diff --git a/changelog b/changelog index bbe9b39..ab1d5a2 100644 --- a/changelog +++ b/changelog @@ -1,5 +1,8 @@ -20100618 tpd src/axiom-website/patches.html 20100619.02.tpd.patch -20100618 tpd src/input/richhyper1000-1098.input rule-based hyper integration +20100619 tpd src/axiom-website/patches.html 20100619.03.tpd.patch +20100619 tpd src/input/Makefile rule-based inverse hyperbolic integration +20100619 tpd src/input/richinvhyper000-099.input inverse hyperbolic int. +20100619 tpd src/axiom-website/patches.html 20100619.02.tpd.patch +20100619 tpd src/input/richhyper1000-1098.input rule-based hyper integration 20100618 tpd src/axiom-website/patches.html 20100619.01.tpd.patch 20100619 tpd books/bookvol5 change )version to include *build-version* info 20100618 tpd src/axiom-website/patches.html 20100618.02.tpd.patch diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 6cddd5f..95601e2 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2922,6 +2922,9 @@ src/input/richinvtrig000-092.input rule-based inverse trig int.
books/bookvol5 change )version to include *build-version* info
20100619.02.tpd.patch src/input/richhyper1000-1098.input rule-based hyper integration
+20100619.03.tpd.patch +src/input/richinvhyper000-099.input inverse hyperbolic integration
+ diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 0b9bcb6..5ea8f2a 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -386,6 +386,7 @@ REGRES= ackermann.regress \ richhyper800-899.regress \ richhyper900-999.regress \ richhyper1000-1098.regress \ + richinvhyper000-099.regress \ richinvtrig000-092.regress \ richlog000-099.regress \ richlog100-199.regress \ @@ -731,6 +732,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richhyper800-899.input \ ${OUT}/richhyper900-999.input \ ${OUT}/richhyper1000-1098.input \ + ${OUT}/richinvhyper000-099.input \ ${OUT}/richinvtrig000-092.input \ ${OUT}/richlog000-099.input \ ${OUT}/richlog100-199.input \ @@ -1105,6 +1107,7 @@ DOCFILES= \ ${DOC}/richhyper800-899.input.dvi \ ${DOC}/richhyper900-999.input.dvi \ ${DOC}/richhyper1000-1098.input.dvi \ + ${DOC}/richinvhyper000-099.input.dvi \ ${DOC}/richinvtrig000-092.input.dvi \ ${DOC}/richlog000-099.input.dvi \ ${DOC}/richlog100-199.input.dvi \ diff --git a/src/input/richinvhyper000-099.input.pamphlet b/src/input/richinvhyper000-099.input.pamphlet new file mode 100644 index 0000000..0b091d1 --- /dev/null +++ b/src/input/richinvhyper000-099.input.pamphlet @@ -0,0 +1,9336 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richinvhyper000-099.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richinvhyper000-099.output +)spool richinvhyper000-099.output +)set message auto off +)clear all + +--S 1 of 510 +t0000:= asinh(x)^2 +--R +--R +--R 2 +--R (1) asinh(x) +--R Type: Expression Integer +--E 1 + +--S 2 of 510 +r0000:= 2*x-2*(1+x^2)^(1/2)*asinh(x)+x*asinh(x)^2 +--R +--R +--R +------+ +--R | 2 2 +--R (2) - 2asinh(x)\|x + 1 + x asinh(x) + 2x +--R Type: Expression Integer +--E 2 + +--S 3 of 510 +a0000:= integrate(t0000,x) +--R +--R +--R (3) +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (2x\|x + 1 - 2x - 2)log(\|x + 1 + x) + 2x\|x + 1 - 2x +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 510 +m0000:= a0000-r0000 +--R +--R +--R (4) +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x + 1 - 2x - 2)log(\|x + 1 + x) +--R + +--R +------+ +--R 2 | 2 2 2 2 +--R (- x asinh(x) - 2x asinh(x))\|x + 1 + x asinh(x) + (2x + 2)asinh(x) +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Expression Integer +--E 4 + +--S 5 of 510 +d0000:= D(m0000,x) +--R +--R +--R +------+ 2 +--R | 2 2 +--R (5) log(\|x + 1 + x) - asinh(x) +--R Type: Expression Integer +--E 5 + +--S 6 of 510 +t0001:= asinh(x)^3 +--R +--R +--R 3 +--R (6) asinh(x) +--R Type: Expression Integer +--E 6 + +--S 7 of 510 +r0001:= -6*(1+x^2)^(1/2)+6*x*asinh(x)-3*(1+x^2)^(1/2)*asinh(x)^2+x*asinh(x)^3 +--R +--R +--R +------+ +--R 2 | 2 3 +--R (7) (- 3asinh(x) - 6)\|x + 1 + x asinh(x) + 6x asinh(x) +--R Type: Expression Integer +--E 7 + +--S 8 of 510 +a0001:= integrate(t0001,x) +--R +--R +--R (8) +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (3x\|x + 1 - 3x - 3)log(\|x + 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (6x\|x + 1 - 6x )log(\|x + 1 + x) + 6x\|x + 1 - 6x - 6 +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 510 +m0001:= a0001-r0001 +--R +--R +--R (9) +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (3x\|x + 1 - 3x - 3)log(\|x + 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (6x\|x + 1 - 6x )log(\|x + 1 + x) +--R + +--R +------+ +--R 3 2 | 2 2 3 +--R (- x asinh(x) - 3x asinh(x) - 6x asinh(x))\|x + 1 + x asinh(x) +--R + +--R 2 2 2 +--R (3x + 3)asinh(x) + 6x asinh(x) +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Expression Integer +--E 9 + +--S 10 of 510 +d0001:= D(m0001,x) +--R +--R +--R +------+ 3 +--R | 2 3 +--R (10) log(\|x + 1 + x) - asinh(x) +--R Type: Expression Integer +--E 10 + +--S 11 of 510 +t0002:= asinh(x)^4 +--R +--R +--R 4 +--R (11) asinh(x) +--R Type: Expression Integer +--E 11 + +--S 12 of 510 +r0002:= 24*x-24*(1+x^2)^(1/2)*asinh(x)+12*x*asinh(x)^2-_ + 4*(1+x^2)^(1/2)*asinh(x)^3+x*asinh(x)^4 +--R +--R +--R (12) +--R +------+ +--R 3 | 2 4 2 +--R (- 4asinh(x) - 24asinh(x))\|x + 1 + x asinh(x) + 12x asinh(x) + 24x +--R Type: Expression Integer +--E 12 + +--S 13 of 510 +a0002:= integrate(t0002,x) +--R +--R +--R (13) +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (4x\|x + 1 - 4x - 4)log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (12x\|x + 1 - 12x )log(\|x + 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (24x\|x + 1 - 24x - 24)log(\|x + 1 + x) + 24x\|x + 1 - 24x +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 510 +m0002:= a0002-r0002 +--R +--R +--R (14) +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (4x\|x + 1 - 4x - 4)log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (12x\|x + 1 - 12x )log(\|x + 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (24x\|x + 1 - 24x - 24)log(\|x + 1 + x) +--R + +--R +------+ +--R 4 3 2 | 2 +--R (- x asinh(x) - 4x asinh(x) - 12x asinh(x) - 24x asinh(x))\|x + 1 +--R + +--R 2 4 2 3 2 2 2 +--R x asinh(x) + (4x + 4)asinh(x) + 12x asinh(x) + (24x + 24)asinh(x) +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Expression Integer +--E 14 + +--S 15 of 510 +d0002:= D(m0002,x) +--R +--R +--R +------+ 4 +--R | 2 4 +--R (15) log(\|x + 1 + x) - asinh(x) +--R Type: Expression Integer +--E 15 + +--S 16 of 510 +t0003:= asinh(x)^5 +--R +--R +--R 5 +--R (16) asinh(x) +--R Type: Expression Integer +--E 16 + +--S 17 of 510 +r0003:= -120*(1+x^2)^(1/2)+120*x*asinh(x)-60*(1+x^2)^(1/2)*asinh(x)^2+_ + 20*x*asinh(x)^3-5*(1+x^2)^(1/2)*asinh(x)^4+x*asinh(x)^5 +--R +--R +--R (17) +--R +------+ +--R 4 2 | 2 5 3 +--R (- 5asinh(x) - 60asinh(x) - 120)\|x + 1 + x asinh(x) + 20x asinh(x) +--R + +--R 120x asinh(x) +--R Type: Expression Integer +--E 17 + +--S 18 of 510 +a0003:= integrate(t0003,x) +--R +--R +--R (18) +--R +------+ +------+ 5 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (5x\|x + 1 - 5x - 5)log(\|x + 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (20x\|x + 1 - 20x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (60x\|x + 1 - 60x - 60)log(\|x + 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (120x\|x + 1 - 120x )log(\|x + 1 + x) + 120x\|x + 1 - 120x - 120 +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 510 +m0003:= a0003-r0003 +--R +--R +--R (19) +--R +------+ +------+ 5 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (5x\|x + 1 - 5x - 5)log(\|x + 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (20x\|x + 1 - 20x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (60x\|x + 1 - 60x - 60)log(\|x + 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (120x\|x + 1 - 120x )log(\|x + 1 + x) +--R + +--R 5 4 3 2 +--R - x asinh(x) - 5x asinh(x) - 20x asinh(x) - 60x asinh(x) +--R + +--R - 120x asinh(x) +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 2 5 2 4 2 3 2 2 +--R x asinh(x) + (5x + 5)asinh(x) + 20x asinh(x) + (60x + 60)asinh(x) +--R + +--R 2 +--R 120x asinh(x) +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Expression Integer +--E 19 + +--S 20 of 510 +d0003:= D(m0003,x) +--R +--R +--R +------+ 5 +--R | 2 5 +--R (20) log(\|x + 1 + x) - asinh(x) +--R Type: Expression Integer +--E 20 + +--S 21 of 510 +t0004:= 1/asinh(x) +--R +--R +--R 1 +--R (21) -------- +--R asinh(x) +--R Type: Expression Integer +--E 21 + +--S 22 of 510 +r0004:= Chi(asinh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R 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. +--E 22 + +--S 23 of 510 +a0004:= integrate(t0004,x) +--R +--R +--R x +--R ++ 1 +--R (22) | --------- d%P +--R ++ asinh(%P) +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 510 +--m0004:= a0004-r0004 +--E 24 + +--S 25 of 510 +--d0004:= D(m0004,x) +--E 25 + +--S 26 of 510 +t0005:= 1/asinh(x)^2 +--R +--R +--R 1 +--R (23) --------- +--R 2 +--R asinh(x) +--R Type: Expression Integer +--E 26 + +--S 27 of 510 +r0005:= -(1+x^2)^(1/2)/asinh(x)+Shi(asinh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 510 +a0005:= integrate(t0005,x) +--R +--R +--R x +--R ++ 1 +--R (24) | ---------- d%P +--R ++ 2 +--R asinh(%P) +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 510 +--m0005:= a0005-r0005 +--E 29 + +--S 30 of 510 +--d0005:= D(m0005,x) +--E 30 + +--S 31 of 510 +t0006:= 1/asinh(x)^3 +--R +--R +--R 1 +--R (25) --------- +--R 3 +--R asinh(x) +--R Type: Expression Integer +--E 31 + +--S 32 of 510 +r0006:= 1/2*(-(1+x^2)^(1/2)-x*asinh(x)+Chi(asinh(x))*asinh(x)^2)/asinh(x)^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 510 +a0006:= integrate(t0006,x) +--R +--R +--R x +--R ++ 1 +--R (26) | ---------- d%P +--R ++ 3 +--R asinh(%P) +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 510 +--m0006:= a0006-r0006 +--E 34 + +--S 35 of 510 +--d0006:= D(m0006,x) +--E 35 + +--S 36 of 510 +t0007:= asinh(a*x)/x +--R +--R +--R asinh(a x) +--R (27) ---------- +--R x +--R Type: Expression Integer +--E 36 + +--S 37 of 510 +r0007:= 1/2*asinh(a*x)^2+asinh(a*x)*log(1-exp(1)^(-2*asinh(a*x)))-_ + 1/2*polylog(2,exp(1)^(-2*asinh(a*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--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. +--E 37 + +--S 38 of 510 +a0007:= integrate(t0007,x) +--R +--R +--R x +--R ++ asinh(%P a) +--R (28) | ----------- d%P +--R ++ %P +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 510 +--m0007:= a0007-r0007 +--E 39 + +--S 40 of 510 +--d0007:= D(m0007,x) +--E 40 + +--S 41 of 510 +t0008:= 1/(a+b*asinh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (29) ----------------------- +--R +--------------------+ +--R \|b asinh(d x + c) + a +--R Type: Expression Integer +--E 41 + +--S 42 of 510 +r0008:= -1/2*%pi^(1/2)*(-exp(2*a/b)*erf((a+b*asinh(c+d*x))^(1/2)/b^(1/2))+_ + %i*erf(%i*(a+b*asinh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d +--R +--R +--R (30) +--R a 2a +--R - - -- +--------------------+ +--R b b +---+ \|b asinh(d x + c) + a +--R %e %e \|%pi erf(-----------------------) +--R +-+ +--R \|b +--R + +--R a +--R - - +--------------------+ +--R b +---+ %i\|b asinh(d x + c) + a +--R - %i %e \|%pi erf(-------------------------) +--R +-+ +--R \|b +--R / +--R +-+ +--R 2d\|b +--R Type: Expression Complex Integer +--E 42 + +--S 43 of 510 +a0008:= integrate(t0008,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 43 + +--S 44 of 510 +--m0008:= a0008-r0008 +--E 44 + +--S 45 of 510 +--d0008:= D(m0008,x) +--E 45 + +--S 46 of 510 +t0009:= 1/(a-b*asinh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (31) ------------------------- +--R +----------------------+ +--R \|- b asinh(d x + c) + a +--R Type: Expression Integer +--E 46 + +--S 47 of 510 +r0009:= -1/2*%pi^(1/2)*(exp(2*a/b)*erf((a-b*asinh(c+d*x))^(1/2)/b^(1/2))-_ + %i*erf(%i*(a-b*asinh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d +--R +--R +--R (32) +--R a 2a +--R - - -- +----------------------+ +--R b b +---+ \|- b asinh(d x + c) + a +--R - %e %e \|%pi erf(-------------------------) +--R +-+ +--R \|b +--R + +--R a +--R - - +----------------------+ +--R b +---+ %i\|- b asinh(d x + c) + a +--R %i %e \|%pi erf(---------------------------) +--R +-+ +--R \|b +--R / +--R +-+ +--R 2d\|b +--R Type: Expression Complex Integer +--E 47 + +--S 48 of 510 +a0009:= integrate(t0009,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 48 + +--S 49 of 510 +--m0009:= a0009-r0009 +--E 49 + +--S 50 of 510 +--d0009:= D(m0009,x) +--E 50 + +--S 51 of 510 +t0010:= asinh(x^(1/2))/x +--R +--R +--R +-+ +--R asinh(\|x ) +--R (33) ----------- +--R x +--R Type: Expression Integer +--E 51 + +--S 52 of 510 +r0010:= asinh(x^(1/2))^2+2*asinh(x^(1/2))*log(1-exp(1)^(-2*asinh(x^(1/2))))-_ + polylog(2,exp(1)^(-2*asinh(x^(1/2)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--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. +--E 52 + +--S 53 of 510 +a0010:= integrate(t0010,x) +--R +--R +--R x +--+ +--R ++ asinh(\|%P ) +--R (34) | ------------ d%P +--R ++ %P +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 510 +--m0010:= a0010-r0010 +--E 54 + +--S 55 of 510 +--d0010:= D(m0010,x) +--E 55 + +--S 56 of 510 +t0011:= acosh(x)^2 +--R +--R +--R 2 +--R (35) acosh(x) +--R Type: Expression Integer +--E 56 + +--S 57 of 510 +r0011:= 2*x-2*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)+x*acosh(x)^2 +--R +--R +--R +-----+ +-----+ 2 +--R (36) - 2acosh(x)\|x - 1 \|x + 1 + x acosh(x) + 2x +--R Type: Expression Integer +--E 57 + +--S 58 of 510 +a0011:= integrate(t0011,x) +--R +--R +--R (37) +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (2x\|x - 1 - 2x + 2)log(\|x - 1 + x) + 2x\|x - 1 - 2x +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 510 +m0011:= a0011-r0011 +--R +--R +--R (38) +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x - 1 - 2x + 2)log(\|x - 1 + x) +--R + +--R +------+ +--R +-----+ +-----+ 2 | 2 +--R (2acosh(x)\|x - 1 \|x + 1 - x acosh(x) )\|x - 1 +--R + +--R +-----+ +-----+ 2 2 +--R - 2x acosh(x)\|x - 1 \|x + 1 + x acosh(x) +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Expression Integer +--E 59 + +--S 60 of 510 +d0011:= D(m0011,x) +--R +--R +--R (39) +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) +--R * +--R +------+ 2 +--R | 2 +--R log(\|x - 1 + x) +--R + +--R 2 2 2 2 +-----+ +-----+ +--R ((- 2x + 1)acosh(x) + 4x acosh(x) - 4x + 2)\|x - 1 \|x + 1 +--R + +--R 3 3 +--R (4x - 2x)acosh(x) - 4x + 4x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 3 2 3 3 +-----+ +-----+ +--R ((2x - 2x)acosh(x) + (- 4x + 2x)acosh(x) + 4x - 4x)\|x - 1 \|x + 1 +--R + +--R 4 2 4 2 +--R (- 4x + 4x )acosh(x) + 4x - 6x + 2 +--R / +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R (2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 60 + +--S 61 of 510 +t0012:= acosh(x)^3 +--R +--R +--R 3 +--R (40) acosh(x) +--R Type: Expression Integer +--E 61 + +--S 62 of 510 +r0012:= -6*(-1+x)^(1/2)*(1+x)^(1/2)+6*x*acosh(x)-_ + 3*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)^2+x*acosh(x)^3 +--R +--R +--R 2 +-----+ +-----+ 3 +--R (41) (- 3acosh(x) - 6)\|x - 1 \|x + 1 + x acosh(x) + 6x acosh(x) +--R Type: Expression Integer +--E 62 + +--S 63 of 510 +a0012:= integrate(t0012,x) +--R +--R +--R (42) +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (3x\|x - 1 - 3x + 3)log(\|x - 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (6x\|x - 1 - 6x )log(\|x - 1 + x) + 6x\|x - 1 - 6x + 6 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 510 +m0012:= a0012-r0012 +--R +--R +--R (43) +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (3x\|x - 1 - 3x + 3)log(\|x - 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (6x\|x - 1 - 6x )log(\|x - 1 + x) +--R + +--R 2 +-----+ +-----+ 3 +--R ((3acosh(x) + 6)\|x - 1 \|x + 1 - x acosh(x) - 6x acosh(x) + 6x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 2 +-----+ +-----+ 2 3 2 2 +--R (- 3x acosh(x) - 6x)\|x - 1 \|x + 1 + x acosh(x) + 6x acosh(x) - 6x + 6 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Expression Integer +--E 64 + +--S 65 of 510 +d0012:= D(m0012,x) +--R +--R +--R (44) +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) +--R * +--R +------+ 3 +--R | 2 +--R log(\|x - 1 + x) +--R + +--R 2 3 2 2 2 2 +--R ((- 2x + 1)acosh(x) + 6x acosh(x) + (- 12x + 6)acosh(x) + 12x ) +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 3 2 3 3 +--R (6x - 3x)acosh(x) + (- 12x + 12x)acosh(x) + 12x - 6x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 3 3 3 2 3 +--R (2x - 2x)acosh(x) + (- 6x + 3x)acosh(x) + (12x - 12x)acosh(x) +--R + +--R 3 +--R - 12x + 6x +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 4 2 2 4 2 4 2 +--R (- 6x + 6x )acosh(x) + (12x - 18x + 6)acosh(x) - 12x + 12x +--R / +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R (2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 65 + +--S 66 of 510 +t0013:= acosh(x)^4 +--R +--R +--R 4 +--R (45) acosh(x) +--R Type: Expression Integer +--E 66 + +--S 67 of 510 +r0013:= 24*x-24*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)+12*x*acosh(x)^2-_ + 4*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)^3+x*acosh(x)^4 +--R +--R +--R (46) +--R 3 +-----+ +-----+ 4 2 +--R (- 4acosh(x) - 24acosh(x))\|x - 1 \|x + 1 + x acosh(x) + 12x acosh(x) +--R + +--R 24x +--R Type: Expression Integer +--E 67 + +--S 68 of 510 +a0013:= integrate(t0013,x) +--R +--R +--R (47) +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (4x\|x - 1 - 4x + 4)log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (12x\|x - 1 - 12x )log(\|x - 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (24x\|x - 1 - 24x + 24)log(\|x - 1 + x) + 24x\|x - 1 - 24x +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 510 +m0013:= a0013-r0013 +--R +--R +--R (48) +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (4x\|x - 1 - 4x + 4)log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (12x\|x - 1 - 12x )log(\|x - 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (24x\|x - 1 - 24x + 24)log(\|x - 1 + x) +--R + +--R 3 +-----+ +-----+ 4 +--R (4acosh(x) + 24acosh(x))\|x - 1 \|x + 1 - x acosh(x) +--R + +--R 2 +--R - 12x acosh(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 3 +-----+ +-----+ 2 4 +--R (- 4x acosh(x) - 24x acosh(x))\|x - 1 \|x + 1 + x acosh(x) +--R + +--R 2 2 +--R 12x acosh(x) +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Expression Integer +--E 69 + +--S 70 of 510 +d0013:= D(m0013,x) +--R +--R +--R (49) +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) +--R * +--R +------+ 4 +--R | 2 +--R log(\|x - 1 + x) +--R + +--R 2 4 2 3 2 2 +--R (- 2x + 1)acosh(x) + 8x acosh(x) + (- 24x + 12)acosh(x) +--R + +--R 2 2 +--R 48x acosh(x) - 48x + 24 +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 3 3 3 2 3 +--R (8x - 4x)acosh(x) + (- 24x + 24x)acosh(x) + (48x - 24x)acosh(x) +--R + +--R 3 +--R - 48x + 48x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 3 4 3 3 3 2 +--R (2x - 2x)acosh(x) + (- 8x + 4x)acosh(x) + (24x - 24x)acosh(x) +--R + +--R 3 3 +--R (- 48x + 24x)acosh(x) + 48x - 48x +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 4 2 3 4 2 2 +--R (- 8x + 8x )acosh(x) + (24x - 36x + 12)acosh(x) +--R + +--R 4 2 4 2 +--R (- 48x + 48x )acosh(x) + 48x - 72x + 24 +--R / +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R (2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 70 + +--S 71 of 510 +t0014:= acosh(x)^5 +--R +--R +--R 5 +--R (50) acosh(x) +--R Type: Expression Integer +--E 71 + +--S 72 of 510 +r0014:= -120*(-1+x)^(1/2)*(1+x)^(1/2)+120*x*acosh(x)-60*(-1+x)^(1/2)*_ + (1+x)^(1/2)*acosh(x)^2+20*x*acosh(x)^3-_ + 5*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)^4+x*acosh(x)^5 +--R +--R +--R (51) +--R 4 2 +-----+ +-----+ 5 +--R (- 5acosh(x) - 60acosh(x) - 120)\|x - 1 \|x + 1 + x acosh(x) +--R + +--R 3 +--R 20x acosh(x) + 120x acosh(x) +--R Type: Expression Integer +--E 72 + +--S 73 of 510 +a0014:= integrate(t0014,x) +--R +--R +--R (52) +--R +------+ +------+ 5 