos(x) ---R (404) ------------------- +--R (289) ------------------- --R +------+ --R 3cos(x)\|cos(x) --R Type: Expression Integer ---R --E 456 --S 457 of 504 ---Ra0190:= integrate(t0190,x) +a0190:= integrate(t0190,x) --R --R --R +------+ --R (2x sin(x) - 4cos(x))\|cos(x) ---R (405) ------------------------------ +--R (290) ------------------------------ --R 2 --R 3cos(x) --R Type: Union(Expression Integer,...) ---R --E 457 --S 458 of 504 ---Rm0190:= a0190-r0190 +m0190:= a0190-r0190 --R --R ---R (406) 0 +--R (291) 0 --R Type: Expression Integer ---R --E 458 --S 459 of 504 ---Rd0190:= D(m0190,x) +d0190:= D(m0190,x) --R --R ---R (407) 0 +--R (292) 0 --R Type: Expression Integer ---R --E 459 --S 460 of 504 ---Rt0191:= x/cos(x)^(7/2)+3/5*x*cos(x)^(1/2) +t0191:= x/cos(x)^(7/2)+3/5*x*cos(x)^(1/2) --R --R --R 4 --R 3x cos(x) + 5x ---R (408) ----------------- +--R (293) ----------------- --R 3 +------+ --R 5cos(x) \|cos(x) --R Type: Expression Integer ---R --E 460 --S 461 of 504 ---Rr0191:= 2/15*(-2*cos(x)+18*cos(x)^3+3*x*sin(x)+9*x*sin(x)*cos(x)^2)/cos(x)^(5/2) +r0191:= 2/15*(-2*cos(x)+18*cos(x)^3+_ + 3*x*sin(x)+9*x*sin(x)*cos(x)^2)/cos(x)^(5/2) --R --R --R 2 3 --R (18x cos(x) + 6x)sin(x) + 36cos(x) - 4cos(x) ---R (409) ---------------------------------------------- +--R (294) ---------------------------------------------- --R 2 +------+ --R 15cos(x) \|cos(x) --R Type: Expression Integer ---R --E 461 --S 462 of 504 ---Ra0191:= integrate(t0191,x) +a0191:= integrate(t0191,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 462 --S 463 of 504 ---Rm0191:= a0191-r0191 ---R ---R ---R (410) ---R 2 +------+ 2 3 ---R 15a0191 cos(x) \|cos(x) + (- 18x cos(x) - 6x)sin(x) - 36cos(x) + 4cos(x) ---R --------------------------------------------------------------------------- ---R 2 +------+ ---R 15cos(x) \|cos(x) ---R Type: Expression Integer ---R +--m0191:= a0191-r0191 --E 463 --S 464 of 504 ---Rd0191:= D(m0191,x) ---R ---R ---R 2 2 4 2 ---R (- 3x cos(x) - 5x)sin(x) - 6x cos(x) - 2x cos(x) ---R (411) ---------------------------------------------------- ---R 3 +------+ ---R 5cos(x) \|cos(x) ---R Type: Expression Integer ---R +--d0191:= D(m0191,x) --E 464 --S 465 of 504 ---Rt0192:= x^2/cos(x)^(3/2)+x^2*cos(x)^(1/2) +t0192:= x^2/cos(x)^(3/2)+x^2*cos(x)^(1/2) --R --R --R 2 2 2 --R x cos(x) + x ---R (412) --------------- +--R (295) --------------- --R +------+ --R cos(x)\|cos(x) --R Type: Expression Integer ---R --E 465 --S 466 of 504 ---Rr0192:= 8*x*cos(x)^(1/2)-16*EllipticE(1/2*x,2)+2*x^2*sin(x)/cos(x)^(1/2) +r0192:= 8*x*cos(x)^(1/2)-16*EllipticE(1/2*x,2)+2*x^2*sin(x)/cos(x)^(1/2) --R --R There are no library operations named EllipticE --R Use HyperDoc Browse or issue @@ -18890,6 +14526,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Polynomial Fraction Integer @@ -18897,80 +14534,66 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R --R Perhaps you should use "@" to indicate the required return type, --R or "$" to specify which version of the function you need. ---R --E 466 --S 467 of 504 ---Ra0192:= integrate(t0192,x) +a0192:= integrate(t0192,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R --R Continuing to read the file... --R ---R --E 467 --S 468 of 504 ---Rm0192:= a0192-r0192 ---R ---R ---R (413) - r0192 + a0192 ---R Type: Polynomial Integer ---R +--m0192:= a0192-r0192 --E 468 --S 469 of 504 ---Rd0192:= D(m0192,x) ---R ---R ---R (414) 0 ---R Type: Polynomial Integer ---R +--d0192:= D(m0192,x) --E 469 --S 470 of 504 ---Rt0193:= cos(a+b*log(c*x^n)) +t0193:= cos(a+b*log(c*x^n)) --R --R --R n ---R (415) cos(b log(c x ) + a) +--R (296) cos(b log(c x ) + a) --R Type: Expression Integer ---R --E 470 --S 471 of 504 ---Rr0193:= x*(cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(1+b^2*n^2) +r0193:= x*(cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(1+b^2*n^2) --R --R --R n n --R b n x sin(b log(c x ) + a) + x cos(b log(c x ) + a) ---R (416) --------------------------------------------------- +--R (297) --------------------------------------------------- --R 2 2 --R b n + 1 --R Type: Expression Integer ---R --E 471 --S 472 of 504 ---Ra0193:= integrate(t0193,x) +a0193:= integrate(t0193,x) --R --R ---R (417) +--R (298) --R b n x sin(b n log(x) + b log(c) + a) + x cos(b n log(x) + b log(c) + a) --R ----------------------------------------------------------------------- --R 2 2 --R b n + 1 --R Type: Union(Expression Integer,...) ---R --E 472 --S 473 of 504 ---Rm0193:= a0193-r0193 +m0193:= a0193-r0193 --R --R ---R (418) +--R (299) --R n n --R - b n x sin(b log(c x ) + a) - x cos(b log(c x ) + a) --R + @@ -18979,14 +14602,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R b n + 1 --R Type: Expression Integer ---R --E 473 --S 474 of 504 ---Rd0193:= D(m0193,x) +d0193:= D(m0193,x) --R --R ---R (419) +--R (300) --R n n - 1 n --R (- b n x + b n x x )sin(b log(c x ) + a) --R + @@ -18999,51 +14621,47 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 n --R (b n + 1)x --R Type: Expression Integer ---R --E 474 --S 475 of 504 ---Rt0194:= x*cos(a+b*log(c*x^n)) +t0194:= x*cos(a+b*log(c*x^n)) --R --R --R n ---R (420) x cos(b log(c x ) + a) +--R (301) x cos(b log(c x ) + a) --R Type: Expression Integer ---R --E 475 --S 476 of 504 ---Rr0194:= x^2*(2*cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(4+b^2*n^2) +r0194:= x^2*(2*cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(4+b^2*n^2) --R --R --R 2 n 2 n --R b n x sin(b log(c x ) + a) + 2x cos(b log(c x ) + a) ---R (421) ---------------------------------------------------- +--R (302) ---------------------------------------------------- --R 2 2 --R b n + 4 --R Type: Expression Integer ---R --E 476 --S 477 of 504 ---Ra0194:= integrate(t0194,x) +a0194:= integrate(t0194,x) --R --R ---R (422) +--R (303) --R 2 2 --R b n x sin(b n log(x) + b log(c) + a) + 2x cos(b n log(x) + b log(c) + a) --R ------------------------------------------------------------------------ --R 2 2 --R b n + 4 --R Type: Union(Expression Integer,...) ---R --E 477 --S 478 of 504 ---Rm0194:= a0194-r0194 +m0194:= a0194-r0194 --R --R ---R (423) +--R (304) --R 2 n 2 n --R - b n x sin(b log(c x ) + a) - 2x cos(b log(c x ) + a) --R + @@ -19053,14 +14671,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R b n + 4 --R Type: Expression Integer ---R --E 478 --S 479 of 504 ---Rd0194:= D(m0194,x) +d0194:= D(m0194,x) --R --R ---R (424) +--R (305) --R n 2 n - 1 n --R (- 2b n x x + 2b n x x )sin(b log(c x ) + a) --R + @@ -19073,51 +14690,47 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 n --R (b n + 4)x --R Type: Expression Integer ---R --E 479 --S 480 of 504 ---Rt0195:= x^2*cos(a+b*log(c*x^n)) +t0195:= x^2*cos(a+b*log(c*x^n)) --R --R --R 2 n ---R (425) x cos(b log(c x ) + a) +--R (306) x cos(b log(c x ) + a) --R Type: Expression Integer ---R --E 480 --S 481 of 504 ---Rr0195:= x^3*(3*cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(9+b^2*n^2) +r0195:= x^3*(3*cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(9+b^2*n^2) --R --R --R 3 n 3 n --R b n x sin(b log(c x ) + a) + 3x cos(b log(c x ) + a) ---R (426) ---------------------------------------------------- +--R (307) ---------------------------------------------------- --R 2 2 --R b n + 9 --R Type: Expression Integer ---R --E 481 --S 482 of 504 ---Ra0195:= integrate(t0195,x) +a0195:= integrate(t0195,x) --R --R ---R (427) +--R (308) --R 3 3 --R b n x sin(b n log(x) + b log(c) + a) + 