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (5x\|x - 1 - 5x + 5)log(\|x - 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (20x\|x - 1 - 20x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (60x\|x - 1 - 60x + 60)log(\|x - 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (120x\|x - 1 - 120x )log(\|x - 1 + x) + 120x\|x - 1 - 120x + 120 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 510 +m0014:= a0014-r0014 +--R +--R +--R (53) +--R +------+ +------+ 5 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (5x\|x - 1 - 5x + 5)log(\|x - 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (20x\|x - 1 - 20x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (60x\|x - 1 - 60x + 60)log(\|x - 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (120x\|x - 1 - 120x )log(\|x - 1 + x) +--R + +--R 4 2 +-----+ +-----+ 5 +--R (5acosh(x) + 60acosh(x) + 120)\|x - 1 \|x + 1 - x acosh(x) +--R + +--R 3 +--R - 20x acosh(x) - 120x acosh(x) + 120x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 +-----+ +-----+ 2 5 +--R (- 5x acosh(x) - 60x acosh(x) - 120x)\|x - 1 \|x + 1 + x acosh(x) +--R + +--R 2 3 2 2 +--R 20x acosh(x) + 120x acosh(x) - 120x + 120 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Expression Integer +--E 74 + +--S 75 of 510 +d0014:= D(m0014,x) +--R +--R +--R (54) +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) +--R * +--R +------+ 5 +--R | 2 +--R log(\|x - 1 + x) +--R + +--R 2 5 2 4 2 3 +--R (- 2x + 1)acosh(x) + 10x acosh(x) + (- 40x + 20)acosh(x) +--R + +--R 2 2 2 2 +--R 120x acosh(x) + (- 240x + 120)acosh(x) + 240x +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 3 4 3 3 +--R (10x - 5x)acosh(x) + (- 40x + 40x)acosh(x) +--R + +--R 3 2 3 3 +--R (120x - 60x)acosh(x) + (- 240x + 240x)acosh(x) + 240x - 120x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 3 5 3 4 3 3 +--R (2x - 2x)acosh(x) + (- 10x + 5x)acosh(x) + (40x - 40x)acosh(x) +--R + +--R 3 2 3 3 +--R (- 120x + 60x)acosh(x) + (240x - 240x)acosh(x) - 240x + 120x +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 4 2 4 4 2 3 +--R (- 10x + 10x )acosh(x) + (40x - 60x + 20)acosh(x) +--R + +--R 4 2 2 4 2 4 2 +--R (- 120x + 120x )acosh(x) + (240x - 360x + 120)acosh(x) - 240x + 240x +--R / +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R (2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 75 + +--S 76 of 510 +t0015:= 1/acosh(x) +--R +--R +--R 1 +--R (55) -------- +--R acosh(x) +--R Type: Expression Integer +--E 76 + +--S 77 of 510 +r0015:= Shi(acosh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 510 +a0015:= integrate(t0015,x) +--R +--R +--R x +--R ++ 1 +--R (56) | --------- d%P +--R ++ acosh(%P) +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 510 +--m0015:= a0015-r0015 +--E 79 + +--S 80 of 510 +--d0015:= D(m0015,x) +--E 80 + +--S 81 of 510 +t0016:= 1/acosh(x)^2 +--R +--R +--R 1 +--R (57) --------- +--R 2 +--R acosh(x) +--R Type: Expression Integer +--E 81 + +--S 82 of 510 +r0016:= -(-1+x)^(1/2)*(1+x)^(1/2)/acosh(x)+Chi(acosh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 510 +a0016:= integrate(t0016,x) +--R +--R +--R x +--R ++ 1 +--R (58) | ---------- d%P +--R ++ 2 +--R acosh(%P) +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 510 +--m0016:= a0016-r0016 +--E 84 + +--S 85 of 510 +--d0016:= D(m0016,x) +--E 85 + +--S 86 of 510 +t0017:= 1/acosh(x)^3 +--R +--R +--R 1 +--R (59) --------- +--R 3 +--R acosh(x) +--R Type: Expression Integer +--E 86 + +--S 87 of 510 +r0017:= -1/2*((-1+x)^(1/2)*(1+x)^(1/2)+x*acosh(x)-_ + Shi(acosh(x))*acosh(x)^2)/acosh(x)^2 +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R 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. +--E 87 + +--S 88 of 510 +a0017:= integrate(t0017,x) +--R +--R +--R x +--R ++ 1 +--R (60) | ---------- d%P +--R ++ 3 +--R acosh(%P) +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 510 +--m0017:= a0017-r0017 +--E 89 + +--S 90 of 510 +--d0017:= D(m0017,x) +--E 90 + +--S 91 of 510 +t0018:= x*acosh(a*x) +--R +--R +--R (61) x acosh(a x) +--R Type: Expression Integer +--E 91 + +--S 92 of 510 +r0018:= -1/4*(x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a+acosh(a*x)-_ + 2*x^2*acosh(a*x)*a^2)/a^2 +--R +--R +--R +-------+ +-------+ 2 2 +--R - a x\|a x - 1 \|a x + 1 + (2a x - 1)acosh(a x) +--R (62) ------------------------------------------------- +--R 2 +--R 4a +--R Type: Expression Integer +--E 92 + +--S 93 of 510 +a0018:= integrate(t0018,x) +--R +--R +--R (63) +--R +--------+ +--------+ +--R 3 3 | 2 2 4 4 2 2 | 2 2 +--R ((4a x - 2a x)\|a x - 1 - 4a x + 4a x - 1)log(\|a x - 1 + a x) +--R + +--R +--------+ +--R 3 3 | 2 2 4 4 2 2 +--R (2a x - a x)\|a x - 1 - 2a x + 2a x +--R / +--R +--------+ +--R 3 | 2 2 4 2 2 +--R 8a x\|a x - 1 - 8a x + 4a +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 510 +m0018:= a0018-r0018 +--R +--R +--R (64) +--R +--------+ +--------+ +--R 3 3 | 2 2 4 4 2 2 | 2 2 +--R ((4a x - 2a x)\|a x - 1 - 4a x + 4a x - 1)log(\|a x - 1 + a x) +--R + +--R 2 2 +-------+ +-------+ 3 3 3 3 +--R (2a x \|a x - 1 \|a x + 1 + (- 4a x + 2a x)acosh(a x) + 2a x - a x) +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 3 3 +-------+ +-------+ 4 4 2 2 +--R (- 2a x + a x)\|a x - 1 \|a x + 1 + (4a x - 4a x + 1)acosh(a x) +--R + +--R 4 4 2 2 +--R - 2a x + 2a x +--R / +--R +--------+ +--R 3 | 2 2 4 2 2 +--R 8a x\|a x - 1 - 8a x + 4a +--R Type: Expression Integer +--E 94 + +--S 95 of 510 +d0018:= D(m0018,x) +--R +--R +--R (65) +--R +--------+ +--R 5 5 3 3 +-------+ +-------+ | 2 2 +--R (32a x - 32a x + 4a x)\|a x - 1 \|a x + 1 \|a x - 1 +--R + +--R 6 6 4 4 2 2 +-------+ +-------+ +--R (- 32a x + 48a x - 16a x )\|a x - 1 \|a x + 1 +--R * +--R +--------+ +--R | 2 2 +--R log(\|a x - 1 + a x) +--R + +--R 5 5 3 3 5 5 3 3 +--R ((- 32a x + 32a x - 4a x)acosh(a x) + 16a x - 16a x + 4a x) +--R * +--R +-------+ +-------+ +--R \|a x - 1 \|a x + 1 +--R + +--R 6 6 4 4 2 2 +--R 16a x - 24a x + 10a x - 1 +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 6 6 4 4 2 2 6 6 4 4 2 2 +--R ((32a x - 48a x + 16a x )acosh(a x) - 16a x + 24a x - 10a x + 1) +--R * +--R +-------+ +-------+ +--R \|a x - 1 \|a x + 1 +--R + +--R 7 7 5 5 3 3 +--R - 16a x + 32a x - 20a x + 4a x +--R / +--R +--------+ +--R 5 4 3 2 +-------+ +-------+ | 2 2 +--R (32a x - 32a x + 4a)\|a x - 1 \|a x + 1 \|a x - 1 +--R + +--R 6 5 4 3 2 +-------+ +-------+ +--R (- 32a x + 48a x - 16a x)\|a x - 1 \|a x + 1 +--R Type: Expression Integer +--E 95 + +--S 96 of 510 +t0019:= x^3*acosh(a*x) +--R +--R +--R 3 +--R (66) x acosh(a x) +--R Type: Expression Integer +--E 96 + +--S 97 of 510 +r0019:= -1/32*(3*x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a+_ + 2*x^3*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a^3+3*acosh(a*x)-_ + 8*x^4*acosh(a*x)*a^4)/a^4 +--R +--R +--R 3 3 +-------+ +-------+ 4 4 +--R (- 2a x - 3a x)\|a x - 1 \|a x + 1 + (8a x - 3)acosh(a x) +--R (67) ------------------------------------------------------------ +--R 4 +--R 32a +--R Type: Expression Integer +--E 97 + +--S 98 of 510 +a0019:= integrate(t0019,x) +--R +--R +--R (68) +--R +--------+ +--R 7 7 5 5 3 3 | 2 2 8 8 6 6 +--R (64a x - 32a x - 24a x + 12a x)\|a x - 1 - 64a x + 64a x +--R + +--R 4 4 2 2 +--R 16a x - 24a x + 3 +--R * +--R +--------+ +--R | 2 2 +--R log(\|a x - 1 + a x) +--R + +--R +--------+ +--R 7 7 5 5 3 3 | 2 2 8 8 4 4 2 2 +--R (16a x + 8a x - 22a x + 3a x)\|a x - 1 - 16a x + 28a x - 12a x +--R / +--R +--------+ +--R 7 3 5 | 2 2 8 4 6 2 4 +--R (256a x - 128a x)\|a x - 1 - 256a x + 256a x - 32a +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 of 510 +m0019:= a0019-r0019 +--R +--R +--R (69) +--R +--------+ +--R 7 7 5 5 3 3 | 2 2 8 8 6 6 +--R (64a x - 32a x - 24a x + 12a x)\|a x - 1 - 64a x + 64a x +--R + +--R 4 4 2 2 +--R 16a x - 24a x + 3 +--R * +--R +--------+ +--R | 2 2 +--R log(\|a x - 1 + a x) +--R + +--R 6 6 4 4 2 2 +-------+ +-------+ +--R (16a x + 16a x - 12a x )\|a x - 1 \|a x + 1 +--R + +--R 7 7 5 5 3 3 7 7 5 5 +--R (- 64a x + 32a x + 24a x - 12a x)acosh(a x) + 16a x + 8a x +--R + +--R 3 3 +--R - 22a x + 3a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 7 7 5 5 3 3 +-------+ +-------+ +--R (- 16a x - 8a x + 22a x - 3a x)\|a x - 1 \|a x + 1 +--R + +--R 8 8 6 6 4 4 2 2 8 8 4 4 +--R (64a x - 64a x - 16a x + 24a x - 3)acosh(a x) - 16a x + 28a x +--R + +--R 2 2 +--R - 12a x +--R / +--R +--------+ +--R 7 3 5 | 2 2 8 4 6 2 4 +--R (256a x - 128a x)\|a x - 1 - 256a x + 256a x - 32a +--R Type: Expression Integer +--E 99 + +--S 100 of 510 +d0019:= D(m0019,x) +--R +--R +--R (70) +--R 11 11 9 9 7 7 5 5 3 3 +-------+ +--R (4096a x - 8192a x + 5120a x - 1024a x + 32a x )\|a x - 1 +--R * +--R +--------+ +--R +-------+ | 2 2 +--R \|a x + 1 \|a x - 1 +--R + +--R 12 12 10 10 8 8 6 6 4 4 +--R (- 4096a x + 10240a x - 8704a x + 2816a x - 256a x ) +--R * +--R +-------+ +-------+ +--R \|a x - 1 \|a x + 1 +--R * +--R +--------+ +--R | 2 2 +--R log(\|a x - 1 + a x) +--R + +--R 11 11 9 9 7 7 5 5 3 3 +--R (- 4096a x + 8192a x - 5120a x + 1024a x - 32a x ) +--R * +--R acosh(a x) +--R + +--R 11 11 9 9 7 7 5 5 3 3 +--R 1024a x - 1536a x + 256a x + 512a x - 240a x + 24a x +--R * +--R +-------+ +-------+ +--R \|a x - 1 \|a x + 1 +--R + +--R 12 12 10 10 8 8 6 6 4 4 2 2 +--R 1024a x - 2048a x + 896a x + 512a x - 472a x + 96a x - 3 +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 12 12 10 10 8 8 6 6 4 4 +--R (4096a x - 10240a x + 8704a x - 2816a x + 256a x )acosh(a x) +--R + +--R 12 12 10 10 8 8 6 6 4 4 2 2 +--R - 1024a x + 2048a x - 896a x - 512a x + 472a x - 96a x + 3 +--R * +--R +-------+ +-------+ +--R \|a x - 1 \|a x + 1 +--R + +--R 13 13 11 11 9 9 7 7 5 5 3 3 +--R - 1024a x + 2560a x - 1792a x - 256a x + 752a x - 264a x + 24a x +--R / +--R 11 8 9 6 7 4 5 2 3 +-------+ +-------+ +--R (4096a x - 8192a x + 5120a x - 1024a x + 32a )\|a x - 1 \|a x + 1 +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 12 9 10 7 8 5 6 3 4 +-------+ +--R (- 4096a x + 10240a x - 8704a x + 2816a x - 256a x)\|a x - 1 +--R * +--R +-------+ +--R \|a x + 1 +--R Type: Expression Integer +--E 100 + +--S 101 of 510 +t0020:= acosh(a*x)/x +--R +--R +--R acosh(a x) +--R (71) ---------- +--R x +--R Type: Expression Integer +--E 101 + +--S 102 of 510 +r0020:= 1/2*acosh(a*x)^2+acosh(a*x)*log(1+exp(1)^(-2*acosh(a*x)))-_ + 1/2*polylog(2,-exp(1)^(-2*acosh(a*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--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. +--E 102 + +--S 103 of 510 +a0020:= integrate(t0020,x) +--R +--R +--R x +--R ++ acosh(%P a) +--R (72) | ----------- d%P +--R ++ %P +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 510 +--m0020:= a0020-r0020 +--E 104 + +--S 105 of 510 +--d0020:= D(m0020,x) +--E 105 + +--S 106 of 510 +t0021:= acosh(a*x)/x^2 +--R +--R +--R acosh(a x) +--R (73) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 106 + +--S 107 of 510 +r0021:= -acosh(a*x)/x+2*a*atan((-1+a*x)^(1/2)/(1+a*x)^(1/2)) +--R +--R +--R +-------+ +--R \|a x - 1 +--R 2a x atan(----------) - acosh(a x) +--R +-------+ +--R \|a x + 1 +--R (74) ---------------------------------- +--R x +--R Type: Expression Integer +--E 107 + +--S 108 of 510 +a0021:= integrate(t0021,x) +--R +--R +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R - log(\|a x - 1 + a x) + 2a x atan(\|a x - 1 - a x) +--R (75) ------------------------------------------------------- +--R x +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 510 +m0021:= a0021-r0021 +--R +--R +--R (76) +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R - log(\|a x - 1 + a x) + 2a x atan(\|a x - 1 - a x) +--R + +--R +-------+ +--R \|a x - 1 +--R - 2a x atan(----------) + acosh(a x) +--R +-------+ +--R \|a x + 1 +--R / +--R x +--R Type: Expression Integer +--E 109 + +--S 110 of 510 +d0021:= D(m0021,x) +--R +--R +--R (77) +--R +--------+ +--------+ +--R +-------+ +-------+ | 2 2 | 2 2 +--R \|a x - 1 \|a x + 1 \|a x - 1 log(\|a x - 1 + a x) +--R + +--R +--------+ +--R +-------+ +-------+ | 2 2 +--R (- acosh(a x)\|a x - 1 \|a x + 1 - a x)\|a x - 1 +--R + +--R +-------+ +-------+ +--R a x\|a x - 1 \|a x + 1 +--R / +--R +--------+ +--R 2 +-------+ +-------+ | 2 2 +--R x \|a x - 1 \|a x + 1 \|a x - 1 +--R Type: Expression Integer +--E 110 + +--S 111 of 510 +t0022:= acosh(a*x)/x^4 +--R +--R +--R acosh(a x) +--R (78) ---------- +--R 4 +--R x +--R Type: Expression Integer +--E 111 + +--S 112 of 510 +r0022:= 1/6*(x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a-2*acosh(a*x)+_ + 2*a^3*atan((-1+a*x)^(1/2)/(1+a*x)^(1/2))*x^3)/x^3 +--R +--R +--R +-------+ +--R 3 3 \|a x - 1 +-------+ +-------+ +--R 2a x atan(----------) + a x\|a x - 1 \|a x + 1 - 2acosh(a x) +--R +-------+ +--R \|a x + 1 +--R (79) ------------------------------------------------------------- +--R 3 +--R 6x +--R Type: Expression Integer +--E 112 + +--S 113 of 510 +a0022:= integrate(t0022,x) +--R +--R +--R (80) +--R +--------+ +--------+ +--R | 2 2 2 2 | 2 2 +--R (- 4a x\|a x - 1 + 4a x - 2)log(\|a x - 1 + a x) +--R + +--R +--------+ +--------+ +--R 4 4 | 2 2 5 5 3 3 | 2 2 +--R (4a x \|a x - 1 - 4a x + 2a x )atan(\|a x - 1 - a x) +--R + +--R +--------+ +--R 3 3 | 2 2 4 4 2 2 +--R (- 2a x + a x)\|a x - 1 + 2a x - 2a x +--R / +--R +--------+ +--R 4 | 2 2 2 5 3 +--R 12a x \|a x - 1 - 12a x + 6x +--R Type: Union(Expression Integer,...) +--E 113 + +--S 114 of 510 +m0022:= a0022-r0022 +--R +--R +--R (81) +--R +--------+ +--------+ +--R | 2 2 2 2 | 2 2 +--R (- 4a x\|a x - 1 + 4a x - 2)log(\|a x - 1 + a x) +--R + +--R +--------+ +--------+ +--R 4 4 | 2 2 5 5 3 3 | 2 2 +--R (4a x \|a x - 1 - 4a x + 2a x )atan(\|a x - 1 - a x) +--R + +--R +--------+ +-------+ +--R 4 4 | 2 2 5 5 3 3 \|a x - 1 +--R (- 4a x \|a x - 1 + 4a x - 2a x )atan(----------) +--R +-------+ +--R \|a x + 1 +--R + +--R +--------+ +--R 2 2 +-------+ +-------+ 3 3 | 2 2 +--R (- 2a x \|a x - 1 \|a x + 1 + 4a x acosh(a x) - 2a x + a x)\|a x - 1 +--R + +--R 3 3 +-------+ +-------+ 2 2 4 4 2 2 +--R (2a x - a x)\|a x - 1 \|a x + 1 + (- 4a x + 2)acosh(a x) + 2a x - 2a x +--R / +--R +--------+ +--R 4 | 2 2 2 5 3 +--R 12a x \|a x - 1 - 12a x + 6x +--R Type: Expression Integer +--E 114 + +--S 115 of 510 +d0022:= D(m0022,x) +--R +--R +--R (82) +--R +--------+ +--R 4 4 2 2 +-------+ +-------+ | 2 2 +--R (24a x - 24a x + 3)\|a x - 1 \|a x + 1 \|a x - 1 +--R + +--R 5 5 3 3 +-------+ +-------+ +--R (- 24a x + 36a x - 12a x)\|a x - 1 \|a x + 1 +--R * +--R +--------+ +--R | 2 2 +--R log(\|a x - 1 + a x) +--R + +--R 4 4 2 2 4 4 2 2 +-------+ +--R ((- 24a x + 24a x - 3)acosh(a x) - 8a x + 4a x )\|a x - 1 +--R * +--R +-------+ +--R \|a x + 1 +--R + +--R 5 5 3 3 +--R - 8a x + 8a x - a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 5 5 3 3 5 5 3 3 +-------+ +--R ((24a x - 36a x + 12a x)acosh(a x) + 8a x - 8a x + a x)\|a x - 1 +--R * +--R +-------+ +--R \|a x + 1 +--R + +--R 6 6 4 4 2 2 +--R 8a x - 12a x + 4a x +--R / +--R +--------+ +--R 4 8 2 6 4 +-------+ +-------+ | 2 2 +--R (24a x - 24a x + 3x )\|a x - 1 \|a x + 1 \|a x - 1 +--R + +--R 5 9 3 7 5 +-------+ +-------+ +--R (- 24a x + 36a x - 12a x )\|a x - 1 \|a x + 1 +--R Type: Expression Integer +--E 115 + +--S 116 of 510 +t0023:= x^2*acosh(a+b*x) +--R +--R +--R 2 +--R (83) x acosh(b x + a) +--R Type: Expression Integer +--E 116 + +--S 117 of 510 +r0023:= -1/18*(4*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)+_ + 11*a^2*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)-_ + 5*a*x*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b+_ + 2*x^2*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b^2-_ + 6*x^3*acosh(a+b*x)*b^3-18*a*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2))-_ + 12*a^3*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2)))/b^3 +--R +--R +--R (84) +--R +-+ +-----------+ +--R 3 \|2 \|b x + a - 1 +--R (12a + 18a)asinh(------------------) +--R 2 +--R + +--R 2 2 2 +-----------+ +-----------+ +--R (- 2b x + 5a b x - 11a - 4)\|b x + a - 1 \|b x + a + 1 +--R + +--R 3 3 +--R 6b x acosh(b x + a) +--R / +--R 3 +--R 18b +--R Type: Expression Integer +--E 117 + +--S 118 of 510 +a0023:= integrate(t0023,x) +--R +--R +--R (85) +--R 5 5 4 4 2 3 3 3 2 2 +--R 96b x + 192a b x + (96a - 24)b x + (96a + 144a)b x +--R + +--R 4 2 5 3 +--R (192a + 288a )b x + 96a + 120a - 36a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R - 96b x - 288a b x + (- 288a + 72)b x + (- 192a - 72a)b x +--R + +--R 4 2 2 2 5 3 6 4 +--R (- 288a - 432a )b x + (- 288a - 360a + 108a)b x - 96a - 72a +--R + +--R 2 +--R 108a +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 32b x + 16a b x + (32a + 40)b x + (208a + 192a)b x +--R + +--R 4 2 5 3 +--R (224a + 48a - 48)b x + 64a - 76a - 39a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R - 32b x - 48a b x + (- 48a - 24)b x + (- 240a - 240a)b x +--R + +--R 4 2 2 2 5 3 6 4 +--R (- 432a - 216a + 72)b x + (- 288a + 108a + 153a)b x - 64a + 108a +--R + +--R 2 +--R 9a - 16 +--R / +--R +----------------------+ +--R 5 2 4 2 3 | 2 2 2 6 3 +--R (288b x + 576a b x + (288a - 72)b )\|b x + 2a b x + a - 1 - 288b x +--R + +--R 5 2 2 4 3 3 +--R - 864a b x + (- 864a + 216)b x + (- 288a + 216a)b +--R Type: Union(Expression Integer,...) +--E 118 + +--S 119 of 510 +m0023:= a0023-r0023 +--R +--R +--R (86) +--R 5 5 4 4 2 3 3 3 2 2 +--R 96b x + 192a b x + (96a - 24)b x + (96a + 144a)b x +--R + +--R 4 2 5 3 +--R (192a + 288a )b x + 96a + 120a - 36a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R - 96b x - 288a b x + (- 288a + 72)b x + (- 192a - 72a)b x +--R + +--R 4 2 2 2 5 3 6 4 +--R (- 288a - 432a )b x + (- 288a - 360a + 108a)b x - 96a - 72a +--R + +--R 2 +--R 108a +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 3 2 2 4 2 5 3 +--R ((- 192a - 288a)b x + (- 384a - 576a )b x - 192a - 240a + 72a) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 3 3 3 4 2 2 2 5 3 +--R (192a + 288a)b x + (576a + 864a )b x + (576a + 720a - 216a)b x +--R + +--R 6 4 2 +--R 192a + 144a - 216a +--R * +--R +-+ +-----------+ +--R \|2 \|b x + a - 1 +--R asinh(------------------) +--R 2 +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 32b x - 16a b x + (48a + 56)b x + (272a + 148a)b x + 176a +--R + +--R 2 +--R 20a - 16 +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 5 5 4 4 2 3 3 5 5 +--R (- 96b x - 192a b x + (- 96a + 24)b x )acosh(b x + a) + 32b x +--R + +--R 4 4 2 3 3 3 2 2 +--R 16a b x + (32a + 40)b x + (208a + 192a)b x +--R + +--R 4 2 5 3 +--R (224a + 48a - 48)b x + 64a - 76a - 39a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 32b x - 16a b x + (- 32a - 40)b x + (- 320a - 228a)b x +--R + +--R 4 2 5 3 +--R (- 448a - 120a + 48)b x - 176a + 68a + 48a +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R (96b x + 288a b x + (288a - 72)b x + (96a - 72a)b x )acosh(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R - 32b x - 48a b x + (- 48a - 24)b x + (- 240a - 240a)b x +--R + +--R 4 2 2 2 5 3 6 4 +--R (- 432a - 216a + 72)b x + (- 288a + 108a + 153a)b x - 64a + 108a +--R + +--R 2 +--R 9a - 16 +--R / +--R +----------------------+ +--R 5 2 4 2 3 | 2 2 2 6 3 +--R (288b x + 576a b x + (288a - 72)b )\|b x + 2a b x + a - 1 - 288b x +--R + +--R 5 2 2 4 3 3 +--R - 864a b x + (- 864a + 216)b x + (- 288a + 216a)b +--R Type: Expression Integer +--E 119 + +--S 120 of 510 +d0023:= D(m0023,x) +--R +--R +--R (87) +--R 6 8 5 7 2 4 6 3 3 5 +--R 96b x + 576a b x + (1440a - 144)b x + (1920a - 576a)b x +--R + +--R 4 2 2 4 5 3 3 +--R (1440a - 864a + 54)b x + (576a - 576a + 108a)b x +--R + +--R 6 4 2 2 +--R (96a - 144a + 54a - 3)x +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 7 9 6 8 2 5 7 +--R - 96b x - 672a b x + (- 2016a + 192)b x +--R + +--R 3 4 6 4 2 3 5 +--R (- 3360a + 960a)b x + (- 3360a + 1920a - 114)b x +--R + +--R 5 3 2 4 +--R (- 2016a + 1920a - 342a)b x +--R + +--R 6 4 2 3 +--R (- 672a + 960a - 342a + 18)b x +--R + +--R 7 5 3 2 +--R (- 96a + 192a - 114a + 18a)x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 6 8 5 7 2 4 6 +--R - 96b x - 576a b x + (- 1440a + 144)b x +--R + +--R 3 3 5 4 2 2 4 +--R (- 1920a + 576a)b x + (- 1440a + 864a - 54)b x +--R + +--R 5 3 3 6 4 2 2 +--R (- 576a + 576a - 108a)b x + (- 96a + 144a - 54a + 3)x +--R * +--R acosh(b x + a) +--R + +--R 6 8 5 7 2 4 6 3 3 5 +--R 32b x + 160a b x + (320a - 32)b x + (320a - 96a)b x +--R + +--R 4 2 2 4 5 3 3 +--R (160a - 96a + 6)b x + (32a - 32a + 6a)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 7 9 6 8 2 5 7 3 4 6 +--R 32b x + 192a b x + (480a - 48)b x + (640a - 192a)b x +--R + +--R 4 2 3 5 5 3 2 4 +--R (480a - 288a + 18)b x + (192a - 192a + 36a)b x +--R + +--R 6 4 2 3 +--R (32a - 48a + 18a - 1)b x +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 7 9 6 8 2 5 7 3 4 6 +--R 96b x + 672a b x + (2016a - 192)b x + (3360a - 960a)b x +--R + +--R 4 2 3 5 5 3 2 4 +--R (3360a - 1920a + 114)b x + (2016a - 1920a + 342a)b x +--R + +--R 6 4 2 3 7 5 3 2 +--R (672a - 960a + 342a - 18)b x + (96a - 192a + 114a - 18a)x +--R * +--R acosh(b x + a) +--R + +--R 7 9 6 8 2 5 7 3 4 6 +--R - 32b x - 192a b x + (- 480a + 48)b x + (- 640a + 192a)b x +--R + +--R 4 2 3 5 5 3 2 4 +--R (- 480a + 288a - 18)b x + (- 192a + 192a - 36a)b x +--R + +--R 6 4 2 3 +--R (- 32a + 48a - 18a + 1)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 8 10 7 9 2 6 8 3 5 7 +--R - 32b x - 224a b x + (- 672a + 64)b x + (- 1120a + 320a)b x +--R + +--R 4 2 4 6 5 3 3 5 +--R (- 1120a + 640a - 38)b x + (- 672a + 640a - 114a)b x +--R + +--R 6 4 2 2 4 7 5 3 3 +--R (- 224a + 320a - 114a + 6)b x + (- 32a + 64a - 38a + 6a)b x +--R / +--R 6 6 5 5 2 4 4 3 3 3 +--R 96b x + 576a b x + (1440a - 144)b x + (1920a - 576a)b x +--R + +--R 4 2 2 2 5 3 6 4 +--R (1440a - 864a + 54)b x + (576a - 576a + 108a)b x + 96a - 144a +--R + +--R 2 +--R 54a - 3 +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R - 96b x - 672a b x + (- 2016a + 192)b x + (- 3360a + 960a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 3360a + 1920a - 114)b x + (- 2016a + 1920a - 342a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 672a + 960a - 342a + 18)b x - 96a + 192a - 114a + 18a +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R Type: Expression Integer +--E 120 + +--S 121 of 510 +t0024:= x^3*acosh(a+b*x) +--R +--R +--R 3 +--R (88) x acosh(b x + a) +--R Type: Expression Integer +--E 121 + +--S 122 of 510 +r0024:= 1/96*(55*a*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)+_ + 50*a^3*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)-_ + 9*x*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b-_ + 26*a^2*x*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b+_ + 14*a*x^2*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b^2-_ + 6*x^3*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b^3+_ + 24*x^4*acosh(a+b*x)*b^4-144*a^2*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2))-_ + 48*a^4*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2))-_ + 18*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2)))/b^4 +--R +--R +--R (89) +--R +-+ +-----------+ +--R 4 2 \|2 \|b x + a - 1 +--R (- 48a - 144a - 18)asinh(------------------) +--R 2 +--R + +--R 3 3 2 2 2 3 +-----------+ +--R (- 6b x + 14a b x + (- 26a - 9)b x + 50a + 55a)\|b x + a - 1 +--R * +--R +-----------+ +--R \|b x + a + 1 +--R + +--R 4 4 +--R 24b x acosh(b x + a) +--R / +--R 4 +--R 96b +--R Type: Expression Integer +--E 122 + +--S 123 of 510 +a0024:= integrate(t0024,x) +--R +--R +--R (90) +--R 7 7 6 6 2 5 5 3 4 4 +--R 1536b x + 4608a b x + (4608a - 768)b x + (1536a - 768a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 1536a - 4608a - 576)b x + (- 4608a - 13824a - 1728a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 4608a - 13056a + 576a + 288)b x - 1536a - 3840a + 1728a +--R + +--R 288a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 8 8 7 7 2 6 6 +--R - 1536b x - 6144a b x + (- 9216a + 1536)b x +--R + +--R 3 5 5 2 4 4 +--R (- 6144a + 3072a)b x + (6144a + 384)b x +--R + +--R 5 3 3 3 +--R (6144a + 18432a + 2304a)b x +--R + +--R 6 4 2 2 2 +--R (9216a + 26112a - 1152a - 576)b x +--R + +--R 7 5 3 8 6 4 +--R (6144a + 15360a - 6912a - 1152a)b x + 1536a + 3072a - 3840a + 72 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R 384b x + 640a b x + (384a + 192)b x + (- 384a - 1088a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 3864a - 8768a - 528)b x + (- 6984a - 11712a + 2256a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 4680a - 3508a + 5616a + 72)b x - 1048a + 716a + 2064a - 440a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 8 8 7 7 2 6 6 5 5 +--R - 384b x - 1024a b x - 1024a b x + 1024a b x +--R + +--R 4 2 4 4 5 3 3 3 +--R (4248a + 9920a + 672)b x + (10848a + 20224a - 2432a)b x +--R + +--R 6 4 2 2 2 +--R (11664a + 13544a - 11520a - 288)b x +--R + +--R 7 5 3 8 6 4 2 +--R (5728a + 976a - 9984a + 1472a)b x + 1048a - 1240a - 1837a + 1496a +--R / +--R 7 3 6 2 2 5 3 4 +--R (6144b x + 18432a b x + (18432a - 3072)b x + (6144a - 3072a)b ) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 8 4 7 3 2 6 2 +--R - 6144b x - 24576a b x + (- 36864a + 6144)b x +--R + +--R 3 5 4 2 4 +--R (- 24576a + 12288a)b x + (- 6144a + 6144a - 768)b +--R Type: Union(Expression Integer,...) +--E 123 + +--S 124 of 510 +m0024:= a0024-r0024 +--R +--R +--R (91) +--R 7 7 6 6 2 5 5 3 4 4 +--R 1536b x + 4608a b x + (4608a - 768)b x + (1536a - 768a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 1536a - 4608a - 576)b x + (- 4608a - 13824a - 1728a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 4608a - 13056a + 576a + 288)b x - 1536a - 3840a + 1728a +--R + +--R 288a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 8 8 7 7 2 6 6 +--R - 1536b x - 6144a b x + (- 9216a + 1536)b x +--R + +--R 3 5 5 2 4 4 +--R (- 6144a + 3072a)b x + (6144a + 384)b x +--R + +--R 5 3 3 3 +--R (6144a + 18432a + 2304a)b x +--R + +--R 6 4 2 2 2 +--R (9216a + 26112a - 1152a - 576)b x +--R + +--R 7 5 3 8 6 4 +--R (6144a + 15360a - 6912a - 1152a)b x + 1536a + 3072a - 3840a + 72 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 4 2 3 3 5 3 2 2 +--R (3072a + 9216a + 1152)b x + (9216a + 27648a + 3456a)b x +--R + +--R 6 4 2 7 5 3 +--R (9216a + 26112a - 1152a - 576)b x + 3072a + 7680a - 3456a +--R + +--R - 576a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 4 2 4 4 5 3 3 3 +--R (- 3072a - 9216a - 1152)b x + (- 12288a - 36864a - 4608a)b x +--R + +--R 6 4 2 2 2 +--R (- 18432a - 52224a + 2304a + 1152)b x +--R + +--R 7 5 3 8 6 4 +--R (- 12288a - 30720a + 13824a + 2304a)b x - 3072a - 6144a + 7680a +--R + +--R - 144 +--R * +--R +-+ +-----------+ +--R \|2 \|b x + a - 1 +--R asinh(------------------) +--R 2 +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R 384b x + 256a b x + (128a + 384)b x + (- 512a - 1536a)b x +--R + +--R 4 2 2 2 5 3 +--R (- 5504a - 9216a - 288)b x + (- 7936a - 9216a + 1472a)b x +--R + +--R 6 4 2 +--R - 3200a - 1920a + 1760a +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 7 7 6 6 2 5 5 +--R - 1536b x - 4608a b x + (- 4608a + 768)b x +--R + +--R 3 4 4 +--R (- 1536a + 768a)b x +--R * +--R acosh(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R 384b x + 640a b x + (384a + 192)b x + (- 384a - 1088a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 3864a - 8768a - 528)b x + (- 6984a - 11712a + 2256a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 4680a - 3508a + 5616a + 72)b x - 1048a + 716a + 2064a - 440a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R - 384b x - 640a b x + (- 384a - 192)b x + (384a + 1088a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (6016a + 10880a + 528)b x + (13440a + 18048a - 2256a)b x +--R + +--R 6 4 2 7 5 3 +--R (11136a + 8768a - 6672a - 72)b x + 3200a + 320a - 3120a + 440a +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 8 8 7 7 2 6 6 3 5 5 +--R 1536b x + 6144a b x + (9216a - 1536)b x + (6144a - 3072a)b x +--R + +--R 4 2 4 4 +--R (1536a - 1536a + 192)b x +--R * +--R acosh(b x + a) +--R + +--R 8 8 7 7 2 6 6 5 5 +--R - 384b x - 1024a b x - 1024a b x + 1024a b x +--R + +--R 4 2 4 4 5 3 3 3 +--R (4248a + 9920a + 672)b x + (10848a + 20224a - 2432a)b x +--R + +--R 6 4 2 2 2 +--R (11664a + 13544a - 11520a - 288)b x +--R + +--R 7 5 3 8 6 4 2 +--R (5728a + 976a - 9984a + 1472a)b x + 1048a - 1240a - 1837a + 1496a +--R / +--R 7 3 6 2 2 5 3 4 +--R (6144b x + 18432a b x + (18432a - 3072)b x + (6144a - 3072a)b ) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 8 4 7 3 2 6 2 +--R - 6144b x - 24576a b x + (- 36864a + 6144)b x +--R + +--R 3 5 4 2 4 +--R (- 24576a + 12288a)b x + (- 6144a + 6144a - 768)b +--R Type: Expression Integer +--E 124 + +--S 125 of 510 +d0024:= D(m0024,x) +--R +--R +--R (92) +--R 8 11 7 10 2 6 9 +--R 512b x + 4096a b x + (14336a - 1024)b x +--R + +--R 3 5 8 4 2 4 7 +--R (28672a - 6144a)b x + (35840a - 15360a + 640)b x +--R + +--R 5 3 3 6 +--R (28672a - 20480a + 2560a)b x +--R + +--R 6 4 2 2 5 +--R (14336a - 15360a + 3840a - 128)b x +--R + +--R 7 5 3 4 +--R (4096a - 6144a + 2560a - 256a)b x +--R + +--R 8 6 4 2 3 +--R (512a - 1024a + 640a - 128a + 4)x +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 9 12 8 11 2 7 10 +--R - 512b x - 4608a b x + (- 18432a + 1280)b x +--R + +--R 3 6 9 4 2 5 8 +--R (- 43008a + 8960a)b x + (- 64512a + 26880a - 1088)b x +--R + +--R 5 3 4 7 +--R (- 64512a + 44800a - 5440a)b x +--R + +--R 6 4 2 3 6 +--R (- 43008a + 44800a - 10880a + 352)b x +--R + +--R 7 5 3 2 5 +--R (- 18432a + 26880a - 10880a + 1056a)b x +--R + +--R 8 6 4 2 4 +--R (- 4608a + 8960a - 5440a + 1056a - 32)b x +--R + +--R 9 7 5 3 3 +--R (- 512a + 1280a - 1088a + 352a - 32a)x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 8 11 7 10 2 6 9 +--R - 512b x - 4096a b x + (- 14336a + 1024)b x +--R + +--R 3 5 8 4 2 4 7 +--R (- 28672a + 6144a)b x + (- 35840a + 15360a - 640)b x +--R + +--R 5 3 3 6 +--R (- 28672a + 20480a - 2560a)b x +--R + +--R 6 4 2 2 5 +--R (- 14336a + 15360a - 3840a + 128)b x +--R + +--R 7 5 3 4 +--R (- 4096a + 6144a - 2560a + 256a)b x +--R + +--R 8 6 4 2 3 +--R (- 512a + 1024a - 640a + 128a - 4)x +--R * +--R acosh(b x + a) +--R + +--R 8 11 7 10 2 6 9 3 5 8 +--R 128b x + 896a b x + (2688a - 192)b x + (4480a - 960a)b x +--R + +--R 4 2 4 7 5 3 3 6 +--R (4480a - 1920a + 80)b x + (2688a - 1920a + 240a)b x +--R + +--R 6 4 2 2 5 7 5 3 4 +--R (896a - 960a + 240a - 8)b x + (128a - 192a + 80a - 8a)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 9 12 8 11 2 7 10 3 6 9 +--R 128b x + 1024a b x + (3584a - 256)b x + (7168a - 1536a)b x +--R + +--R 4 2 5 8 5 3 4 7 +--R (8960a - 3840a + 160)b x + (7168a - 5120a + 640a)b x +--R + +--R 6 4 2 3 6 +--R (3584a - 3840a + 960a - 32)b x +--R + +--R 7 5 3 2 5 +--R (1024a - 1536a + 640a - 64a)b x +--R + +--R 8 6 4 2 4 +--R (128a - 256a + 160a - 32a + 1)b x +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 9 12 8 11 2 7 10 +--R 512b x + 4608a b x + (18432a - 1280)b x +--R + +--R 3 6 9 4 2 5 8 +--R (43008a - 8960a)b x + (64512a - 26880a + 1088)b x +--R + +--R 5 3 4 7 +--R (64512a - 44800a + 5440a)b x +--R + +--R 6 4 2 3 6 +--R (43008a - 44800a + 10880a - 352)b x +--R + +--R 7 5 3 2 5 +--R (18432a - 26880a + 10880a - 1056a)b x +--R + +--R 8 6 4 2 4 +--R (4608a - 8960a + 5440a - 1056a + 32)b x +--R + +--R 9 7 5 3 3 +--R (512a - 1280a + 1088a - 352a + 32a)x +--R * +--R acosh(b x + a) +--R + +--R 9 12 8 11 2 7 10 +--R - 128b x - 1024a b x + (- 3584a + 256)b x +--R + +--R 3 6 9 4 2 5 8 +--R (- 7168a + 1536a)b x + (- 8960a + 3840a - 160)b x +--R + +--R 5 3 4 7 6 4 2 3 6 +--R (- 7168a + 5120a - 640a)b x + (- 3584a + 3840a - 960a + 32)b x +--R + +--R 7 5 3 2 5 +--R (- 1024a + 1536a - 640a + 64a)b x +--R + +--R 8 6 4 2 4 +--R (- 128a + 256a - 160a + 32a - 1)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 10 13 9 12 2 8 11 +--R - 128b x - 1152a b x + (- 4608a + 320)b x +--R + +--R 3 7 10 4 2 6 9 +--R (- 10752a + 2240a)b x + (- 16128a + 6720a - 272)b x +--R + +--R 5 3 5 8 +--R (- 16128a + 11200a - 1360a)b x +--R + +--R 6 4 2 4 7 +--R (- 10752a + 11200a - 2720a + 88)b x +--R + +--R 7 5 3 3 6 +--R (- 4608a + 6720a - 2720a + 264a)b x +--R + +--R 8 6 4 2 2 5 +--R (- 1152a + 2240a - 1360a + 264a - 8)b x +--R + +--R 9 7 5 3 4 +--R (- 128a + 320a - 272a + 88a - 8a)b x +--R / +--R 8 8 7 7 2 6 6 3 5 5 +--R 512b x + 4096a b x + (14336a - 1024)b x + (28672a - 6144a)b x +--R + +--R 4 2 4 4 5 3 3 3 +--R (35840a - 15360a + 640)b x + (28672a - 20480a + 2560a)b x +--R + +--R 6 4 2 2 2 +--R (14336a - 15360a + 3840a - 128)b x +--R + +--R 7 5 3 8 6 4 2 +--R (4096a - 6144a + 2560a - 256a)b x + 512a - 1024a + 640a - 128a +--R + +--R 4 +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 9 9 8 8 2 7 7 +--R - 512b x - 4608a b x + (- 18432a + 1280)b x +--R + +--R 3 6 6 4 2 5 5 +--R (- 43008a + 8960a)b x + (- 64512a + 26880a - 1088)b x +--R + +--R 5 3 4 4 +--R (- 64512a + 44800a - 5440a)b x +--R + +--R 6 4 2 3 3 +--R (- 43008a + 44800a - 10880a + 352)b x +--R + +--R 7 5 3 2 2 +--R (- 18432a + 26880a - 10880a + 1056a)b x +--R + +--R 8 6 4 2 9 7 +--R (- 4608a + 8960a - 5440a + 1056a - 32)b x - 512a + 1280a +--R + +--R 5 3 +--R - 1088a + 352a - 32a +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R Type: Expression Integer +--E 125 + +--S 126 of 510 +t0025:= acosh(a+b*x)/x^2 +--R +--R +--R acosh(b x + a) +--R (93) -------------- +--R 2 +--R x +--R Type: Expression Integer +--E 126 + +--S 127 of 510 +r0025:= -acosh(a+b*x)/x-2*b*atan((-1-a)^(1/2)*_ + (a+b*x-1)^(1/2)/(-1+a)^(1/2)/(a+1+b*x)^(1/2))/(-1-a)^(1/2)/(-1+a)^(1/2) +--R +--R +--R (94) +--R +-------+ +-----------+ +--R \|- a - 1 \|b x + a - 1 +-------+ +-----+ +--R - 2b x atan(------------------------) - acosh(b x + a)\|- a - 1 \|a - 1 +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R ------------------------------------------------------------------------ +--R +-------+ +-----+ +--R x\|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 127 + +--S 128 of 510 +a0025:= integrate(t0025,x) +--R +--R +--R (95) +--R [ +--R +------+ +----------------------+ +--R | 2 | 2 2 2 +--R - \|a - 1 log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R b x +--R * +--R log +--R +------+ +----------------------+ +--R | 2 2 | 2 2 2 +--R (b x\|a - 1 + a - 1)\|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 2 | 2 2 +--R (- b x - a b x - a + 1)\|a - 1 + (- a + 1)b x +--R / +--R +----------------------+ +--R | 2 2 2 2 +--R x\|b x + 2a b x + a - 1 - b x - a x +--R / +--R +------+ +--R | 2 +--R x\|a - 1 +--R , +--R +--R +--------+ +----------------------+ +--R | 2 | 2 2 2 +--R - \|- a + 1 log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +--------+ +----------------------+ +--------+ +--R | 2 | 2 2 2 | 2 +--R \|- a + 1 \|b x + 2a b x + a - 1 - b x\|- a + 1 +--R - 2b x atan(-----------------------------------------------------) +--R 2 +--R a - 1 +--R / +--R +--------+ +--R | 2 +--R x\|- a + 1 +--R ] +--R Type: Union(List Expression Integer,...) +--E 128 + +--S 129 of 510 +m0025a:= a0025.1-r0025 +--R +--R +--R (96) +--R +------+ +----------------------+ +--R +-------+ +-----+ | 2 | 2 2 2 +--R - \|- a - 1 \|a - 1 \|a - 1 log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +-------+ +-----+ +--R b x\|- a - 1 \|a - 1 +--R * +--R log +--R +------+ +----------------------+ +--R | 2 2 | 2 2 2 +--R (b x\|a - 1 + a - 1)\|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 2 | 2 2 +--R (- b x - a b x - a + 1)\|a - 1 + (- a + 1)b x +--R / +--R +----------------------+ +--R | 2 2 2 2 +--R x\|b x + 2a b x + a - 1 - b x - a x +--R + +--R +------+ +-------+ +-----------+ +--R | 2 \|- a - 1 \|b x + a - 1 +--R 2b x\|a - 1 atan(------------------------) +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R + +--R +------+ +--R +-------+ +-----+ | 2 +--R acosh(b x + a)\|- a - 1 \|a - 1 \|a - 1 +--R / +--R +------+ +--R +-------+ +-----+ | 2 +--R x\|- a - 1 \|a - 1 \|a - 1 +--R Type: Expression Integer +--E 129 + +--S 130 of 510 +d0025a:= D(m0025a,x) +--R +--R +--R (97) +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +-----------+ +-----------+ +--R (- acosh(b x + a)\|b x + a - 1 \|b x + a + 1 - b x) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +-----------+ +-----------+ +--R b x\|b x + a - 1 \|b x + a + 1 +--R / +--R +----------------------+ +--R 2 +-----------+ +-----------+ | 2 2 2 +--R x \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R Type: Expression Integer +--E 130 + +--S 131 of 510 +m0025b:= a0025.2-r0025 +--R +--R +--R (98) +--R +--------+ +----------------------+ +--R | 2 +-------+ +-----+ | 2 2 2 +--R - \|- a + 1 \|- a - 1 \|a - 1 log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R - +--R +-------+ +-----+ +--R 2b x\|- a - 1 \|a - 1 +--R * +--R +--------+ +----------------------+ +--------+ +--R | 2 | 2 2 2 | 2 +--R \|- a + 1 \|b x + 2a b x + a - 1 - b x\|- a + 1 +--R atan(-----------------------------------------------------) +--R 2 +--R a - 1 +--R + +--R +--------+ +-------+ +-----------+ +--R | 2 \|- a - 1 \|b x + a - 1 +--R 2b x\|- a + 1 atan(------------------------) +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R + +--R +--------+ +--R | 2 +-------+ +-----+ +--R acosh(b x + a)\|- a + 1 \|- a - 1 \|a - 1 +--R / +--R +--------+ +--R | 2 +-------+ +-----+ +--R x\|- a + 1 \|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 131 + +--S 132 of 510 +d0025b:= D(m0025b,x) +--R +--R +--R (99) +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +-----------+ +-----------+ +--R (- acosh(b x + a)\|b x + a - 1 \|b x + a + 1 - b x) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +-----------+ +-----------+ +--R b x\|b x + a - 1 \|b x + a + 1 +--R / +--R +----------------------+ +--R 2 +-----------+ +-----------+ | 2 2 2 +--R x \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R Type: Expression Integer +--E 132 + +--S 133 of 510 +t0026:= acosh(a+b*x)/x^3 +--R +--R +--R acosh(b x + a) +--R (100) -------------- +--R 3 +--R x +--R Type: Expression Integer +--E 133 + +--S 134 of 510 +r0026:= 1/2*b*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)/(1-a^2)/x-_ + 1/2*acosh(a+b*x)/x^2-a*b^2*atan((-1-a)^(1/2)*_ + (a+b*x-1)^(1/2)/(-1+a)^(1/2)/(a+1+b*x)^(1/2))/(-1-a)^(3/2)/(-1+a)^(3/2) +--R +--R +--R (101) +--R +-------+ +-----------+ +--R 2 2 \|- a - 1 \|b x + a - 1 +--R 2a b x atan(------------------------) +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R + +--R +-------+ +-----+ +-----------+ +-----------+ +--R - b x\|- a - 1 \|a - 1 \|b x + a - 1 \|b x + a + 1 +--R + +--R 2 +-------+ +-----+ +--R (- a + 1)acosh(b x + a)\|- a - 1 \|a - 1 +--R / +--R 2 2 +-------+ +-----+ +--R (2a - 2)x \|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 134 + +--S 135 of 510 +a0026:= integrate(t0026,x) +--R +--R +--R (102) +--R [ +--R +------+ +----------------------+ +--R 2 | 2 | 2 2 2 +--R (- a + 1)\|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 3 | 2 +--R ((a - 1)b x + a - a)\|a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +----------------------+ +--R 2 2 | 2 2 2 3 3 2 2 2 +--R (a b x \|b x + 2a b x + a - 1 - a b x - a b x ) +--R * +--R log +--R +------+ +----------------------+ +--R | 2 2 | 2 2 2 +--R (b x\|a - 1 - a + 1)\|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 2 | 2 2 +--R (- b x - a b x - a + 1)\|a - 1 + (a - 1)b x +--R / +--R +----------------------+ +--R | 2 2 2 2 +--R x\|b x + 2a b x + a - 1 - b x - a x +--R + +--R +------+ +----------------------+ +--R | 2 | 2 2 2 +--R a b x\|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 2 | 2 +--R (- a b x + (- a + 1)b x)\|a - 1 +--R / +--R +------+ +----------------------+ +--R 2 2 | 2 | 2 2 2 +--R (2a - 2)x \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 3 3 2 | 2 +--R ((- 2a + 2)b x + (- 2a + 2a)x )\|a - 1 +--R , +--R +--R +--------+ +----------------------+ +--R 2 | 2 | 2 2 2 +--R (- a + 1)\|- a + 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 3 | 2 +--R ((a - 1)b x + a - a)\|- a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +----------------------+ +--R 2 2 | 2 2 2 3 3 2 2 2 +--R (2a b x \|b x + 2a b x + a - 1 - 2a b x - 2a b x ) +--R * +--R +--------+ +----------------------+ +--------+ +--R | 2 | 2 2 2 | 2 +--R \|- a + 1 \|b x + 2a b x + a - 1 - b x\|- a + 1 +--R