3x cos(b n log(x) + b log(c) + a) --R ------------------------------------------------------------------------ --R 2 2 --R b n + 9 --R Type: Union(Expression Integer,...) ---R --E 482 --S 483 of 504 ---Rm0195:= a0195-r0195 +m0195:= a0195-r0195 --R --R ---R (428) +--R (309) --R 3 n 3 n --R - b n x sin(b log(c x ) + a) - 3x cos(b log(c x ) + a) --R + @@ -19127,14 +14740,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R b n + 9 --R Type: Expression Integer ---R --E 483 --S 484 of 504 ---Rd0195:= D(m0195,x) +d0195:= D(m0195,x) --R --R ---R (429) +--R (310) --R 2 n 3 n - 1 n --R (- 3b n x x + 3b n x x )sin(b log(c x ) + a) --R + @@ -19147,52 +14759,48 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 n --R (b n + 9)x --R Type: Expression Integer ---R --E 484 --S 485 of 504 ---Rt0196:= cos(a+b*log(c*x^n))/x^2 +t0196:= cos(a+b*log(c*x^n))/x^2 --R --R --R n --R cos(b log(c x ) + a) ---R (430) -------------------- +--R (311) -------------------- --R 2 --R x --R Type: Expression Integer ---R --E 485 --S 486 of 504 ---Rr0196:= -1/(1+b^2*n^2)/x*(cos(a+b*log(c*x^n))-b*n*sin(a+b*log(c*x^n))) +r0196:= -1/(1+b^2*n^2)/x*(cos(a+b*log(c*x^n))-b*n*sin(a+b*log(c*x^n))) --R --R --R n n --R b n sin(b log(c x ) + a) - cos(b log(c x ) + a) ---R (431) ----------------------------------------------- +--R (312) ----------------------------------------------- --R 2 2 --R (b n + 1)x --R Type: Expression Integer ---R --E 486 --S 487 of 504 ---Ra0196:= integrate(t0196,x) +a0196:= integrate(t0196,x) --R --R --R b n sin(b n log(x) + b log(c) + a) - cos(b n log(x) + b log(c) + a) ---R (432) ------------------------------------------------------------------- +--R (313) ------------------------------------------------------------------- --R 2 2 --R (b n + 1)x --R Type: Union(Expression Integer,...) ---R --E 487 --S 488 of 504 ---Rm0196:= a0196-r0196 +m0196:= a0196-r0196 --R --R ---R (433) +--R (314) --R n n --R - b n sin(b log(c x ) + a) + cos(b log(c x ) + a) --R + @@ -19201,14 +14809,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R (b n + 1)x --R Type: Expression Integer ---R --E 488 --S 489 of 504 ---Rd0196:= D(m0196,x) +d0196:= D(m0196,x) --R --R ---R (434) +--R (315) --R n n - 1 n --R (b n x - b n x x )sin(b log(c x ) + a) --R + @@ -19221,37 +14828,35 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 2 n --R (b n + 1)x x --R Type: Expression Integer ---R --E 489 --S 490 of 504 ---Rt0197:= x^m*cos(a+b*log(c*x^n)) +t0197:= x^m*cos(a+b*log(c*x^n)) --R --R --R m n ---R (435) x cos(b log(c x ) + a) +--R (316) x cos(b log(c x ) + a) --R Type: Expression Integer ---R --E 490 --S 491 of 504 ---Rr0197:= (1+m)*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)+b*n*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+b^2*n^2) +r0197:= (1+m)*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)+_ + b*n*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+b^2*n^2) --R --R --R m + 1 n m + 1 n --R b n x sin(b log(c x ) + a) + (m + 1)x cos(b log(c x ) + a) ---R (436) ------------------------------------------------------------------ +--R (317) ------------------------------------------------------------------ --R 2 2 2 --R b n + m + 2m + 1 --R Type: Expression Integer ---R --E 491 --S 492 of 504 ---Ra0197:= integrate(t0197,x) +a0197:= integrate(t0197,x) --R --R ---R (437) +--R (318) --R m log(x) --R b n x %e sin(b n log(x) + b log(c) + a) --R + @@ -19261,14 +14866,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 2 --R b n + m + 2m + 1 --R Type: Union(Expression Integer,...) ---R --E 492 --S 493 of 504 ---Rm0197:= a0197-r0197 +m0197:= a0197-r0197 --R --R ---R (438) +--R (319) --R m + 1 n m + 1 n --R - b n x sin(b log(c x ) + a) + (- m - 1)x