atan(-----------------------------------------------------) +--R 2 +--R a - 1 +--R + +--R +--------+ +----------------------+ +--R | 2 | 2 2 2 +--R a b x\|- a + 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 2 2 | 2 +--R (- a b x + (- a + 1)b x)\|- a + 1 +--R / +--R +--------+ +----------------------+ +--R 2 2 | 2 | 2 2 2 +--R (2a - 2)x \|- a + 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 3 3 2 | 2 +--R ((- 2a + 2)b x + (- 2a + 2a)x )\|- a + 1 +--R ] +--R Type: Union(List Expression Integer,...) +--E 135 + +--S 136 of 510 +m0026a:= a0026.1-r0026 +--R +--R +--R (103) +--R +------+ +----------------------+ +--R 2 +-------+ +-----+ | 2 | 2 2 2 +--R (- a + 1)\|- a - 1 \|a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 3 +-------+ +-----+ | 2 +--R ((a - 1)b x + a - a)\|- a - 1 \|a - 1 \|a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +----------------------+ +--R 2 2 +-------+ +-----+ | 2 2 2 +--R a b x \|- a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R 3 3 2 2 2 +-------+ +-----+ +--R (- a b x - a b x )\|- a - 1 \|a - 1 +--R * +--R log +--R +------+ +----------------------+ +--R | 2 2 | 2 2 2 +--R (b x\|a - 1 - a + 1)\|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 2 | 2 2 +--R (- b x - a b x - a + 1)\|a - 1 + (a - 1)b x +--R / +--R +----------------------+ +--R | 2 2 2 2 +--R x\|b x + 2a b x + a - 1 - b x - a x +--R + +--R +------+ +----------------------+ +--R 2 2 | 2 | 2 2 2 +--R - 2a b x \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 3 3 2 2 2 | 2 +--R (2a b x + 2a b x )\|a - 1 +--R * +--R +-------+ +-----------+ +--R \|- a - 1 \|b x + a - 1 +--R atan(------------------------) +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R + +--R +------+ +--R +-------+ +-----+ | 2 +-----------+ +-----------+ +--R b x\|- a - 1 \|a - 1 \|a - 1 \|b x + a - 1 \|b x + a + 1 +--R + +--R +------+ +--R 2 +-------+ +-----+ | 2 +--R ((a - 1)acosh(b x + a) + a b x)\|- a - 1 \|a - 1 \|a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 +-------+ +-----+ | 2 +-----------+ +-----------+ +--R (- b x - a b x)\|- a - 1 \|a - 1 \|a - 1 \|b x + a - 1 \|b x + a + 1 +--R + +--R 2 3 2 2 2 +--R (((- a + 1)b x - a + a)acosh(b x + a) - a b x + (- a + 1)b x) +--R * +--R +------+ +--R +-------+ +-----+ | 2 +--R \|- a - 1 \|a - 1 \|a - 1 +--R / +--R +------+ +----------------------+ +--R 2 2 +-------+ +-----+ | 2 | 2 2 2 +--R (2a - 2)x \|- a - 1 \|a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 3 3 2 +-------+ +-----+ | 2 +--R ((- 2a + 2)b x + (- 2a + 2a)x )\|- a - 1 \|a - 1 \|a - 1 +--R Type: Expression Integer +--E 136 + +--S 137 of 510 +d0026a:= D(m0026a,x) +--R +--R +--R (104) +--R 6 6 5 5 2 4 4 3 3 3 +--R 32b x + 160a b x + (336a - 56)b x + (384a - 184a)b x +--R + +--R 4 2 2 2 5 3 6 +--R (256a - 232a + 26)b x + (96a - 136a + 42a)b x + 16a +--R + +--R 4 2 +--R - 32a + 18a - 2 +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 5 5 3 4 4 +--R (- 32a + 32)b x + (- 144a + 144a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 256a + 296a - 40)b x + (- 224a + 328a - 104a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 96a + 184a - 98a + 10)b x - 16a + 40a - 32a + 8a +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 7 7 6 6 2 5 5 +--R - 32b x - 192a b x + (- 496a + 72)b x +--R + +--R 3 4 4 4 2 3 3 +--R (- 720a + 304a)b x + (- 640a + 520a - 50)b x +--R + +--R 5 3 2 2 +--R (- 352a + 456a - 124a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 112a + 208a - 106a + 10)b x - 16a + 40a - 32a + 8a +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 6 6 3 5 5 4 2 4 4 +--R (32a - 32)b x + (176a - 176a)b x + (400a - 456a + 56)b x +--R + +--R 5 3 3 3 6 4 2 2 2 +--R (480a - 680a + 200a)b x + (320a - 584a + 290a - 26)b x +--R + +--R 7 5 3 8 6 4 2 +--R (112a - 264a + 196a - 44a)b x + 16a - 48a + 50a - 20a + 2 +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 6 6 5 5 2 4 4 +--R - 32b x - 160a b x + (- 336a + 56)b x +--R + +--R 3 3 3 4 2 2 2 +--R (- 384a + 184a)b x + (- 256a + 232a - 26)b x +--R + +--R 5 3 6 4 2 +--R (- 96a + 136a - 42a)b x - 16a + 32a - 18a + 2 +--R * +--R acosh(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R - 16b x - 64a b x + (- 104a + 20)b x + (- 88a + 48a)b x +--R + +--R 4 2 2 2 5 3 +--R (- 40a + 40a - 5)b x + (- 8a + 12a - 4a)b x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 5 5 3 4 4 +--R (32a - 32)b x + (144a - 144a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (256a - 296a + 40)b x + (224a - 328a + 104a)b x +--R + +--R 6 4 2 7 5 3 +--R (96a - 184a + 98a - 10)b x + 16a - 40a + 32a - 8a +--R * +--R acosh(b x + a) +--R + +--R 2 5 5 3 4 4 4 2 3 3 +--R (16a - 16)b x + (56a - 56a)b x + (72a - 84a + 12)b x +--R + +--R 5 3 2 2 6 4 2 +--R (40a - 60a + 20a)b x + (8a - 16a + 9a - 1)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R - 16b x - 80a b x + (- 168a + 28)b x + (- 192a + 92a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 128a + 116a - 13)b x + (- 48a + 68a - 21a)b x +--R + +--R 6 4 2 +--R (- 8a + 16a - 9a + 1)b x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 6 6 3 5 5 4 2 4 4 +--R (16a - 16)b x + (72a - 72a)b x + (128a - 148a + 20)b x +--R + +--R 5 3 3 3 6 4 2 2 2 +--R (112a - 164a + 52a)b x + (48a - 92a + 49a - 5)b x +--R + +--R 7 5 3 +--R (8a - 20a + 16a - 4a)b x +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R 32b x + 192a b x + (496a - 72)b x + (720a - 304a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (640a - 520a + 50)b x + (352a - 456a + 124a)b x +--R + +--R 6 4 2 7 5 3 +--R (112a - 208a + 106a - 10)b x + 16a - 40a + 32a - 8a +--R * +--R acosh(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R 16b x + 80a b x + (168a - 28)b x + (192a - 92a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (128a - 116a + 13)b x + (48a - 68a + 21a)b x +--R + +--R 6 4 2 +--R (8a - 16a + 9a - 1)b x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 6 6 3 5 5 +--R (- 32a + 32)b x + (- 176a + 176a)b x +--R + +--R 4 2 4 4 5 3 3 3 +--R (- 400a + 456a - 56)b x + (- 480a + 680a - 200a)b x +--R + +--R 6 4 2 2 2 +--R (- 320a + 584a - 290a + 26)b x +--R + +--R 7 5 3 8 6 4 2 +--R (- 112a + 264a - 196a + 44a)b x - 16a + 48a - 50a + 20a - 2 +--R * +--R acosh(b x + a) +--R + +--R 2 6 6 3 5 5 4 2 4 4 +--R (- 16a + 16)b x + (- 72a + 72a)b x + (- 128a + 148a - 20)b x +--R + +--R 5 3 3 3 6 4 2 2 2 +--R (- 112a + 164a - 52a)b x + (- 48a + 92a - 49a + 5)b x +--R + +--R 7 5 3 +--R (- 8a + 20a - 16a + 4a)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 8 8 7 7 2 6 6 3 5 5 +--R 16b x + 96a b x + (248a - 36)b x + (360a - 152a)b x +--R + +--R 4 2 4 4 5 3 3 3 +--R (320a - 260a + 25)b x + (176a - 228a + 62a)b x +--R + +--R 6 4 2 2 2 7 5 3 +--R (56a - 104a + 53a - 5)b x + (8a - 20a + 16a - 4a)b x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 7 7 3 6 6 4 2 5 5 +--R (- 16a + 16)b x + (- 88a + 88a)b x + (- 200a + 228a - 28)b x +--R + +--R 5 3 4 4 6 4 2 3 3 +--R (- 240a + 340a - 100a)b x + (- 160a + 292a - 145a + 13)b x +--R + +--R 7 5 3 2 2 8 6 4 2 +--R (- 56a + 132a - 98a + 22a)b x + (- 8a + 24a - 25a + 10a - 1)b x +--R / +--R 6 9 5 8 2 4 7 3 3 6 +--R 32b x + 160a b x + (336a - 56)b x + (384a - 184a)b x +--R + +--R 4 2 2 5 5 3 4 +--R (256a - 232a + 26)b x + (96a - 136a + 42a)b x +--R + +--R 6 4 2 3 +--R (16a - 32a + 18a - 2)x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 5 8 3 4 7 4 2 3 6 +--R (- 32a + 32)b x + (- 144a + 144a)b x + (- 256a + 296a - 40)b x +--R + +--R 5 3 2 5 6 4 2 4 +--R (- 224a + 328a - 104a)b x + (- 96a + 184a - 98a + 10)b x +--R + +--R 7 5 3 3 +--R (- 16a + 40a - 32a + 8a)x +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 7 10 6 9 2 5 8 3 4 7 +--R - 32b x - 192a b x + (- 496a + 72)b x + (- 720a + 304a)b x +--R + +--R 4 2 3 6 5 3 2 5 +--R (- 640a + 520a - 50)b x + (- 352a + 456a - 124a)b x +--R + +--R 6 4 2 4 7 5 3 3 +--R (- 112a + 208a - 106a + 10)b x + (- 16a + 40a - 32a + 8a)x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 6 9 3 5 8 4 2 4 7 +--R (32a - 32)b x + (176a - 176a)b x + (400a - 456a + 56)b x +--R + +--R 5 3 3 6 6 4 2 2 5 +--R (480a - 680a + 200a)b x + (320a - 584a + 290a - 26)b x +--R + +--R 7 5 3 4 8 6 4 2 3 +--R (112a - 264a + 196a - 44a)b x + (16a - 48a + 50a - 20a + 2)x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R Type: Expression Integer +--E 137 + +--S 138 of 510 +m0026b:= a0026.2-r0026 +--R +--R +--R (105) +--R +--------+ +----------------------+ +--R 2 | 2 +-------+ +-----+ | 2 2 2 +--R (- a + 1)\|- a + 1 \|- a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 3 | 2 +-------+ +-----+ +--R ((a - 1)b x + a - a)\|- a + 1 \|- a - 1 \|a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +----------------------+ +--R 2 2 +-------+ +-----+ | 2 2 2 +--R 2a b x \|- a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R 3 3 2 2 2 +-------+ +-----+ +--R (- 2a b x - 2a b x )\|- a - 1 \|a - 1 +--R * +--R +--------+ +----------------------+ +--------+ +--R | 2 | 2 2 2 | 2 +--R \|- a + 1 \|b x + 2a b x + a - 1 - b x\|- a + 1 +--R atan(-----------------------------------------------------) +--R 2 +--R a - 1 +--R + +--R +--------+ +----------------------+ +--R 2 2 | 2 | 2 2 2 +--R - 2a b x \|- a + 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 3 3 2 2 2 | 2 +--R (2a b x + 2a b x )\|- a + 1 +--R * +--R +-------+ +-----------+ +--R \|- a - 1 \|b x + a - 1 +--R atan(------------------------) +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R + +--R +--------+ +--R | 2 +-------+ +-----+ +-----------+ +-----------+ +--R b x\|- a + 1 \|- a - 1 \|a - 1 \|b x + a - 1 \|b x + a + 1 +--R + +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R ((a - 1)acosh(b x + a) + a b x)\|- a + 1 \|- a - 1 \|a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 2 | 2 +-------+ +-----+ +-----------+ +-----------+ +--R (- b x - a b x)\|- a + 1 \|- a - 1 \|a - 1 \|b x + a - 1 \|b x + a + 1 +--R + +--R 2 3 2 2 2 +--R (((- a + 1)b x - a + a)acosh(b x + a) - a b x + (- a + 1)b x) +--R * +--R +--------+ +--R | 2 +-------+ +-----+ +--R \|- a + 1 \|- a - 1 \|a - 1 +--R / +--R +--------+ +----------------------+ +--R 2 2 | 2 +-------+ +-----+ | 2 2 2 +--R (2a - 2)x \|- a + 1 \|- a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 3 3 2 | 2 +-------+ +-----+ +--R ((- 2a + 2)b x + (- 2a + 2a)x )\|- a + 1 \|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 138 + +--S 139 of 510 +d0026b:= D(m0026b,x) +--R +--R +--R (106) +--R 2 2 2 +-----------+ +-----------+ +--R (4b x + 8a b x + 4a - 2)\|b x + a - 1 \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 3 3 2 2 2 3 +-----------+ +--R (- 4b x - 12a b x + (- 12a + 4)b x - 4a + 4a)\|b x + a - 1 +--R * +--R +-----------+ +--R \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 2 2 2 2 2 +--R ((- 4b x - 8a b x - 4a + 2)acosh(b x + a) - 2b x - 2a b x) +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 3 3 2 2 2 +--R - 2b x - 4a b x + (- 2a + 1)b x +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 3 3 2 2 2 3 3 3 +--R (4b x + 12a b x + (12a - 4)b x + 4a - 4a)acosh(b x + a) + 2b x +--R + +--R 2 2 2 +--R 4a b x + (2a - 1)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 4 4 3 3 2 2 2 3 +--R 2b x + 6a b x + (6a - 2)b x + (2a - 2a)b x +--R / +--R 2 5 4 2 3 +-----------+ +-----------+ +--R (4b x + 8a b x + (4a - 2)x )\|b x + a - 1 \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 3 6 2 5 2 4 3 3 +-----------+ +--R (- 4b x - 12a b x + (- 12a + 4)b x + (- 4a + 4a)x )\|b x + a - 1 +--R * +--R +-----------+ +--R \|b x + a + 1 +--R Type: Expression Integer +--E 139 + +--S 140 of 510 +t0027:= 1/(a+b*acosh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (107) ----------------------- +--R +--------------------+ +--R \|b acosh(d x + c) + a +--R Type: Expression Integer +--E 140 + +--S 141 of 510 +r0027:= -1/2*%pi^(1/2)*(exp(2*a/b)*erf((a+b*acosh(c+d*x))^(1/2)/b^(1/2))+_ + %i*erf(%i*(a+b*acosh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d +--R +--R +--R (108) +--R a 2a +--R - - -- +--------------------+ +--R b b +---+ \|b acosh(d x + c) + a +--R - %e %e \|%pi erf(-----------------------) +--R +-+ +--R \|b +--R + +--R a +--R - - +--------------------+ +--R b +---+ %i\|b acosh(d x + c) + a +--R - %i %e \|%pi erf(-------------------------) +--R +-+ +--R \|b +--R / +--R +-+ +--R 2d\|b +--R Type: Expression Complex Integer +--E 141 + +--S 142 of 510 +a0027:= integrate(t0027,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 142 + +--S 143 of 510 +--m0027:= a0027-r0027 +--E 143 + +--S 144 of 510 +--d0027:= D(m0027,x) +--E 144 + +--S 145 of 510 +t0028:= 1/(a-b*acosh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (109) ------------------------- +--R +----------------------+ +--R \|- b acosh(d x + c) + a +--R Type: Expression Integer +--E 145 + +--S 146 of 510 +r0028:= -1/2*%pi^(1/2)*(exp(2*a/b)*erf((a-b*acosh(c+d*x))^(1/2)/b^(1/2))+_ + %i*erf(%i*(a-b*acosh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d +--R +--R +--R (110) +--R a 2a +--R - - -- +----------------------+ +--R b b +---+ \|- b acosh(d x + c) + a +--R - %e %e \|%pi erf(-------------------------) +--R +-+ +--R \|b +--R + +--R a +--R - - +----------------------+ +--R b +---+ %i\|- b acosh(d x + c) + a +--R - %i %e \|%pi erf(---------------------------) +--R +-+ +--R \|b +--R / +--R +-+ +--R 2d\|b +--R Type: Expression Complex Integer +--E 146 + +--S 147 of 510 +a0028:= integrate(t0028,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 147 + +--S 148 of 510 +--m0028:= a0028-r0028 +--E 148 + +--S 149 of 510 +--d0028:= D(m0028,x) +--E 149 + +--S 150 of 510 +t0029:= acosh(x^(1/2)) +--R +--R +--R +-+ +--R (111) acosh(\|x ) +--R Type: Expression Integer +--E 150 + +--S 151 of 510 +r0029:= -1/2*(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)*x^(1/2)-_ + 1/2*acosh(x^(1/2))+x*acosh(x^(1/2)) +--R +--R +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ +-+ +--R - \|x \|\|x - 1 \|\|x + 1 + (2x - 1)acosh(\|x ) +--R (112) -------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 151 + +--S 152 of 510 +a0029:= integrate(t0029,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 152 + +--S 153 of 510 +m0029:= a0029-r0029 +--R +--R +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ +-+ +--R \|x \|\|x - 1 \|\|x + 1 + (- 2x + 1)acosh(\|x ) + 2a0029 +--R (113) ----------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 153 + +--S 154 of 510 +d0029:= D(m0029,x) +--R +--R +--R (114) +--R +--------+ +--------+ +--R +-----+ +-+ +-+ | +-+ | +-+ +--R (- 4\|x - 1 \|x acosh(\|x ) - 2x + 1)\|\|x - 1 \|\|x + 1 +--R + +--R +-----+ +--R (2x - 1)\|x - 1 +--R / +--R +--------+ +--------+ +--R +-----+ +-+ | +-+ | +-+ +--R 4\|x - 1 \|x \|\|x - 1 \|\|x + 1 +--R Type: Expression Integer +--E 154 + +--S 155 of 510 +t0030:= acosh(x^(1/2))/x +--R +--R +--R +-+ +--R acosh(\|x ) +--R (115) ----------- +--R x +--R Type: Expression Integer +--E 155 + +--S 156 of 510 +r0030:= acosh(x^(1/2))^2+2*acosh(x^(1/2))*log(1+exp(1)^(-2*acosh(x^(1/2))))-_ + polylog(2,-exp(1)^(-2*acosh(x^(1/2)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 156 + +--S 157 of 510 +a0030:= integrate(t0030,x) +--R +--R +--R x +--+ +--R ++ acosh(\|%P ) +--R (116) | ------------ d%P +--R ++ %P +--R Type: Union(Expression Integer,...) +--E 157 + +--S 158 of 510 +--m0030:= a0030-r0030 +--E 158 + +--S 159 of 510 +--d0030:= D(m0030,x) +--E 159 + +--S 160 of 510 +t0031:= x*atanh(a*x) +--R +--R +--R (117) x atanh(a x) +--R Type: Expression Integer +--E 160 + +--S 161 of 510 +r0031:= 1/2*(a*x-atanh(a*x)+x^2*atanh(a*x)*a^2)/a^2 +--R +--R +--R 2 2 +--R (a x - 1)atanh(a x) + a x +--R (118) -------------------------- +--R 2 +--R 2a +--R Type: Expression Integer +--E 161 + +--S 162 of 510 +a0031:= integrate(t0031,x) +--R +--R +--R 2 2 - a x - 1 +--R (a x - 1)log(---------) + 2a x +--R a x - 1 +--R (119) ------------------------------- +--R 2 +--R 4a +--R Type: Union(Expression Integer,...) +--E 162 + +--S 163 of 510 +m0031:= a0031-r0031 +--R +--R +--R 2 2 - a x - 1 2 2 +--R (a x - 1)log(---------) + (- 2a x + 2)atanh(a x) +--R a x - 1 +--R (120) -------------------------------------------------- +--R 2 +--R 4a +--R Type: Expression Integer +--E 163 + +--S 164 of 510 +d0031:= D(m0031,x) +--R +--R +--R - a x - 1 +--R x log(---------) - 2x atanh(a x) +--R a x - 1 +--R (121) -------------------------------- +--R 2 +--R Type: Expression Integer +--E 164 + +--S 165 of 510 +t0032:= atanh(a*x)/x +--R +--R +--R atanh(a x) +--R (122) ---------- +--R x +--R Type: Expression Integer +--E 165 + +--S 166 of 510 +r0032:= -1/2*polylog(2,-a*x)+1/2*polylog(2,a*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 166 + +--S 167 of 510 +a0032:= integrate(t0032,x) +--R +--R +--R x +--R ++ atanh(%P a) +--R (123) | ----------- d%P +--R ++ %P +--R Type: Union(Expression Integer,...) +--E 167 + +--S 168 of 510 +--m0032:= a0032-r0032 +--E 168 + +--S 169 of 510 +--d0032:= D(m0032,x) +--E 169 + +--S 170 of 510 +t0033:= atanh(a*x)/x^3 +--R +--R +--R atanh(a x) +--R (124) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 170 + +--S 171 of 510 +r0033:= 1/2*(-atanh(a*x)+x^2*atanh(a*x)*a^2-a*x)/x^2 +--R +--R +--R 2 2 +--R (a x - 1)atanh(a x) - a x +--R (125) -------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 171 + +--S 172 of 510 +a0033:= integrate(t0033,x) +--R +--R +--R 2 2 - a x - 1 +--R (a x - 1)log(---------) - 2a x +--R a x - 1 +--R (126) ------------------------------- +--R 2 +--R 4x +--R Type: Union(Expression Integer,...) +--E 172 + +--S 173 of 510 +m0033:= a0033-r0033 +--R +--R +--R 2 2 - a x - 1 2 2 +--R (a x - 1)log(---------) + (- 2a x + 2)atanh(a x) +--R a x - 1 +--R (127) -------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 173 + +--S 174 of 510 +d0033:= D(m0033,x) +--R +--R +--R - a x - 1 +--R log(---------) - 2atanh(a x) +--R a x - 1 +--R (128) ---------------------------- +--R 3 +--R 2x +--R Type: Expression Integer +--E 174 + +--S 175 of 510 +t0034:= (a+b*x)*atanh(a+b*x) +--R +--R +--R (129) (b x + a)atanh(b x + a) +--R Type: Expression Integer +--E 175 + +--S 176 of 510 +r0034:= 1/2/b*(a+b*x)-1/2*atanh(a+b*x)/b+1/2*(a+b*x)^2*atanh(a+b*x)/b +--R +--R +--R 2 2 2 +--R (b x + 2a b x + a - 1)atanh(b x + a) + b x + a +--R (130) ------------------------------------------------ +--R 2b +--R Type: Expression Integer +--E 176 + +--S 177 of 510 +a0034:= integrate(t0034,x) +--R +--R +--R 2 2 2 - b x - a - 1 +--R (b x + 2a b x + a - 1)log(-------------) + 2b x +--R b x + a - 1 +--R (131) ------------------------------------------------- +--R 4b +--R Type: Union(Expression Integer,...) +--E 177 + +--S 178 of 510 +m0034:= a0034-r0034 +--R +--R +--R (132) +--R 2 2 2 - b x - a - 1 +--R (b x + 2a b x + a - 1)log(-------------) +--R b x + a - 1 +--R + +--R 2 2 2 +--R (- 2b x - 4a b x - 2a + 2)atanh(b x + a) - 2a +--R / +--R 4b +--R Type: Expression Integer +--E 178 + +--S 179 of 510 +d0034:= D(m0034,x) +--R +--R +--R - b x - a - 1 +--R (b x + a)log(-------------) + (- 2b x - 2a)atanh(b x + a) +--R b x + a - 1 +--R (133) --------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 179 + +--S 180 of 510 +t0035:= (a+b*x)^2*atanh(a+b*x) +--R +--R +--R 2 2 2 +--R (134) (b x + 2a b x + a )atanh(b x + a) +--R Type: Expression Integer +--E 180 + +--S 181 of 510 +r0035:= 1/6*(a+b*x)^2/b+1/3*(a+b*x)^3*atanh(a+b*x)/b+1/6*log(1-(a+b*x)^2)/b +--R +--R +--R (135) +--R 2 2 2 +--R log(- b x - 2a b x - a + 1) +--R + +--R 3 3 2 2 2 3 2 2 2 +--R (2b x + 6a b x + 6a b x + 2a )atanh(b x + a) + b x + 2a b x + a +--R / +--R 6b +--R Type: Expression Integer +--E 181 + +--S 182 of 510 +a0035:= integrate(t0035,x) +--R +--R +--R (136) +--R 3 3 +--R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) +--R + +--R 3 3 2 2 2 - b x - a - 1 2 2 +--R (b x + 3a b x + 3a b x)log(-------------) + b x + 2a b x +--R b x + a - 1 +--R / +--R 6b +--R Type: Union(Expression Integer,...) +--E 182 + +--S 183 of 510 +m0035:= a0035-r0035 +--R +--R +--R (137) +--R 3 3 +--R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) +--R + +--R 3 3 2 2 2 - b x - a - 