cos(b log(c x ) + a) --R + @@ -19281,14 +14885,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 2 --R b n + m + 2m + 1 --R Type: Expression Integer ---R --E 493 --S 494 of 504 ---Rd0197:= D(m0197,x) +d0197:= D(m0197,x) --R --R ---R (439) +--R (320) --R m n m + 1 n - 1 n --R ((- b m - b)n x x + (b m + b)n x x )sin(b log(c x ) + a) --R + @@ -19301,24 +14904,23 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 2 n --R (b n + m + 2m + 1)x --R Type: Expression Integer ---R --E 494 --S 495 of 504 ---Rt0198:= cos(a+b*log(c*x^n))^2 +t0198:= cos(a+b*log(c*x^n))^2 --R --R --R n 2 ---R (440) cos(b log(c x ) + a) +--R (321) cos(b log(c x ) + a) --R Type: Expression Integer ---R --E 495 --S 496 of 504 ---Rr0198:= x*(2*b^2*n^2+cos(a+b*log(c*x^n))^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n)))/(1+4*b^2*n^2) +r0198:= x*(2*b^2*n^2+cos(a+b*log(c*x^n))^2+_ + 2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n)))/(1+4*b^2*n^2) --R --R ---R (441) +--R (322) --R n n n 2 --R 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) + x cos(b log(c x ) + a) --R + @@ -19328,14 +14930,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 4b n + 1 --R Type: Expression Integer ---R --E 496 --S 497 of 504 ---Ra0198:= integrate(t0198,x) +a0198:= integrate(t0198,x) --R --R ---R (442) +--R (323) --R 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) --R + --R 2 2 2 @@ -19344,14 +14945,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 4b n + 1 --R Type: Union(Expression Integer,...) ---R --E 497 --S 498 of 504 ---Rm0198:= a0198-r0198 +m0198:= a0198-r0198 --R --R ---R (443) +--R (324) --R n n --R - 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) --R + @@ -19366,14 +14966,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 4b n + 1 --R Type: Expression Integer ---R --E 498 --S 499 of 504 ---Rd0198:= D(m0198,x) +d0198:= D(m0198,x) --R --R ---R (444) +--R (325) --R 2 2 n - 1 n 2 --R 2b n x x sin(b log(c x ) + a) --R + @@ -19392,24 +14991,23 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 n --R (4b n + 1)x --R Type: Expression Integer ---R --E 499 --S 500 of 504 ---Rt0199:= x*cos(a+b*log(c*x^n))^2 +t0199:= x*cos(a+b*log(c*x^n))^2 --R --R --R n 2 ---R (445) x cos(b log(c x ) + a) +--R (326) x cos(b log(c x ) + a) --R Type: Expression Integer ---R --E 500 --S 501 of 504 ---Rr0199:= 1/4/(1+b^2*n^2)*x^2*(b^2*n^2+2*cos(a+b*log(c*x^n))^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))) +r0199:= 1/4/(1+b^2*n^2)*x^2*(b^2*n^2+2*cos(a+b*log(c*x^n))^2+_ + 2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))) --R --R ---R (446) +--R (327) --R 2 n n --R 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) --R + @@ -19419,14 +15017,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 4b n + 4 --R Type: Expression Integer ---R --E 501 --S 502 of 504 ---Ra0199:= integrate(t0199,x) +a0199:= integrate(t0199,x) --R --R ---R (447) +--R (328) --R 2 --R 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) --R + @@ -19436,14 +15033,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 4b n + 4 --R Type: Union(Expression Integer,...) ---R --E 502 --S 503 of 504 ---Rm0199:= a0199-r0199 +m0199:= a0199-r0199 --R --R ---R (448) +--R (329) --R 2 n n --R - b n x cos(b log(c x ) + a)sin(b log(c x ) + a) --R + @@ -19459,14 +15055,13 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R 2 2 --R 2b n + 2 --R Type: Expression Integer ---R --E 503 --S 504 of 504 ---Rd0199:= D(m0199,x) +d0199:= D(m0199,x) --R --R ---R (449) +--R (330) --R 2 2 2 n - 1 n 2 --R b n x x sin(b log(c x ) + a) --R + @@ -19487,7 +15082,7 @@ t0100:= x*sin(a+b*log(c*x^n))^2 --R Type: Expression Integer --E 504 )spool - + \end{chunk} \eject \begin{thebibliography}{99}