1 +--R (b x + 3a b x + 3a b x)log(-------------) +--R b x + a - 1 +--R + +--R 2 2 2 +--R - log(- b x - 2a b x - a + 1) +--R + +--R 3 3 2 2 2 3 2 +--R (- 2b x - 6a b x - 6a b x - 2a )atanh(b x + a) - a +--R / +--R 6b +--R Type: Expression Integer +--E 183 + +--S 184 of 510 +d0035:= D(m0035,x) +--R +--R +--R (138) +--R 2 2 2 - b x - a - 1 +--R (b x + 2a b x + a )log(-------------) +--R b x + a - 1 +--R + +--R 2 2 2 +--R (- 2b x - 4a b x - 2a )atanh(b x + a) +--R / +--R 2 +--R Type: Expression Integer +--E 184 + +--S 185 of 510 +t0036:= atanh(1+x)/(2+2*x) +--R +--R +--R atanh(x + 1) +--R (139) ------------ +--R 2x + 2 +--R Type: Expression Integer +--E 185 + +--S 186 of 510 +r0036:= -1/4*polylog(2,-1-x)+1/4*polylog(2,1+x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 186 + +--S 187 of 510 +a0036:= integrate(t0036,x) +--R +--R +--R x +--R ++ atanh(%P + 1) +--R (140) | ------------- d%P +--R ++ 2%P + 2 +--R Type: Union(Expression Integer,...) +--E 187 + +--S 188 of 510 +--m0036:= a0036-r0036 +--E 188 + +--S 189 of 510 +--d0036:= D(m0036,x) +--E 189 + +--S 190 of 510 +t0037:= atanh(a+b*x)/(a+b*x) +--R +--R +--R atanh(b x + a) +--R (141) -------------- +--R b x + a +--R Type: Expression Integer +--E 190 + +--S 191 of 510 +r0037:= -1/2*(polylog(2,-a-b*x)-polylog(2,a+b*x))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 191 + +--S 192 of 510 +a0037:= integrate(t0037,x) +--R +--R +--R x +--R ++ atanh(%P b + a) +--R (142) | --------------- d%P +--R ++ %P b + a +--R Type: Union(Expression Integer,...) +--E 192 + +--S 193 of 510 +--m0037:= a0037-r0037 +--E 193 + +--S 194 of 510 +--d0037:= D(m0037,x) +--E 194 + +--S 195 of 510 +t0038:= atanh(x)/(1-x^2)^2 +--R +--R +--R atanh(x) +--R (143) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 195 + +--S 196 of 510 +r0038:= 1/4*(1-2*x*atanh(x)-atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) +--R +--R +--R 2 2 +--R (x - 1)atanh(x) - 2x atanh(x) + 1 +--R (144) ----------------------------------- +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 196 + +--S 197 of 510 +a0038:= integrate(t0038,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R (x - 1)log(-------) - 4x log(-------) + 4 +--R x - 1 x - 1 +--R (145) ------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Union(Expression Integer,...) +--E 197 + +--S 198 of 510 +m0038:= a0038-r0038 +--R +--R +--R (146) +--R 2 - x - 1 2 - x - 1 2 2 +--R (x - 1)log(-------) - 4x log(-------) + (- 4x + 4)atanh(x) + 8x atanh(x) +--R x - 1 x - 1 +--R ---------------------------------------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Expression Integer +--E 198 + +--S 199 of 510 +d0038:= D(m0038,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (147) ------------------------ +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression Integer +--E 199 + +--S 200 of 510 +t0039:= atanh(x)^2/(1-x^2)^2 +--R +--R +--R 2 +--R atanh(x) +--R (148) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 200 + +--S 201 of 510 +r0039:= 1/12*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2-2*atanh(x)^3+_ + 2*x^2*atanh(x)^3)/(-1+x^2) +--R +--R +--R 2 3 2 2 +--R (2x - 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x +--R (149) ---------------------------------------------------------- +--R 2 +--R 12x - 12 +--R Type: Expression Integer +--E 201 + +--S 202 of 510 +a0039:= integrate(t0039,x) +--R +--R +--R (150) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) - 12x +--R x - 1 x - 1 x - 1 +--R ---------------------------------------------------------------------- +--R 2 +--R 48x - 48 +--R Type: Union(Expression Integer,...) +--E 202 + +--S 203 of 510 +m0039:= a0039-r0039 +--R +--R +--R (151) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R 2 3 2 2 +--R (- 8x + 8)atanh(x) + 24x atanh(x) + (- 12x - 12)atanh(x) +--R / +--R 2 +--R 48x - 48 +--R Type: Expression Integer +--E 203 + +--S 204 of 510 +d0039:= D(m0039,x) +--R +--R +--R - x - 1 2 2 +--R log(-------) - 4atanh(x) +--R x - 1 +--R (152) -------------------------- +--R 4 2 +--R 4x - 8x + 4 +--R Type: Expression Integer +--E 204 + +--S 205 of 510 +t0040:= 1/(a-a*x^2)/(b-2*b*atanh(x)) +--R +--R +--R 1 +--R (153) --------------------------------------- +--R 2 2 +--R (2a b x - 2a b)atanh(x) - a b x + a b +--R Type: Expression Integer +--E 205 + +--S 206 of 510 +r0040:= -1/2*log(1-2*atanh(x))/a/b +--R +--R +--R log(- 2atanh(x) + 1) +--R (154) - -------------------- +--R 2a b +--R Type: Expression Integer +--E 206 + +--S 207 of 510 +a0040:= integrate(t0040,x) +--R +--R +--R - x - 1 +--R log(log(-------) - 1) +--R x - 1 +--R (155) - --------------------- +--R 2a b +--R Type: Union(Expression Integer,...) +--E 207 + +--S 208 of 510 +m0040:= a0040-r0040 +--R +--R +--R - x - 1 +--R - log(log(-------) - 1) + log(- 2atanh(x) + 1) +--R x - 1 +--R (156) ---------------------------------------------- +--R 2a b +--R Type: Expression Integer +--E 208 + +--S 209 of 510 +d0040:= D(m0040,x) +--R +--R +--R (157) +--R - x - 1 +--R - log(-------) + 2atanh(x) +--R x - 1 +--R / +--R 2 2 - x - 1 +--R ((2a b x - 2a b)atanh(x) - a b x + a b)log(-------) +--R x - 1 +--R + +--R 2 2 +--R (- 2a b x + 2a b)atanh(x) + a b x - a b +--R Type: Expression Integer +--E 209 + +--S 210 of 510 +t0041:= x*atanh(x)/(1-x^2) +--R +--R +--R x atanh(x) +--R (158) - ---------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 210 + +--S 211 of 510 +r0041:= -1/2*atanh(x)^2+atanh(x)*log(2/(1-x))+1/2*polylog(2,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 510 +a0041:= integrate(t0041,x) +--R +--R +--R x +--R ++ %P atanh(%P) +--R (159) | - ------------ d%P +--R ++ 2 +--R %P - 1 +--R Type: Union(Expression Integer,...) +--E 212 + +--S 213 of 510 +--m0041:= a0041-r0041 +--E 213 + +--S 214 of 510 +--d0041:= D(m0041,x) +--E 214 + +--S 215 of 510 +t0042:= x*atanh(x)/(1-x^2)^2 +--R +--R +--R x atanh(x) +--R (160) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 215 + +--S 216 of 510 +r0042:= -1/4*(-x+atanh(x)+x^2*atanh(x))/(-1+x^2) +--R +--R +--R 2 +--R (- x - 1)atanh(x) + x +--R (161) ---------------------- +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 216 + +--S 217 of 510 +a0042:= integrate(t0042,x) +--R +--R +--R 2 - x - 1 +--R (- x - 1)log(-------) + 2x +--R x - 1 +--R (162) --------------------------- +--R 2 +--R 8x - 8 +--R Type: Union(Expression Integer,...) +--E 217 + +--S 218 of 510 +m0042:= a0042-r0042 +--R +--R +--R 2 - x - 1 2 +--R (- x - 1)log(-------) + (2x + 2)atanh(x) +--R x - 1 +--R (163) ------------------------------------------ +--R 2 +--R 8x - 8 +--R Type: Expression Integer +--E 218 + +--S 219 of 510 +d0042:= D(m0042,x) +--R +--R +--R - x - 1 +--R x log(-------) - 2x atanh(x) +--R x - 1 +--R (164) ---------------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression Integer +--E 219 + +--S 220 of 510 +t0043:= x*atanh(x)/(1-x^2)^3 +--R +--R +--R x atanh(x) +--R (165) - ------------------ +--R 6 4 2 +--R x - 3x + 3x - 1 +--R Type: Expression Integer +--E 220 + +--S 221 of 510 +r0043:= -1/32*(5*x-3*x^3-5*atanh(x)-6*x^2*atanh(x)+3*atanh(x)*x^4)/(-1+x^2)^2 +--R +--R +--R 4 2 3 +--R (- 3x + 6x + 5)atanh(x) + 3x - 5x +--R (166) ------------------------------------ +--R 4 2 +--R 32x - 64x + 32 +--R Type: Expression Integer +--E 221 + +--S 222 of 510 +a0043:= integrate(t0043,x) +--R +--R +--R 4 2 - x - 1 3 +--R (- 3x + 6x + 5)log(-------) + 6x - 10x +--R x - 1 +--R (167) ----------------------------------------- +--R 4 2 +--R 64x - 128x + 64 +--R Type: Union(Expression Integer,...) +--E 222 + +--S 223 of 510 +m0043:= a0043-r0043 +--R +--R +--R 4 2 - x - 1 4 2 +--R (- 3x + 6x + 5)log(-------) + (6x - 12x - 10)atanh(x) +--R x - 1 +--R (168) --------------------------------------------------------- +--R 4 2 +--R 64x - 128x + 64 +--R Type: Expression Integer +--E 223 + +--S 224 of 510 +d0043:= D(m0043,x) +--R +--R +--R - x - 1 +--R - x log(-------) + 2x atanh(x) +--R x - 1 +--R (169) ------------------------------ +--R 6 4 2 +--R 2x - 6x + 6x - 2 +--R Type: Expression Integer +--E 224 + +--S 225 of 510 +t0044:= x^3*atanh(x)/(1-x^2) +--R +--R +--R 3 +--R x atanh(x) +--R (170) - ---------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 225 + +--S 226 of 510 +r0044:= -1/2*x+1/2*atanh(x)-1/2*x^2*atanh(x)-1/2*atanh(x)^2+_ + atanh(x)*log(2/(1-x))+1/2*polylog(2,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 226 + +--S 227 of 510 +a0044:= integrate(t0044,x) +--R +--R +--R x 3 +--R ++ %P atanh(%P) +--R (171) | - ------------ d%P +--R ++ 2 +--R %P - 1 +--R Type: Union(Expression Integer,...) +--E 227 + +--S 228 of 510 +--m0044:= a0044-r0044 +--E 228 + +--S 229 of 510 +--d0044:= D(m0044,x) +--E 229 + +--S 230 of 510 +t0045:= x^2*atanh(x)/(1-x^2) +--R +--R +--R 2 +--R x atanh(x) +--R (172) - ---------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 230 + +--S 231 of 510 +r0045:= -x*atanh(x)+1/2*atanh(x)^2-1/2*log(1-x^2) +--R +--R +--R 2 2 +--R - log(- x + 1) + atanh(x) - 2x atanh(x) +--R (173) ----------------------------------------- +--R 2 +--R Type: Expression Integer +--E 231 + +--S 232 of 510 +a0045:= integrate(t0045,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R - 4log(x - 1) + log(-------) - 4x log(-------) +--R x - 1 x - 1 +--R (174) ------------------------------------------------ +--R 8 +--R Type: Union(Expression Integer,...) +--E 232 + +--S 233 of 510 +m0045:= a0045-r0045 +--R +--R +--R (175) +--R 2 - x - 1 2 - x - 1 2 +--R - 4log(x - 1) + log(-------) - 4x log(-------) + 4log(- x + 1) +--R x - 1 x - 1 +--R + +--R 2 +--R - 4atanh(x) + 8x atanh(x) +--R / +--R 8 +--R Type: Expression Integer +--E 233 + +--S 234 of 510 +d0045:= D(m0045,x) +--R +--R +--R 2 - x - 1 2 +--R - x log(-------) + 2x atanh(x) +--R x - 1 +--R (176) ------------------------------ +--R 2 +--R 2x - 2 +--R Type: Expression Integer +--E 234 + +--S 235 of 510 +t0046:= x*atanh(x)/(1-x^2) +--R +--R +--R x atanh(x) +--R (177) - ---------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 235 + +--S 236 of 510 +r0046:= -1/2*atanh(x)^2+atanh(x)*log(2/(1-x))+1/2*polylog(2,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 236 + +--S 237 of 510 +a0046:= integrate(t0046,x) +--R +--R +--R x +--R ++ %P atanh(%P) +--R (178) | - ------------ d%P +--R ++ 2 +--R %P - 1 +--R Type: Union(Expression Integer,...) +--E 237 + +--S 238 of 510 +--m0046:= a0046-r0046 +--E 238 + +--S 239 of 510 +--d0046:= D(m0046,x) +--E 239 + +--S 240 of 510 +t0047:= atanh(x)/x/(1-x^2) +--R +--R +--R atanh(x) +--R (179) - -------- +--R 3 +--R x - x +--R Type: Expression Integer +--E 240 + +--S 241 of 510 +r0047:= -1/2*atanh(x)^2+atanh(x)*log(-2*x/(1-x))+1/2*polylog(2,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 241 + +--S 242 of 510 +a0047:= integrate(t0047,x) +--R +--R +--R x +--R ++ atanh(%P) +--R (180) | - --------- d%P +--R ++ 3 +--R %P - %P +--R Type: Union(Expression Integer,...) +--E 242 + +--S 243 of 510 +--m0047:= a0047-r0047 +--E 243 + +--S 244 of 510 +--d0047:= D(m0047,x) +--E 244 + +--S 245 of 510 +t0048:= atanh(x)/x^2/(1-x^2) +--R +--R +--R atanh(x) +--R (181) - -------- +--R 4 2 +--R x - x +--R Type: Expression Integer +--E 245 + +--S 246 of 510 +r0048:= -atanh(x)/x+1/2*atanh(x)^2+log(x/(1-x^2)^(1/2)) +--R +--R +--R x 2 +--R 2x log(-----------) + x atanh(x) - 2atanh(x) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R (182) --------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 246 + +--S 247 of 510 +a0048:= integrate(t0048,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R - 4x log(x - 1) + 8x log(x) + x log(-------) - 4log(-------) +--R x - 1 x - 1 +--R (183) -------------------------------------------------------------- +--R 8x +--R Type: Union(Expression Integer,...) +--E 247 + +--S 248 of 510 +m0048:= a0048-r0048 +--R +--R +--R (184) +--R x 2 - x - 1 2 +--R - 8x log(-----------) - 4x log(x - 1) + 8x log(x) + x log(-------) +--R +--------+ x - 1 +--R | 2 +--R \|- x + 1 +--R + +--R - x - 1 2 +--R - 4log(-------) - 4x atanh(x) + 8atanh(x) +--R x - 1 +--R / +--R 8x +--R Type: Expression Integer +--E 248 + +--S 249 of 510 +d0048:= D(m0048,x) +--R +--R +--R - x - 1 +--R - log(-------) + 2atanh(x) +--R x - 1 +--R (185) -------------------------- +--R 4 2 +--R 2x - 2x +--R Type: Expression Integer +--E 249 + +--S 250 of 510 +t0049:= atanh(x)/x^3/(1-x^2) +--R +--R +--R atanh(x) +--R (186) - -------- +--R 5 3 +--R x - x +--R Type: Expression Integer +--E 250 + +--S 251 of 510 +r0049:= -1/2/x+1/2*atanh(x)-1/2*atanh(x)/x^2-1/2*atanh(x)^2+_ + atanh(x)*log(-2*x/(1-x))+1/2*polylog(2,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 251 + +--S 252 of 510 +a0049:= integrate(t0049,x) +--R +--R +--R x +--R ++ atanh(%P) +--R (187) | - --------- d%P +--R ++ 5 3 +--R %P - %P +--R Type: Union(Expression Integer,...) +--E 252 + +--S 253 of 510 +--m0049:= a0049-r0049 +--E 253 + +--S 254 of 510 +--d0049:= D(m0049,x) +--E 254 + +--S 255 of 510 +t0050:= x^3*atanh(x)^2/(1-x^2) +--R +--R +--R 3 2 +--R x atanh(x) +--R (188) - ----------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 255 + +--S 256 of 510 +r0050:= -x*atanh(x)+1/2*atanh(x)^2-1/2*x^2*atanh(x)^2-_ + 1/3*atanh(x)^3+atanh(x)^2*log(2/(1-x))-_ + 1/2*log(1-x^2)+atanh(x)*polylog(2,1-2/(1-x))-_ + 1/2*polylog(3,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 256 + +--S 257 of 510 +a0050:= integrate(t0050,x) +--R +--R +--R x 3 2 +--R ++ %P atanh(%P) +--R (189) | - ------------- d%P +--R ++ 2 +--R %P - 1 +--R Type: Union(Expression Integer,...) +--E 257 + +--S 258 of 510 +--m0050:= a0050-r0050 +--E 258 + +--S 259 of 510 +--d0050:= D(m0050,x) +--E 259 + +--S 260 of 510 +t0051:= x^2*atanh(x)^2/(1-x^2) +--R +--R +--R 2 2 +--R x atanh(x) +--R (190) - ----------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 260 + +--S 261 of 510 +r0051:= -atanh(x)^2-x*atanh(x)^2+1/3*atanh(x)^3+_ + 2*atanh(x)*log(2/(1-x))+polylog(2,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 261 + +--S 262 of 510 +a0051:= integrate(t0051,x) +--R +--R +--R x 2 2 +--R ++ %P atanh(%P) +--R (191) | - ------------- d%P +--R ++ 2 +--R %P - 1 +--R Type: Union(Expression Integer,...) +--E 262 + +--S 263 of 510 +--m0051:= a0051-r0051 +--E 263 + +--S 264 of 510 +--d0051:= D(m0051,x) +--E 264 + +--S 265 of 510 +t0052:= x*atanh(x)^2/(1-x^2) +--R +--R +--R 2 +--R x atanh(x) +--R (192) - ----------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 265 + +--S 266 of 510 +r0052:= -1/3*atanh(x)^3+atanh(x)^2*log(2/(1-x))+_ + atanh(x)*polylog(2,1-2/(1-x))-1/2*polylog(3,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 266 + +--S 267 of 510 +a0052:= integrate(t0052,x) +--R +--R +--R x 2 +--R ++ %P atanh(%P) +--R (193) | - ------------- d%P +--R ++ 2 +--R %P - 1 +--R Type: Union(Expression Integer,...) +--E 267 + +--S 268 of 510 +--m0052:= a0052-r0052 +--E 268 + +--S 269 of 510 +--d0052:= D(m0052,x) +--E 269 + +--S 270 of 510 +t0053:= atanh(x)^2/x/(1-x^2) +--R +--R +--R 2 +--R atanh(x) +--R (194) - --------- +--R 3 +--R x - x +--R Type: Expression Integer +--E 270 + +--S 271 of 510 +r0053:= -1/3*atanh(x)^3+atanh(x)^2*log(-2*x/(1-x))+_ + atanh(x)*polylog(2,-1+2/(1-x))-1/2*polylog(3,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 271 + +--S 272 of 510 +a0053:= integrate(t0053,x) +--R +--R +--R x 2 +--R ++ atanh(%P) +--R (195) | - ---------- d%P +--R ++ 3 +--R %P - %P +--R Type: Union(Expression Integer,...) +--E 272 + +--S 273 of 510 +--m0053:= a0053-r0053 +--E 273 + +--S 274 of 510 +--d0053:= D(m0053,x) +--E 274 + +--S 275 of 510 +t0054:= atanh(x)^2/x^2/(1-x^2) +--R +--R +--R 2 +--R atanh(x) +--R (196) - --------- +--R 4 2 +--R x - x +--R Type: Expression Integer +--E 275 + +--S 276 of 510 +r0054:= -atanh(x)^2-atanh(x)^2/x+1/3*atanh(x)^3+_ + 2*atanh(x)*log(-2*x/(1-x))+polylog(2,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 276 + +--S 277 of 510 +a0054:= integrate(t0054,x) +--R +--R +--R x 2 +--R ++ atanh(%P) +--R (197) | - ---------- d%P +--R ++ 4 2 +--R %P - %P +--R Type: Union(Expression Integer,...) +--E 277 + +--S 278 of 510 +--m0054:= a0054-r0054 +--E 278 + +--S 279 of 510 +--d0054:= D(m0054,x) +--E 279 + +--S 280 of 510 +t0055:= atanh(x)^2/x^3/(1-x^2) +--R +--R +--R 2 +--R atanh(x) +--R (198) - --------- +--R 5 3 +--R x - x +--R Type: Expression Integer +--E 280 + +--S 281 of 510 +r0055:= -atanh(x)/x+1/2*atanh(x)^2-1/2*atanh(x)^2/x^2-_ + 1/3*atanh(x)^3+atanh(x)^2*log(-2*x/(1-x))+_ + log(x/(1-x^2)^(1/2))+atanh(x)*polylog(2,-1+2/(1-x))-_ + 1/2*polylog(3,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 281 + +--S 282 of 510 +a0055:= integrate(t0055,x) +--R +--R +--R x 2 +--R ++ atanh(%P) +--R (199) | - ---------- d%P +--R ++ 5 3 +--R %P - %P +--R Type: Union(Expression Integer,...) +--E 282 + +--S 283 of 510 +--m0055:= a0055-r0055 +--E 283 + +--S 284 of 510 +--d0055:= D(m0055,x) +--E 284 + +--S 285 of 510 +t0056:= x^3*atanh(x)^3/(1-x^2) +--R +--R +--R 3 3 +--R x atanh(x) +--R (200) - ----------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 285 + +--S 286 of 510 +r0056:= -3/2*atanh(x)^2-3/2*x*atanh(x)^2+1/2*atanh(x)^3-_ + 1/2*x^2*atanh(x)^3-1/4*atanh(x)^4+_ + 3*atanh(x)*log(2/(1-x))+atanh(x)^3*log(2/(1-x))+_ + 3/2*(1+atanh(x)^2)*polylog(2,1-2/(1-x))-_ + 3/2*atanh(x)*polylog(3,1-2/(1-x))+3/4*polylog(4,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 286 + +--S 287 of 510 +a0056:= integrate(t0056,x) +--R +--R +--R x 3 3 +--R ++ %P atanh(%P) +--R (201) | - ------------- d%P +--R ++ 2 +--R %P - 1 +--R Type: Union(Expression Integer,...) +--E 287 + +--S 288 of 510 +--m0056:= a0056-r0056 +--E 288 + +--S 289 of 510 +--d0056:= D(m0056,x) +--E 289 + +--S 290 of 510 +t0057:= x^2*atanh(x)^3/(1-x^2) +--R +--R +--R 2 3 +--R x atanh(x) +--R (202) - ----------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 290 + +--S 291 of 510 +r0057:= -atanh(x)^3-x*atanh(x)^3+1/4*atanh(x)^4+_ + 3*atanh(x)^2*log(2/(1-x))+3*atanh(x)*polylog(2,1-2/(1-x))-_ + 3/2*polylog(3,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 291 + +--S 292 of 510 +a0057:= integrate(t0057,x) +--R +--R +--R x 2 3 +--R ++ %P atanh(%P) +--R (203) | - ------------- d%P +--R ++ 2 +--R %P - 1 +--R Type: Union(Expression Integer,...) +--E 292 + +--S 293 of 510 +--m0057:= a0057-r0057 +--E 293 + +--S 294 of 510 +--d0057:= D(m0057,x) +--E 294 + +--S 295 of 510 +t0058:= x*atanh(x)^3/(1-x^2) +--R +--R +--R 3 +--R x atanh(x) +--R (204) - ----------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 295 + +--S 296 of 510 +r0058:= -1/4*atanh(x)^4+atanh(x)^3*log(2)+atanh(x)^3*log(-1/(-1+x))+_ + 3/2*polylog(2,(1+x)/(-1+x))*atanh(x)^2-_ + 3/2*atanh(x)*polylog(3,(1+x)/(-1+x))+3/4*polylog(4,(1+x)/(-1+x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 296 + +--S 297 of 510 +a0058:= integrate(t0058,x) +--R +--R +--R x 3 +--R ++ %P atanh(%P) +--R (205) | - ------------- d%P +--R ++ 2 +--R %P - 1 +--R Type: Union(Expression Integer,...) +--E 297 + +--S 298 of 510 +--m0058:= a0058-r0058 +--E 298 + +--S 299 of 510 +--d0058:= D(m0058,x) +--E 299 + +--S 300 of 510 +t0059:= atanh(x)^3/x/(1-x^2) +--R +--R +--R 3 +--R atanh(x) +--R (206) - --------- +--R 3 +--R x - x +--R Type: Expression Integer +--E 300 + +--S 301 of 510 +r0059:= -1/4*atanh(x)^4+atanh(x)^3*log(-2*x/(1-x))+_ + 3/2*atanh(x)^2*polylog(2,-1+2/(1-x))-_ + 3/2*atanh(x)*polylog(3,-1+2/(1-x))+3/4*polylog(4,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 301 + +--S 302 of 510 +a0059:= integrate(t0059,x) +--R +--R +--R x 3 +--R ++ atanh(%P) +--R (207) | - ---------- d%P +--R ++ 3 +--R %P - %P +--R Type: Union(Expression Integer,...) +--E 302 + +--S 303 of 510 +--m0059:= a0059-r0059 +--E 303 + +--S 304 of 510 +--d0059:= D(m0059,x) +--E 304 + +--S 305 of 510 +t0060:= atanh(x)^3/x^2/(1-x^2) +--R +--R +--R 3 +--R atanh(x) +--R (208) - --------- +--R 4 2 +--R x - x +--R Type: Expression Integer +--E 305 + +--S 306 of 510 +r0060:= -atanh(x)^3-atanh(x)^3/x+1/4*atanh(x)^4+_ + 3*atanh(x)^2*log(-2*x/(1-x))+_ + 3*atanh(x)*polylog(2,-1+2/(1-x))-3/2*polylog(3,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 306 + +--S 307 of 510 +a0060:= integrate(t0060,x) +--R +--R +--R x 3 +--R ++ atanh(%P) +--R (209) | - ---------- d%P +--R ++ 4 2 +--R %P - %P +--R Type: Union(Expression Integer,...) +--E 307 + +--S 308 of 510 +--m0060:= a0060-r0060 +--E 308 + +--S 309 of 510 +--d0060:= D(m0060,x) +--E 309 + +--S 310 of 510 +t0061:= atanh(x)^3/x^3/(1-x^2) +--R +--R +--R 3 +--R atanh(x) +--R (210) - --------- +--R 5 3 +--R x - x +--R Type: Expression Integer +--E 310 + +--S 311 of 510 +r0061:= -3/2*atanh(x)^2-3/2*atanh(x)^2/x+1/2*atanh(x)^3-_ + 1/2*atanh(x)^3/x^2-1/4*atanh(x)^4+3*atanh(x)*log(-2*x/(1-x))+_ + atanh(x)^3*log(-2*x/(1-x))+_ + 3/2*(1+atanh(x)^2)*polylog(2,-1+2/(1-x))-_ + 3/2*atanh(x)*polylog(3,-1+2/(1-x))+3/4*polylog(4,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 311 + +--S 312 of 510 +a0061:= integrate(t0061,x) +--R +--R +--R x 3 +--R ++ atanh(%P) +--R (211) | - ---------- d%P +--R ++ 5 3 +--R %P - %P +--R Type: Union(Expression Integer,...) +--E 312 + +--S 313 of 510 +--m0061:= a0061-r0061 +--E 313 + +--S 314 of 510 +--d0061:= D(m0061,x) +--E 314 + +--S 315 of 510 +t0062:= x^3*atanh(x)/(1-x^2)^2 +--R +--R +--R 3 +--R x atanh(x) +--R (212) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 315 + +--S 316 of 510 +r0062:= 1/2*atanh(x)^2+1/4*atanh(x)*cosh(2*atanh(x))-_ + atanh(x)*log(2/(1-x))-1/2*polylog(2,1-2/(1-x))-1/8*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 316 + +--S 317 of 510 +a0062:= integrate(t0062,x) +--R +--R +--R x 3 +--R ++ %P atanh(%P) +--R (213) | -------------- d%P +--R ++ 4 2 +--R %P - 2%P + 1 +--R Type: Union(Expression Integer,...) +--E 317 + +--S 318 of 510 +--m0062:= a0062-r0062 +--E 318 + +--S 319 of 510 +--d0062:= D(m0062,x) +--E 319 + +--S 320 of 510 +t0063:= x^2*atanh(x)/(1-x^2)^2 +--R +--R +--R 2 +--R x atanh(x) +--R (214) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 320 + +--S 321 of 510 +r0063:= -x^2/(4-4*x^2)+x*atanh(x)/(2-2*x^2)-1/4*atanh(x)^2 +--R +--R +--R 2 2 2 +--R (- x + 1)atanh(x) - 2x atanh(x) + x +--R (215) -------------------------------------- +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 321 + +--S 322 of 510 +a0063:= integrate(t0063,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R (- x + 1)log(-------) - 4x log(-------) + 4 +--R x - 1 x - 1 +--R (216) --------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Union(Expression Integer,...) +--E 322 + +--S 323 of 510 +m0063:= a0063-r0063 +--R +--R +--R (217) +--R 2 - x - 1 2 - x - 1 2 2 +--R (- x + 1)log(-------) - 4x log(-------) + (4x - 4)atanh(x) +--R x - 1 x - 1 +--R + +--R 2 +--R 8x atanh(x) - 4x + 4 +--R / +--R 2 +--R 16x - 16 +--R Type: Expression Integer +--E 323 + +--S 324 of 510 +d0063:= D(m0063,x) +--R +--R +--R 2 - x - 1 2 +--R x log(-------) - 2x atanh(x) +--R x - 1 +--R (218) ---------------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression Integer +--E 324 + +--S 325 of 510 +t0064:= x*atanh(x)/(1-x^2)^2 +--R +--R +--R x atanh(x) +--R (219) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 325 + +--S 326 of 510 +r0064:= -1/4*(-x+atanh(x)+x^2*atanh(x))/(-1+x^2) +--R +--R +--R 2 +--R (- x - 1)atanh(x) + x +--R (220) ---------------------- +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 326 + +--S 327 of 510 +a0064:= integrate(t0064,x) +--R +--R +--R 2 - x - 1 +--R (- x - 1)log(-------) + 2x +--R x - 1 +--R (221) --------------------------- +--R 2 +--R 8x - 8 +--R Type: Union(Expression Integer,...) +--E 327 + +--S 328 of 510 +m0064:= a0064-r0064 +--R +--R +--R 2 - x - 1 2 +--R (- x - 1)log(-------) + (2x + 2)atanh(x) +--R x - 1 +--R (222) ------------------------------------------ +--R 2 +--R 8x - 8 +--R Type: Expression Integer +--E 328 + +--S 329 of 510 +d0064:= D(m0064,x) +--R +--R +--R - x - 1 +--R x log(-------) - 2x atanh(x) +--R x - 1 +--R (223) ---------------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression Integer +--E 329 + +--S 330 of 510 +t0065:= atanh(x)/(1-x^2)^2 +--R +--R +--R atanh(x) +--R (224) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 330 + +--S 331 of 510 +r0065:= 1/4*(1-2*x*atanh(x)-atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) +--R +--R +--R 2 2 +--R (x - 1)atanh(x) - 2x atanh(x) + 1 +--R (225) ----------------------------------- +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 331 + +--S 332 of 510 +a0065:= integrate(t0065,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R (x - 1)log(-------) - 4x log(-------) + 4 +--R x - 1 x - 1 +--R (226) ------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Union(Expression Integer,...) +--E 332 + +--S 333 of 510 +m0065:= a0065-r0065 +--R +--R +--R (227) +--R 2 - x - 1 2 - x - 1 2 2 +--R (x - 1)log(-------) - 4x log(-------) + (- 4x + 4)atanh(x) + 8x atanh(x) +--R x - 1 x - 1 +--R ---------------------------------------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Expression Integer +--E 333 + +--S 334 of 510 +d0065:= D(m0065,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (228) ------------------------ +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression Integer +--E 334 + +--S 335 of 510 +t0066:= atanh(x)/x/(1-x^2)^2 +--R +--R +--R atanh(x) +--R (229) ------------ +--R 5 3 +--R x - 2x + x +--R Type: Expression Integer +--E 335 + +--S 336 of 510 +r0066:= -1/2*atanh(x)^2+1/4*atanh(x)*cosh(2*atanh(x))+_ + atanh(x)*log(-2*x/(1-x))+1/2*polylog(2,-1+2/(1-x))-1/8*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 336 + +--S 337 of 510 +a0066:= integrate(t0066,x) +--R +--R +--R x +--R ++ atanh(%P) +--R (230) | --------------- d%P +--R ++ 5 3 +--R %P - 2%P + %P +--R Type: Union(Expression Integer,...) +--E 337 + +--S 338 of 510 +--m0066:= a0066-r0066 +--E 338 + +--S 339 of 510 +--d0066:= D(m0066,x) +--E 339 + +--S 340 of 510 +t0067:= atanh(x)/x^2/(1-x^2)^2 +--R +--R +--R atanh(x) +--R (231) ------------- +--R 6 4 2 +--R x - 2x + x +--R Type: Expression Integer +--E 340 + +--S 341 of 510 +r0067:= -atanh(x)/x+3/4*atanh(x)^2-1/8*cosh(2*atanh(x))+_ + log(x/(1-x^2)^(1/2))+1/4*atanh(x)*sinh(2*atanh(x)) +--R +--R +--R (232) +--R x +--R 2x atanh(x)sinh(2atanh(x)) + 8x log(-----------) - x cosh(2atanh(x)) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 2 +--R 6x atanh(x) - 8atanh(x) +--R / +--R 8x +--R Type: Expression Integer +--E 341 + +--S 342 of 510 +a0067:= integrate(t0067,x) +--R +--R +--R (233) +--R 3 2 3 3 - x - 1 2 +--R (- 8x + 8x)log(x - 1) + (16x - 16x)log(x) + (3x - 3x)log(-------) +--R x - 1 +--R + +--R 2 - x - 1 +--R (- 12x + 8)log(-------) + 4x +--R x - 1 +--R / +--R 3 +--R 16x - 16x +--R Type: Union(Expression Integer,...) +--E 342 + +--S 343 of 510 +m0067:= a0067-r0067 +--R +--R +--R (234) +--R 3 3 x +--R (- 4x + 4x)atanh(x)sinh(2atanh(x)) + (- 16x + 16x)log(-----------) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 3 3 2 3 +--R (2x - 2x)cosh(2atanh(x)) + (- 8x + 8x)log(x - 1) + (16x - 16x)log(x) +--R + +--R 3 - x - 1 2 2 - x - 1 +--R (3x - 3x)log(-------) + (- 12x + 8)log(-------) +--R x - 1 x - 1 +--R + +--R 3 2 2 +--R (- 12x + 12x)atanh(x) + (16x - 16)atanh(x) + 4x +--R / +--R 3 +--R 16x - 16x +--R Type: Expression Integer +--E 343 + +--S 344 of 510 +d0067:= D(m0067,x) +--R +--R +--R (235) +--R 4 2 - x - 1 4 2 +--R (x - x )atanh(x)cosh(2atanh(x)) + log(-------) + (x + x - 2)atanh(x) +--R x - 1 +--R ----------------------------------------------------------------------- +--R 6 4 2 +--R 2x - 4x + 2x +--R Type: Expression Integer +--E 344 + +--S 345 of 510 +t0068:= atanh(x)/x^3/(1-x^2)^2 +--R +--R +--R atanh(x) +--R (236) ------------- +--R 7 5 3 +--R x - 2x + x +--R Type: Expression Integer +--E 345 + +--S 346 of 510 +r0068:= -1/2/x-1/2*(1-x^2)*atanh(x)/x^2-atanh(x)^2+_ + 1/4*atanh(x)*cosh(2*atanh(x))+2*atanh(x)*log(-2*x/(1-x))+_ + polylog(2,-1+2/(1-x))-1/8*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 346 + +--S 347 of 510 +a0068:= integrate(t0068,x) +--R +--R +--R x +--R ++ atanh(%P) +--R (237) | ---------------- d%P +--R ++ 7 5 3 +--R %P - 2%P + %P +--R Type: Union(Expression Integer,...) +--E 347 + +--S 348 of 510 +--m0068:= a0068-r0068 +--E 348 + +--S 349 of 510 +--d0068:= D(m0068,x) +--E 349 + +--S 350 of 510 +t0069:= x^3*atanh(x)^2/(1-x^2)^2 +--R +--R +--R 3 2 +--R x atanh(x) +--R (238) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 350 + +--S 351 of 510 +r0069:= 1/3*atanh(x)^3+1/8*cosh(2*atanh(x))+_ + 1/4*atanh(x)^2*cosh(2*atanh(x))-atanh(x)^2*log(2/(1-x))-_ + atanh(x)*polylog(2,1-2/(1-x))+1/2*polylog(3,1-2/(1-x))-_ + 1/4*atanh(x)*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 351 + +--S 352 of 510 +a0069:= integrate(t0069,x) +--R +--R +--R x 3 2 +--R ++ %P atanh(%P) +--R (239) | -------------- d%P +--R ++ 4 2 +--R %P - 2%P + 1 +--R Type: Union(Expression Integer,...) +--E 352 + +--S 353 of 510 +--m0069:= a0069-r0069 +--E 353 + +--S 354 of 510 +--d0069:= D(m0069,x) +--E 354 + +--S 355 of 510 +t0070:= x^2*atanh(x)^2/(1-x^2)^2 +--R +--R +--R 2 2 +--R x atanh(x) +--R (240) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 355 + +--S 356 of 510 +r0070:= -1/12*(3*x-3*atanh(x)-3*x^2*atanh(x)+6*x*atanh(x)^2-_ + 2*atanh(x)^3+2*x^2*atanh(x)^3)/(-1+x^2) +--R +--R +--R 2 3 2 2 +--R (- 2x + 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x +--R (241) ------------------------------------------------------------ +--R 2 +--R 12x - 12 +--R Type: Expression Integer +--E 356 + +--S 357 of 510 +a0070:= integrate(t0070,x) +--R +--R +--R (242) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (- x + 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) - 12x +--R x - 1 x - 1 x - 1 +--R ------------------------------------------------------------------------ +--R 2 +--R 48x - 48 +--R Type: Union(Expression Integer,...) +--E 357 + +--S 358 of 510 +m0070:= a0070-r0070 +--R +--R +--R (243) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (- x + 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R 2 3 2 2 +--R (8x - 8)atanh(x) + 24x atanh(x) + (- 12x - 12)atanh(x) +--R / +--R 2 +--R 48x - 48 +--R Type: Expression Integer +--E 358 + +--S 359 of 510 +d0070:= D(m0070,x) +--R +--R +--R 2 - x - 1 2 2 2 +--R x log(-------) - 4x atanh(x) +--R x - 1 +--R (244) ------------------------------ +--R 4 2 +--R 4x - 8x + 4 +--R Type: Expression Integer +--E 359 + +--S 360 of 510 +t0071:= x*atanh(x)^2/(1-x^2)^2 +--R +--R +--R 2 +--R x atanh(x) +--R (245) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 360 + +--S 361 of 510 +r0071:= -1/4*(1-2*x*atanh(x)+atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) +--R +--R +--R 2 2 +--R (- x - 1)atanh(x) + 2x atanh(x) - 1 +--R (246) ------------------------------------- +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 361 + +--S 362 of 510 +a0071:= integrate(t0071,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R (- x - 1)log(-------) + 4x log(-------) - 4 +--R x - 1 x - 1 +--R (247) --------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Union(Expression Integer,...) +--E 362 + +--S 363 of 510 +m0071:= a0071-r0071 +--R +--R +--R (248) +--R 2 - x - 1 2 - x - 1 2 2 +--R (- x - 1)log(-------) + 4x log(-------) + (4x + 4)atanh(x) - 8x atanh(x) +--R x - 1 x - 1 +--R ---------------------------------------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Expression Integer +--E 363 + +--S 364 of 510 +d0071:= D(m0071,x) +--R +--R +--R - x - 1 2 2 +--R x log(-------) - 4x atanh(x) +--R x - 1 +--R (249) ------------------------------ +--R 4 2 +--R 4x - 8x + 4 +--R Type: Expression Integer +--E 364 + +--S 365 of 510 +t0072:= atanh(x)^2/(1-x^2)^2 +--R +--R +--R 2 +--R atanh(x) +--R (250) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 365 + +--S 366 of 510 +r0072:= 1/12*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2-_ + 2*atanh(x)^3+2*x^2*atanh(x)^3)/(-1+x^2) +--R +--R +--R 2 3 2 2 +--R (2x - 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x +--R (251) ---------------------------------------------------------- +--R 2 +--R 12x - 12 +--R Type: Expression Integer +--E 366 + +--S 367 of 510 +a0072:= integrate(t0072,x) +--R +--R +--R (252) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) - 12x +--R x - 1 x - 1 x - 1 +--R ---------------------------------------------------------------------- +--R 2 +--R 48x - 48 +--R Type: Union(Expression Integer,...) +--E 367 + +--S 368 of 510 +m0072:= a0072-r0072 +--R +--R +--R (253) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R 2 3 2 2 +--R (- 8x + 8)atanh(x) + 24x atanh(x) + (- 12x - 12)atanh(x) +--R / +--R 2 +--R 48x - 48 +--R Type: Expression Integer +--E 368 + +--S 369 of 510 +d0072:= D(m0072,x) +--R +--R +--R - x - 1 2 2 +--R log(-------) - 4atanh(x) +--R x - 1 +--R (254) -------------------------- +--R 4 2 +--R 4x - 8x + 4 +--R Type: Expression Integer +--E 369 + +--S 370 of 510 +t0073:= atanh(x)^2/x/(1-x^2)^2 +--R +--R +--R 2 +--R atanh(x) +--R (255) ------------ +--R 5 3 +--R x - 2x + x +--R Type: Expression Integer +--E 370 + +--S 371 of 510 +r0073:= -1/3*atanh(x)^3+1/8*cosh(2*atanh(x))+_ + 1/4*atanh(x)^2*cosh(2*atanh(x))+atanh(x)^2*log(-2*x/(1-x))+_ + atanh(x)*polylog(2,-1+2/(1-x))-1/2*polylog(3,-1+2/(1-x))-_ + 1/4*atanh(x)*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 371 + +--S 372 of 510 +a0073:= integrate(t0073,x) +--R +--R +--R x 2 +--R ++ atanh(%P) +--R (256) | --------------- d%P +--R ++ 5 3 +--R %P - 2%P + %P +--R Type: Union(Expression Integer,...) +--E 372 + +--S 373 of 510 +--m0073:= a0073-r0073 +--E 373 + +--S 374 of 510 +--d0073:= D(m0073,x) +--E 374 + +--S 375 of 510 +t0074:= atanh(x)^2/x^2/(1-x^2)^2 +--R +--R +--R 2 +--R atanh(x) +--R (257) ------------- +--R 6 4 2 +--R x - 2x + x +--R Type: Expression Integer +--E 375 + +--S 376 of 510 +r0074:= -atanh(x)^2-atanh(x)^2/x+1/2*atanh(x)^3-_ + 1/4*atanh(x)*cosh(2*atanh(x))+2*atanh(x)*log(-2*x/(1-x))+_ + polylog(2,-1+2/(1-x))+1/8*sinh(2*atanh(x))+_ + 1/4*atanh(x)^2*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 376 + +--S 377 of 510 +a0074:= integrate(t0074,x) +--R +--R +--R x 2 +--R ++ atanh(%P) +--R (258) | ---------------- d%P +--R ++ 6 4 2 +--R %P - 2%P + %P +--R Type: Union(Expression Integer,...) +--E 377 + +--S 378 of 510 +--m0074:= a0074-r0074 +--E 378 + +--S 379 of 510 +--d0074:= D(m0074,x) +--E 379 + +--S 380 of 510 +t0075:= atanh(x)^2/x^3/(1-x^2)^2 +--R +--R +--R 2 +--R atanh(x) +--R (259) ------------- +--R 7 5 3 +--R x - 2x + x +--R Type: Expression Integer +--E 380 + +--S 381 of 510 +r0075:= -atanh(x)/x-1/2*(1-x^2)*atanh(x)^2/x^2-2/3*atanh(x)^3+_ + 1/8*cosh(2*atanh(x))+1/4*atanh(x)^2*cosh(2*atanh(x))+_ + 2*atanh(x)^2*log(-2*x/(1-x))+log(x/(1-x^2)^(1/2))+_ + 2*atanh(x)*polylog(2,-1+2/(1-x))-polylog(3,-1+2/(1-x))-_ + 1/4*atanh(x)*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 381 + +--S 382 of 510 +a0075:= integrate(t0075,x) +--R +--R +--R x 2 +--R ++ atanh(%P) +--R (260) | ---------------- d%P +--R ++ 7 5 3 +--R %P - 2%P + %P +--R Type: Union(Expression Integer,...) +--E 382 + +--S 383 of 510 +--m0075:= a0075-r0075 +--E 383 + +--S 384 of 510 +--d0075:= D(m0075,x) +--E 384 + +--S 385 of 510 +t0076:= x^3*atanh(x)^3/(1-x^2)^2 +--R +--R +--R 3 3 +--R x atanh(x) +--R (261) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 385 + +--S 386 of 510 +r0076:= 1/4*atanh(x)^4+3/8*atanh(x)*cosh(2*atanh(x))+_ + 1/4*atanh(x)^3*cosh(2*atanh(x))-atanh(x)^3*log(2/(1-x))-_ + 3/2*atanh(x)^2*polylog(2,1-2/(1-x))+_ + 3/2*atanh(x)*polylog(3,1-2/(1-x))-_ + 3/4*polylog(4,1-2/(1-x))-3/16*sinh(2*atanh(x))-_ + 3/8*atanh(x)^2*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 386 + +--S 387 of 510 +a0076:= integrate(t0076,x) +--R +--R +--R x 3 3 +--R ++ %P atanh(%P) +--R (262) | -------------- d%P +--R ++ 4 2 +--R %P - 2%P + 1 +--R Type: Union(Expression Integer,...) +--E 387 + +--S 388 of 510 +--m0076:= a0076-r0076 +--E 388 + +--S 389 of 510 +--d0076:= D(m0076,x) +--E 389 + +--S 390 of 510 +t0077:= x^2*atanh(x)^3/(1-x^2)^2 +--R +--R +--R 2 3 +--R x atanh(x) +--R (263) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 390 + +--S 391 of 510 +r0077:= -1/8*(-3*x^2+6*x*atanh(x)-3*atanh(x)^2-3*x^2*atanh(x)^2+_ + 4*x*atanh(x)^3-atanh(x)^4+atanh(x)^4*x^2)/(-1+x^2) +--R +--R +--R (264) +--R 2 4 3 2 2 2 +--R (- x + 1)atanh(x) - 4x atanh(x) + (3x + 3)atanh(x) - 6x atanh(x) + 3x +--R --------------------------------------------------------------------------- +--R 2 +--R 8x - 8 +--R Type: Expression Integer +--E 391 + +--S 392 of 510 +a0077:= integrate(t0077,x) +--R +--R +--R (265) +--R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 +--R (- x + 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R - x - 1 +--R - 48x log(-------) + 48 +--R x - 1 +--R / +--R 2 +--R 128x - 128 +--R Type: Union(Expression Integer,...) +--E 392 + +--S 393 of 510 +m0077:= a0077-r0077 +--R +--R +--R (266) +--R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 +--R (- x + 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R - x - 1 2 4 3 +--R - 48x log(-------) + (16x - 16)atanh(x) + 64x atanh(x) +--R x - 1 +--R + +--R 2 2 2 +--R (- 48x - 48)atanh(x) + 96x atanh(x) - 48x + 48 +--R / +--R 2 +--R 128x - 128 +--R Type: Expression Integer +--E 393 + +--S 394 of 510 +d0077:= D(m0077,x) +--R +--R +--R 2 - x - 1 3 2 3 +--R x log(-------) - 8x atanh(x) +--R x - 1 +--R (267) ------------------------------ +--R 4 2 +--R 8x - 16x + 8 +--R Type: Expression Integer +--E 394 + +--S 395 of 510 +t0078:= x*atanh(x)^3/(1-x^2)^2 +--R +--R +--R 3 +--R x atanh(x) +--R (268) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 395 + +--S 396 of 510 +r0078:= -1/8*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2+2*atanh(x)^3+_ + 2*x^2*atanh(x)^3)/(-1+x^2) +--R +--R +--R 2 3 2 2 +--R (- 2x - 2)atanh(x) + 6x atanh(x) + (- 3x - 3)atanh(x) + 3x +--R (269) -------------------------------------------------------------- +--R 2 +--R 8x - 8 +--R Type: Expression Integer +--E 396 + +--S 397 of 510 +a0078:= integrate(t0078,x) +--R +--R +--R (270) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (- x - 1)log(-------) + 6x log(-------) + (- 6x - 6)log(-------) + 12x +--R x - 1 x - 1 x - 1 +--R -------------------------------------------------------------------------- +--R 2 +--R 32x - 32 +--R Type: Union(Expression Integer,...) +--E 397 + +--S 398 of 510 +m0078:= a0078-r0078 +--R +--R +--R (271) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (- x - 1)log(-------) + 6x log(-------) + (- 6x - 6)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R 2 3 2 2 +--R (8x + 8)atanh(x) - 24x atanh(x) + (12x + 12)atanh(x) +--R / +--R 2 +--R 32x - 32 +--R Type: Expression Integer +--E 398 + +--S 399 of 510 +d0078:= D(m0078,x) +--R +--R +--R - x - 1 3 3 +--R x log(-------) - 8x atanh(x) +--R x - 1 +--R (272) ------------------------------ +--R 4 2 +--R 8x - 16x + 8 +--R Type: Expression Integer +--E 399 + +--S 400 of 510 +t0079:= atanh(x)^3/(1-x^2)^2 +--R +--R +--R 3 +--R atanh(x) +--R (273) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 400 + +--S 401 of 510 +r0079:= 1/8*(3-6*x*atanh(x)+3*atanh(x)^2+3*x^2*atanh(x)^2-_ + 4*x*atanh(x)^3-atanh(x)^4+atanh(x)^4*x^2)/(-1+x^2) +--R +--R +--R (274) +--R 2 4 3 2 2 +--R (x - 1)atanh(x) - 4x atanh(x) + (3x + 3)atanh(x) - 6x atanh(x) + 3 +--R ----------------------------------------------------------------------- +--R 2 +--R 8x - 8 +--R Type: Expression Integer +--E 401 + +--S 402 of 510 +a0079:= integrate(t0079,x) +--R +--R +--R (275) +--R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 +--R (x - 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R - x - 1 +--R - 48x log(-------) + 48 +--R x - 1 +--R / +--R 2 +--R 128x - 128 +--R Type: Union(Expression Integer,...) +--E 402 + +--S 403 of 510 +m0079:= a0079-r0079 +--R +--R +--R (276) +--R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 +--R (x - 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R - x - 1 2 4 3 +--R - 48x log(-------) + (- 16x + 16)atanh(x) + 64x atanh(x) +--R x - 1 +--R + +--R 2 2 +--R (- 48x - 48)atanh(x) + 96x atanh(x) +--R / +--R 2 +--R 128x - 128 +--R Type: Expression Integer +--E 403 + +--S 404 of 510 +d0079:= D(m0079,x) +--R +--R +--R - x - 1 3 3 +--R log(-------) - 8atanh(x) +--R x - 1 +--R (277) -------------------------- +--R 4 2 +--R 8x - 16x + 8 +--R Type: Expression Integer +--E 404 + +--S 405 of 510 +t0080:= atanh(x)^3/x/(1-x^2)^2 +--R +--R +--R 3 +--R atanh(x) +--R (278) ------------ +--R 5 3 +--R x - 2x + x +--R Type: Expression Integer +--E 405 + +--S 406 of 510 +r0080:= -1/4*atanh(x)^4+3/8*atanh(x)*cosh(2*atanh(x))+_ + 1/4*atanh(x)^3*cosh(2*atanh(x))+atanh(x)^3*log(-2*x/(1-x))+_ + 3/2*atanh(x)^2*polylog(2,-1+2/(1-x))-_ + 3/2*atanh(x)*polylog(3,-1+2/(1-x))+3/4*polylog(4,-1+2/(1-x))-_ + 3/16*sinh(2*atanh(x))-3/8*atanh(x)^2*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 406 + +--S 407 of 510 +a0080:= integrate(t0080,x) +--R +--R +--R x 3 +--R ++ atanh(%P) +--R (279) | --------------- d%P +--R ++ 5 3 +--R %P - 2%P + %P +--R Type: Union(Expression Integer,...) +--E 407 + +--S 408 of 510 +--m0080:= a0080-r0080 +--E 408 + +--S 409 of 510 +--d0080:= D(m0080,x) +--E 409 + +--S 410 of 510 +t0081:= atanh(x)^3/x^2/(1-x^2)^2 +--R +--R +--R 3 +--R atanh(x) +--R (280) ------------- +--R 6 4 2 +--R x - 2x + x +--R Type: Expression Integer +--E 410 + +--S 411 of 510 +r0081:= -atanh(x)^3-atanh(x)^3/x+3/8*atanh(x)^4-_ + 3/16*cosh(2*atanh(x))-3/8*atanh(x)^2*cosh(2*atanh(x))+_ + 3*atanh(x)^2*log(-2*x/(1-x))+3*atanh(x)*polylog(2,-1+2/(1-x))-_ + 3/2*polylog(3,-1+2/(1-x))+_ + 3/8*atanh(x)*sinh(2*atanh(x))+1/4*atanh(x)^3*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 411 + +--S 412 of 510 +a0081:= integrate(t0081,x) +--R +--R +--R x 3 +--R ++ atanh(%P) +--R (281) | ---------------- d%P +--R ++ 6 4 2 +--R %P - 2%P + %P +--R Type: Union(Expression Integer,...) +--E 412 + +--S 413 of 510 +--m0081:= a0081-r0081 +--E 413 + +--S 414 of 510 +--d0081:= D(m0081,x) +--E 414 + +--S 415 of 510 +t0082:= atanh(x)^3/x^3/(1-x^2)^2 +--R +--R +--R 3 +--R atanh(x) +--R (282) ------------- +--R 7 5 3 +--R x - 2x + x +--R Type: Expression Integer +--E 415 + +--S 416 of 510 +r0082:= -3/2*atanh(x)^2-3/2*atanh(x)^2/x-1/2*(1-x^2)*atanh(x)^3/x^2-_ + 1/2*atanh(x)^4+3/8*atanh(x)*cosh(2*atanh(x))+_ + 1/4*atanh(x)^3*cosh(2*atanh(x))+3*atanh(x)*log(-2*x/(1-x))+_ + 2*atanh(x)^3*log(-2*x/(1-x))+_ + 3/2*(1+2*atanh(x)^2)*polylog(2,-1+2/(1-x))-_ + 3*atanh(x)*polylog(3,-1+2/(1-x))+_ + 3/2*polylog(4,-1+2/(1-x))-3/16*sinh(2*atanh(x))-_ + 3/8*atanh(x)^2*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 416 + +--S 417 of 510 +a0082:= integrate(t0082,x) +--R +--R +--R x 3 +--R ++ atanh(%P) +--R (283) | ---------------- d%P +--R ++ 7 5 3 +--R %P - 2%P + %P +--R Type: Union(Expression Integer,...) +--E 417 + +--S 418 of 510 +--m0082:= a0082-r0082 +--E 418 + +--S 419 of 510 +--d0082:= D(m0082,x) +--E 419 + +--S 420 of 510 +t0083:= x^2/(1-x^2)^2/atanh(x) +--R +--R +--R 2 +--R x +--R (284) ---------------------- +--R 4 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression Integer +--E 420 + +--S 421 of 510 +r0083:= 1/2*Chi(2*atanh(x))-1/2*log(atanh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 421 + +--S 422 of 510 +a0083:= integrate(t0083,x) +--R +--R +--R x 2 +--R ++ %P +--R (285) | ------------------------- d%P +--R ++ 4 2 +--R (%P - 2%P + 1)atanh(%P) +--R Type: Union(Expression Integer,...) +--E 422 + +--S 423 of 510 +--m0083:= a0083-r0083 +--E 423 + +--S 424 of 510 +--d0083:= D(m0083,x) +--E 424 + +--S 425 of 510 +t0084:= x/(1-x^2)^2/atanh(x) +--R +--R +--R x +--R (286) ---------------------- +--R 4 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression Integer +--E 425 + +--S 426 of 510 +r0084:= 1/2*Shi(2*atanh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 426 + +--S 427 of 510 +a0084:= integrate(t0084,x) +--R +--R +--R x +--R ++ %P +--R (287) | ------------------------- d%P +--R ++ 4 2 +--R (%P - 2%P + 1)atanh(%P) +--R Type: Union(Expression Integer,...) +--E 427 + +--S 428 of 510 +--m0084:= a0084-r0084 +--E 428 + +--S 429 of 510 +--d0084:= D(m0084,x) +--E 429 + +--S 430 of 510 +t0085:= 1/(1-x^2)^2/atanh(x) +--R +--R +--R 1 +--R (288) ---------------------- +--R 4 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression Integer +--E 430 + +--S 431 of 510 +r0085:= 1/2*Chi(2*atanh(x))+1/2*log(atanh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 431 + +--S 432 of 510 +a0085:= integrate(t0085,x) +--R +--R +--R x +--R ++ 1 +--R (289) | ------------------------- d%P +--R ++ 4 2 +--R (%P - 2%P + 1)atanh(%P) +--R Type: Union(Expression Integer,...) +--E 432 + +--S 433 of 510 +--m0085:= a0085-r0085 +--E 433 + +--S 434 of 510 +--d0085:= D(m0085,x) +--E 434 + +--S 435 of 510 +t0086:= x^2/(1-x^2)^2/atanh(x)^2 +--R +--R +--R 2 +--R x +--R (290) ----------------------- +--R 4 2 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression Integer +--E 435 + +--S 436 of 510 +r0086:= -x^2/(1-x^2)/atanh(x)+Shi(2*atanh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 436 + +--S 437 of 510 +a0086:= integrate(t0086,x) +--R +--R +--R x 2 +--R ++ %P +--R (291) | -------------------------- d%P +--R ++ 4 2 2 +--R (%P - 2%P + 1)atanh(%P) +--R Type: Union(Expression Integer,...) +--E 437 + +--S 438 of 510 +--m0086:= a0086-r0086 +--E 438 + +--S 439 of 510 +--d0086:= D(m0086,x) +--E 439 + +--S 440 of 510 +t0087:= x/(1-x^2)^2/atanh(x)^2 +--R +--R +--R x +--R (292) ----------------------- +--R 4 2 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression Integer +--E 440 + +--S 441 of 510 +r0087:= Chi(2*atanh(x))-1/2*sinh(2*atanh(x))/atanh(x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 441 + +--S 442 of 510 +a0087:= integrate(t0087,x) +--R +--R +--R x +--R ++ %P +--R (293) | -------------------------- d%P +--R ++ 4 2 2 +--R (%P - 2%P + 1)atanh(%P) +--R Type: Union(Expression Integer,...) +--E 442 + +--S 443 of 510 +--m0087:= a0087-r0087 +--E 443 + +--S 444 of 510 +--d0087:= D(m0087,x) +--E 444 + +--S 445 of 510 +t0088:= 1/(1-x^2)^2/atanh(x)^2 +--R +--R +--R 1 +--R (294) ----------------------- +--R 4 2 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression Integer +--E 445 + +--S 446 of 510 +r0088:= -1/(1-x^2)/atanh(x)+Shi(2*atanh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 446 + +--S 447 of 510 +a0088:= integrate(t0088,x) +--R +--R +--R x +--R ++ 1 +--R (295) | -------------------------- d%P +--R ++ 4 2 2 +--R (%P - 2%P + 1)atanh(%P) +--R Type: Union(Expression Integer,...) +--E 447 + +--S 448 of 510 +--m0088:= a0088-r0088 +--E 448 + +--S 449 of 510 +--d0088:= D(m0088,x) +--E 449 + +--S 450 of 510 +t0089:= x^2/(1-x^2)^2/atanh(x)^3 +--R +--R +--R 2 +--R x +--R (296) ----------------------- +--R 4 2 3 +--R (x - 2x + 1)atanh(x) +--R Type: Expression Integer +--E 450 + +--S 451 of 510 +r0089:= -1/2*x^2/(1-x^2)/atanh(x)^2-x/(1-x^2)/atanh(x)+Chi(2*atanh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 451 + +--S 452 of 510 +a0089:= integrate(t0089,x) +--R +--R +--R x 2 +--R ++ %P +--R (297) | -------------------------- d%P +--R ++ 4 2 3 +--R (%P - 2%P + 1)atanh(%P) +--R Type: Union(Expression Integer,...) +--E 452 + +--S 453 of 510 +--m0089:= a0089-r0089 +--E 453 + +--S 454 of 510 +--d0089:= D(m0089,x) +--E 454 + +--S 455 of 510 +t0090:= x/(1-x^2)^2/atanh(x)^3 +--R +--R +--R x +--R (298) ----------------------- +--R 4 2 3 +--R (x - 2x + 1)atanh(x) +--R Type: Expression Integer +--E 455 + +--S 456 of 510 +r0090:= -1/2*cosh(2*atanh(x))/atanh(x)-_ + 1/4*sinh(2*atanh(x))/atanh(x)^2+Shi(2*atanh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 456 + +--S 457 of 510 +a0090:= integrate(t0090,x) +--R +--R +--R x +--R ++ %P +--R (299) | -------------------------- d%P +--R ++ 4 2 3 +--R (%P - 2%P + 1)atanh(%P) +--R Type: Union(Expression Integer,...) +--E 457 + +--S 458 of 510 +--m0090:= a0090-r0090 +--E 458 + +--S 459 of 510 +--d0090:= D(m0090,x) +--E 459 + +--S 460 of 510 +t0091:= 1/(1-x^2)^2/atanh(x)^3 +--R +--R +--R 1 +--R (300) ----------------------- +--R 4 2 3 +--R (x - 2x + 1)atanh(x) +--R Type: Expression Integer +--E 460 + +--S 461 of 510 +r0091:= -1/2/(1-x^2)/atanh(x)^2-x/(1-x^2)/atanh(x)+Chi(2*atanh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R 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. +--E 461 + +--S 462 of 510 +a0091:= integrate(t0091,x) +--R +--R +--R x +--R ++ 1 +--R (301) | -------------------------- d%P +--R ++ 4 2 3 +--R (%P - 2%P + 1)atanh(%P) +--R Type: Union(Expression Integer,...) +--E 462 + +--S 463 of 510 +--m0091:= a0091-r0091 +--E 463 + +--S 464 of 510 +--d0091:= D(m0091,x) +--E 464 + +--S 465 of 510 +t0092:= atanh(x)/(a+b*x^2)^(3/2) +--R +--R +--R atanh(x) +--R (302) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression Integer +--E 465 + +--S 466 of 510 +r0092:= x*atanh(x)/a/(a+b*x^2)^(1/2)-_ + atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a/(a+b)^(1/2) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-----+ +--R - \|b x + a atanh(-----------) + x atanh(x)\|b + a +--R +-----+ +--R \|b + a +--R (303) ---------------------------------------------------- +--R +--------+ +--R +-----+ | 2 +--R a\|b + a \|b x + a +--R Type: Expression Integer +--E 466 + +--S 467 of 510 +a0092:= integrate(t0092,x) +--R +--R +--R (304) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R +--------+ +--R - x - 1 +-----+ | 2 - x - 1 +-+ +-----+ +--R - x log(-------)\|b + a \|b x + a + x log(-------)\|a \|b + a +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-+ +-----+ | 2 2 2 +-----+ +--R 2a\|a \|b + a \|b x + a + (- 2a b x - 2a )\|b + a +--R , +--R +--R +--------+ +--R +-+ | 2 2 +--R (- 2\|a \|b x + a + 2b x + 2a) +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R +--------+ +--R - x - 1 +-------+ | 2 - x - 1 +-------+ +-+ +--R - x log(-------)\|- b - a \|b x + a + x log(-------)\|- b - a \|a +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-------+ +-+ | 2 2 2 +-------+ +--R 2a\|- b - a \|a \|b x + a + (- 2a b x - 2a )\|- b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 467 + +--S 468 of 510 +m0092a:= a0092.1-r0092 +--R +--R +--R (305) +--R +--------+ +--R 2 | 2 2 +-+ +--R ((b x + a)\|b x + a + (- b x - a)\|a ) +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 2 +-+ \|b x + a +--R ((2b x + 2a)\|b x + a + (- 2b x - 2a)\|a )atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +--------+ +--R - x - 1 +-+ +-----+ | 2 +--R (- x log(-------) + 2x atanh(x))\|a \|b + a \|b x + a +--R x - 1 +--R + +--R 3 - x - 1 3 +-----+ +--R ((b x + a x)log(-------) + (- 2b x - 2a x)atanh(x))\|b + a +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-----+ | 2 2 2 +-+ +-----+ +--R (2a b x + 2a )\|b + a \|b x + a + (- 2a b x - 2a )\|a \|b + a +--R Type: Expression Integer +--E 468 + +--S 469 of 510 +d0092a:= D(m0092a,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (306) ------------------------ +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 469 + +--S 470 of 510 +m0092b:= a0092.2-r0092 +--R +--R +--R (307) +--R +--------+ +--R 2 +-------+ | 2 2 +-------+ +-+ +--R ((2b x + 2a)\|- b - a \|b x + a + (- 2b x - 2a)\|- b - a \|a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +--------+ +--R 2 +-----+ | 2 2 +-+ +-----+ +--R ((- 2b x - 2a)\|b + a \|b x + a + (2b x + 2a)\|a \|b + a ) +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R +--------+ +--R - x - 1 +-------+ +-+ +-----+ | 2 +--R (- x log(-------) + 2x atanh(x))\|- b - a \|a \|b + a \|b x + a +--R x - 1 +--R + +--R 3 - x - 1 3 +-------+ +-----+ +--R ((b x + a x)log(-------) + (- 2b x - 2a x)atanh(x))\|- b - a \|b + a +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ +-----+ | 2 +--R (2a b x + 2a )\|- b - a \|b + a \|b x + a +--R + +--R 2 2 +-------+ +-+ +-----+ +--R (- 2a b x - 2a )\|- b - a \|a \|b + a +--R Type: Expression Integer +--E 470 + +--S 471 of 510 +d0092b:= D(m0092b,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (308) ------------------------ +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 471 + +--S 472 of 510 +t0093:= atanh(x)/(a+b*x^2)^(5/2) +--R +--R +--R atanh(x) +--R (309) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression Integer +--E 472 + +--S 473 of 510 +r0093:= 1/3/a/(a+b)/(a+b*x^2)^(1/2)+_ + 1/3*x*(3*a+2*b*x^2)*atanh(x)/a^2/(a+b*x^2)^(3/2)-_ + 1/3*(3*a+2*b)*atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^2/(a+b)^(3/2) +--R +--R +--R (310) +--R +--------+ +--R +--------+ | 2 +--R 2 2 2 | 2 \|b x + a +--R ((- 2b - 3a b)x - 2a b - 3a )\|b x + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 2 2 +-----+ +--R (((2b + 2a b)x + (3a b + 3a )x)atanh(x) + a b x + a )\|b + a +--R / +--R +--------+ +--R 2 2 3 2 3 4 +-----+ | 2 +--R ((3a b + 3a b)x + 3a b + 3a )\|b + a \|b x + a +--R Type: Expression Integer +--E 473 + +--S 474 of 510 +a0093:= integrate(t0093,x) +--R +--R +--R (311) +--R [ +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b + 12a b )x + (32a b + 48a b )x + (40a b + 60a b)x +--R + +--R 3 4 +--R 16a b + 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (- 2b - 3a b )x + (- 20a b - 30a b )x + (- 50a b - 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (- 48a b - 72a b)x - 16a b - 24a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b - 2a b )x + (- 19a b - 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b - 40a b)x + (- 24a b - 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b + 8a b )x + (36a b + 36a b )x + (52a b + 52a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b + 24a b )x + (96a b + 96a b )x + (120a b + 120a b)x +--R + +--R 5 6 +--R 48a b + 48a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b - 6a b )x + (- 60a b - 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b - 150a b )x + (- 144a b - 144a b)x - 48a b - 48a +--R * +--R +-----+ +--R \|b + a +--R , +--R +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (4b + 6a b )x + (40a b + 60a b )x + (100a b + 150a b )x +--R + +--R 3 2 4 2 4 5 +--R (96a b + 144a b)x + 32a b + 48a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b - 2a b )x + (- 19a b - 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b - 40a b)x + (- 24a b - 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b + 8a b )x + (36a b + 36a b )x + (52a b + 52a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b + 24a b )x + (96a b + 96a b )x + (120a b + 120a b)x +--R + +--R 5 6 +--R 48a b + 48a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b - a \|a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b - 6a b )x + (- 60a b - 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b - 150a b )x + (- 144a b - 144a b)x - 48a b - 48a +--R * +--R +-------+ +--R \|- b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 474 + +--S 475 of 510 +m0093a:= a0093.1-r0093 +--R +--R +--R (312) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (2b + 3a b )x + (18a b + 27a b )x + (32a b + 48a b)x +--R + +--R 3 4 +--R 16a b + 24a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 8b - 12a b )x + (- 32a b - 48a b )x + (- 40a b - 60a b)x +--R + +--R 3 4 +--R - 16a b - 24a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b + 6a b )x + (36a b + 54a b )x + (64a b + 96a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b - 8a b )x + (- 28a b - 28a b)x + (- 24a b - 24a )x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b + 16a b )x + (56a b + 56a b)x + (48a b + 48a )x)atanh(x) +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b + 2a b )x + (19a b + 19a b )x + (40a b + 40a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b - 4a b )x + (- 38a b - 38a b )x + (- 80a b - 80a b)x +--R + +--R 3 4 +--R (- 48a b - 48a )x +--R * +--R atanh(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-----+ +--R \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b + 6a b )x + (54a b + 54a b )x + (96a b + 96a b)x + 48a b +--R + +--R 6 +--R 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b - 24a b )x + (- 96a b - 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b - 120a b)x - 48a b - 48a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression Integer +--E 475 + +--S 476 of 510 +d0093a:= D(m0093a,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (313) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 476 + +--S 477 of 510 +m0093b:= a0093.2-r0093 +--R +--R +--R (314) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b + 6a b )x + (36a b + 54a b )x + (64a b + 96a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 4b - 6a b )x + (- 36a b - 54a b )x + (- 64a b - 96a b)x +--R + +--R 3 4 +--R - 32a b - 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (16b + 24a b )x + (64a b + 96a b )x + (80a b + 120a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b - 8a b )x + (- 28a b - 28a b)x + (- 24a b - 24a )x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b + 16a b )x + (56a b + 56a b)x + (48a b + 48a )x)atanh(x) +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b - a \|a \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b + 2a b )x + (19a b + 19a b )x + (40a b + 40a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b - 4a b )x + (- 38a b - 38a b )x + (- 80a b - 80a b)x +--R + +--R 3 4 +--R (- 48a b - 48a )x +--R * +--R atanh(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-------+ +-----+ +--R \|- b - a \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b + 6a b )x + (54a b + 54a b )x + (96a b + 96a b)x + 48a b +--R + +--R 6 +--R 48a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b - a \|b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b - 24a b )x + (- 96a b - 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b - 120a b)x - 48a b - 48a +--R * +--R +-------+ +-+ +-----+ +--R \|- b - a \|a \|b + a +--R Type: Expression Integer +--E 477 + +--S 478 of 510 +d0093b:= D(m0093b,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (315) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 478 + +--S 479 of 510 +t0094:= atanh(x)/(a+b*x^2)^(7/2) +--R +--R +--R atanh(x) +--R (316) ------------------------------------------ +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression Integer +--E 479 + +--S 480 of 510 +r0094:= 1/15/a/(a+b)/(a+b*x^2)^(3/2)+_ + 1/15*(7*a+4*b)/a^2/(a+b)^2/(a+b*x^2)^(1/2)+_ + 1/15*x*(8*(a+b*x^2)^2+a*(7*a+4*b*x^2))*_ + atanh(x)/a^3/(a+b*x^2)^(5/2)-1/15*(15*a^2+20*a*b+8*b^2)*_ + atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^3/(a+b)^(5/2) +--R +--R +--R (317) +--R 4 3 2 2 4 3 2 2 3 2 2 2 +--R (- 8b - 20a b - 15a b )x + (- 16a b - 40a b - 30a b)x - 8a b +--R + +--R 3 4 +--R - 20a b - 15a +--R * +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +--R \|b x + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 3 2 2 5 3 2 2 3 3 +--R (8b + 16a b + 8a b )x + (20a b + 40a b + 20a b)x +--R + +--R 2 2 3 4 +--R (15a b + 30a b + 15a )x +--R * +--R atanh(x) +--R + +--R 3 2 2 4 2 2 3 2 3 4 +--R (4a b + 7a b )x + (9a b + 15a b)x + 5a b + 8a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 5 2 +--R (15a b + 30a b + 15a b )x + (30a b + 60a b + 30a b)x + 15a b +--R + +--R 6 7 +--R 30a b + 15a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R Type: Expression Integer +--E 480 + +--S 481 of 510 +a0094:= integrate(t0094,x) +--R +--R +--R (318) +--R [ +--R 8 7 2 6 12 +--R (64b + 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b + 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b + 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b + 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b + 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b + 11520a b + 8640a b)x + 1024a b + 2560a b + 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (- 8b - 20a b - 15a b )x + (- 280a b - 700a b - 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (- 2072a b - 5180a b - 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (- 6664a b - 16660a b - 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (- 11264a b - 28160a b - 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (- 10496a b - 26240a b - 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (- 5120a b - 12800a b - 9600a b)x - 1024a b - 2560a b - 1920a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 8 7 2 6 13 +--R (- 8b - 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b - 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b - 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b - 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b - 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b - 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b + 114a b )x + (766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b + 4080a b )x + (4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b + 4608a b )x + (896a b + 1280a b)x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b + 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b + 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b + 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b + 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b + 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b + 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b + 3840a b + 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b - 16a b )x + (- 286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b - 2672a b )x + (- 4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b - 8480a b )x + (- 3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b - 1280a b)x +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b + 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b + 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b + 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b + 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b + 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b + 34560a b + 17280a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b - 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b - 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b - 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b - 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b - 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b - 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b - 38400a b - 19200a b)x - 3840a b - 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-----+ +--R \|b + a +--R , +--R +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b +--R + +--R 8 +--R - 3840a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (16b + 40a b + 30a b )x + (560a b + 1400a b + 1050a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (4144a b + 10360a b + 7770a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (13328a b + 33320a b + 24990a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (22528a b + 56320a b + 42240a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (20992a b + 52480a b + 39360a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (10240a b + 25600a b + 19200a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 8 7 2 6 13 +--R (- 8b - 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b - 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b - 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b - 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b - 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b - 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b + 114a b )x + (766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b + 4080a b )x + (4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b + 4608a b )x + (896a b + 1280a b)x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b + 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b + 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b + 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b + 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b + 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b + 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b + 3840a b + 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b - 16a b )x + (- 286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b - 2672a b )x + (- 4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b - 8480a b )x + (- 3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b - 1280a b)x +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b + 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b + 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b + 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b + 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b + 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b + 34560a b + 17280a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b - a \|a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b - 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b - 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b - 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b - 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b - 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b - 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b - 38400a b - 19200a b)x - 3840a b - 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-------+ +--R \|- b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 481 + +--S 482 of 510 +m0094a:= a0094.1-r0094 +--R +--R +--R (319) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (8b + 20a b + 15a b )x + (272a b + 680a b + 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (1800a b + 4500a b + 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (4864a b + 12160a b + 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (6400a b + 16000a b + 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4096a b + 10240a b + 7680a b)x + 1024a b + 2560a b + 1920a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 64b - 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b - 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b - 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b - 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b - 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4608a b - 11520a b - 8640a b)x - 1024a b - 2560a b - 1920a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b + 40a b + 30a b )x + (544a b + 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b + 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b + 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b + 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b + 20480a b + 15360a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b - 3840a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 7 6 2 5 11 +--R (- 64b - 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b - 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b - 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b - 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b - 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b + 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b + 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b + 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b + 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b + 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b + 7680a b + 3840a )x +--R * +--R atanh(x) +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b + 16a b )x + (340a b + 544a b )x + (2250a b + 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b + 9728a b )x + (8000a b + 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b + 8192a b)x + 1280a b + 2048a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b + 16a b + 8a b )x + (276a b + 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b + 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b + 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b + 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b + 12800a b + 6400a b)x + (1920a b + 3840a b + 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b - 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b - 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b - 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b - 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b - 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b - 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b - 7680a b - 3840a )x +--R * +--R atanh(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b - 128a b )x + (- 1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b - 7296a b )x + (- 9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b - 16640a b )x + (- 5760a b - 9216a b)x - 1280a b +--R + +--R 8 +--R - 2048a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b + 60a b + 30a b )x + (1020a b + 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b + 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b + 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b + 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b + 30720a b + 15360a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b - 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b - 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b - 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b - 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b - 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b - 34560a b - 17280a b)x - 3840a b - 7680a b - 3840a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression Integer +--E 482 + +--S 483 of 510 +d0094a:= D(m0094a,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (320) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 483 + +--S 484 of 510 +m0094b:= a0094.2-r0094 +--R +--R +--R (321) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b + 40a b + 30a b )x + (544a b + 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b + 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b + 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b + 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b + 20480a b + 15360a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b - 3840a +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 8 7 2 6 12 +--R (- 16b - 40a b - 30a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 544a b - 1360a b - 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3600a b - 9000a b - 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 9728a b - 24320a b - 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 12800a b - 32000a b - 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 8192a b - 20480a b - 15360a b)x - 2048a b - 5120a b - 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 8 7 2 6 12 +--R (128b + 320a b + 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (1664a b + 4160a b + 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (7296a b + 18240a b + 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (15232a b + 38080a b + 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (16640a b + 41600a b + 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (9216a b + 23040a b + 17280a b)x + 2048a b + 5120a b + 3840a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 7 6 2 5 11 +--R (- 64b - 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b - 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b - 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b - 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b - 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b + 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b + 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b + 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b + 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b + 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b + 7680a b + 3840a )x +--R * +--R atanh(x) +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b + 16a b )x + (340a b + 544a b )x + (2250a b + 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b + 9728a b )x + (8000a b + 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b + 8192a b)x + 1280a b + 2048a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b - a \|a \|b + a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b + 16a b + 8a b )x + (276a b + 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b + 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b + 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b + 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b + 12800a b + 6400a b)x + (1920a b + 3840a b + 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b - 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b - 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b - 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b - 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b - 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b - 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b - 7680a b - 3840a )x +--R * +--R atanh(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b - 128a b )x + (- 1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b - 7296a b )x + (- 9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b - 16640a b )x + (- 5760a b - 9216a b)x - 1280a b +--R + +--R 8 +--R - 2048a +--R * +--R +-------+ +-----+ +--R \|- b - a \|b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b + 60a b + 30a b )x + (1020a b + 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b + 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b + 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b + 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b + 30720a b + 15360a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b - a \|b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b - 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b - 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b - 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b - 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b - 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b - 34560a b - 17280a b)x - 3840a b - 7680a b - 3840a +--R * +--R +-------+ +-+ +-----+ +--R \|- b - a \|a \|b + a +--R Type: Expression Integer +--E 484 + +--S 485 of 510 +d0094b:= D(m0094b,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (322) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 485 + +--S 486 of 510 +t0095:= atanh(x)*(a-a*x^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (323) atanh(x)\|- a x + a +--R Type: Expression Integer +--E 486 + +--S 487 of 510 +r0095:= 1/2/(1-x^2)^(1/2)*(a*(1-x^2))^(1/2)*((1-x^2)^(1/2)+_ + x*(1-x^2)^(1/2)*atanh(x)+2*atan(exp(1)^atanh(x))*atanh(x)-_ + %i*polylog(2,-%i*exp(1)^atanh(x))+%i*polylog(2,%i*exp(1)^atanh(x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 487 + +--S 488 of 510 +a0095:= integrate(t0095,x) +--R +--R +--R x +------------+ +--R ++ | 2 +--R (324) | atanh(%P)\|(- %P + 1)a d%P +--R ++ +--R Type: Union(Expression Integer,...) +--E 488 + +--S 489 of 510 +--m0095:= a0095-r0095 +--E 489 + +--S 490 of 510 +--d0095:= D(m0095,x) +--E 490 + +--S 491 of 510 +t0096:= atanh(x)/(a-a*x^2)^(1/2) +--R +--R +--R atanh(x) +--R (325) ------------- +--R +----------+ +--R | 2 +--R \|- a x + a +--R Type: Expression Integer +--E 491 + +--S 492 of 510 +r0096:= (1-x^2)^(1/2)*(2*atan(exp(1)^atanh(x))*atanh(x)-_ + %i*polylog(2,-%i*exp(1)^atanh(x))+_ + %i*polylog(2,%i*exp(1)^atanh(x)))/(a*(1-x^2))^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 492 + +--S 493 of 510 +a0096:= integrate(t0096,x) +--R +--R +--R x +--R ++ atanh(%P) +--R (326) | --------------- d%P +--R ++ +------------+ +--R | 2 +--R \|(- %P + 1)a +--R Type: Union(Expression Integer,...) +--E 493 + +--S 494 of 510 +--m0096:= a0096-r0096 +--E 494 + +--S 495 of 510 +--d0096:= D(m0096,x) +--E 495 + +--S 496 of 510 +t0097:= atanh(x)/(a-a*x^2)^(3/2) +--R +--R +--R atanh(x) +--R (327) - ----------------------- +--R +----------+ +--R 2 | 2 +--R (a x - a)\|- a x + a +--R Type: Expression Integer +--E 496 + +--S 497 of 510 +r0097:= (x*atanh(x)-1)/(-a*(-1+x^2))^(1/2)/a +--R +--R +--R x atanh(x) - 1 +--R (328) -------------- +--R +----------+ +--R | 2 +--R a\|- a x + a +--R Type: Expression Integer +--E 497 + +--S 498 of 510 +a0097:= integrate(t0097,x) +--R +--R +--R +----------+ +--R - x - 1 2 +-+ - x - 1 | 2 +--R (x log(-------) - 2x )\|a - x log(-------)\|- a x + a +--R x - 1 x - 1 +--R (329) -------------------------------------------------------- +--R +----------+ +--R | 2 +-+ 2 2 2 +--R 2a\|- a x + a \|a + 2a x - 2a +--R Type: Union(Expression Integer,...) +--E 498 + +--S 499 of 510 +m0097:= a0097-r0097 +--R +--R +--R (330) +--R +----------+ +--R - x - 1 2 | 2 +-+ +--R (- x log(-------) + 2x atanh(x) + 2x - 2)\|- a x + a \|a +--R x - 1 +--R + +--R 3 - x - 1 3 2 +--R (- a x + a x)log(-------) + (2a x - 2a x)atanh(x) - 2a x + 2a +--R x - 1 +--R / +--R +----------+ +--R 2 2 2 +-+ 2 2 2 | 2 +--R (2a x - 2a )\|a + (- 2a x + 2a )\|- a x + a +--R Type: Expression Integer +--E 499 + +--S 500 of 510 +d0097:= D(m0097,x) +--R +--R +--R - x - 1 +--R - log(-------) + 2atanh(x) +--R x - 1 +--R (331) -------------------------- +--R +----------+ +--R 2 | 2 +--R (2a x - 2a)\|- a x + a +--R Type: Expression Integer +--E 500 + +--S 501 of 510 +t0098:= atanh(x)/(a-a*x^2)^(5/2) +--R +--R +--R atanh(x) +--R (332) -------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (a x - 2a x + a )\|- a x + a +--R Type: Expression Integer +--E 501 + +--S 502 of 510 +r0098:= 1/9*(7-6*x^2-9*x*atanh(x)+_ + 6*atanh(x)*x^3)/(-1+x^2)/(-a*(-1+x^2))^(1/2)/a^2 +--R +--R +--R 3 2 +--R (6x - 9x)atanh(x) - 6x + 7 +--R (333) ---------------------------- +--R +----------+ +--R 2 2 2 | 2 +--R (9a x - 9a )\|- a x + a +--R Type: Expression Integer +--E 502 + +--S 503 of 510 +a0098:= integrate(t0098,x) +--R +--R +--R (334) +--R 5 3 - x - 1 6 4 2 +-+ +--R ((18x - 51x + 36x)log(-------) - 14x + 48x - 36x )\|a +--R x - 1 +--R + +--R +----------+ +--R 5 3 - x - 1 4 2 | 2 +--R ((- 6x + 33x - 36x)log(-------) - 30x + 36x )\|- a x + a +--R x - 1 +--R / +--R +----------+ +--R 2 4 2 2 2 | 2 +-+ 3 6 3 4 3 2 +--R (54a x - 126a x + 72a )\|- a x + a \|a + 18a x - 108a x + 162a x +--R + +--R 3 +--R - 72a +--R Type: Union(Expression Integer,...) +--E 503 + +--S 504 of 510 +m0098:= a0098-r0098 +--R +--R +--R (335) +--R 5 3 - x - 1 5 3 +--R (- 18x + 51x - 36x)log(-------) + (36x - 102x + 72x)atanh(x) +--R x - 1 +--R + +--R 6 4 2 +--R 14x - 84x + 126x - 56 +--R * +--R +----------+ +--R | 2 +-+ +--R \|- a x + a \|a +--R + +--R 7 5 3 - x - 1 +--R (- 6a x + 39a x - 69a x + 36a x)log(-------) +--R x - 1 +--R + +--R 7 5 3 6 4 2 +--R (12a x - 78a x + 138a x - 72a x)atanh(x) - 42a x + 140a x - 154a x +--R + +--R 56a +--R / +--R 3 6 3 4 3 2 3 +-+ +--R (54a x - 180a x + 198a x - 72a )\|a +--R + +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (- 18a x + 108a x - 162a x + 72a )\|- a x + a +--R Type: Expression Integer +--E 504 + +--S 505 of 510 +d0098:= D(m0098,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (336) ---------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (2a x - 4a x + 2a )\|- a x + a +--R Type: Expression Integer +--E 505 + +--S 506 of 510 +t0099:= atanh(x)/(a-a*x^2)^(7/2) +--R +--R +--R atanh(x) +--R (337) - ---------------------------------------- +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (a x - 3a x + 3a x - a )\|- a x + a +--R Type: Expression Integer +--E 506 + +--S 507 of 510 +r0099:= 1/225*(-149-120*x^4+260*x^2+225*x*atanh(x)+120*x^5*atanh(x)-_ + 300*atanh(x)*x^3)/(-1+x^2)^2/(-a*(-1+x^2))^(1/2)/a^3 +--R +--R +--R 5 3 4 2 +--R (120x - 300x + 225x)atanh(x) - 120x + 260x - 149 +--R (338) ---------------------------------------------------- +--R +----------+ +--R 3 4 3 2 3 | 2 +--R (225a x - 450a x + 225a )\|- a x + a +--R Type: Expression Integer +--E 507 + +--S 508 of 510 +a0099:= integrate(t0099,x) +--R +--R +--R (339) +--R 9 7 5 3 - x - 1 10 +--R (600x - 3900x + 9045x - 9300x + 3600x)log(-------) - 298x +--R x - 1 +--R + +--R 8 6 4 2 +--R 3270x - 8990x + 9600x - 3600x +--R * +--R +-+ +--R \|a +--R + +--R 9 7 5 3 - x - 1 8 +--R (- 120x + 1740x - 5745x + 7500x - 3600x)log(-------) - 1250x +--R x - 1 +--R + +--R 6 4 2 +--R 5540x - 7800x + 3600x +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R / +--R +----------+ +--R 3 8 3 6 3 4 3 2 3 | 2 +-+ +--R (2250a x - 13500a x + 27450a x - 23400a x + 7200a )\|- a x + a \|a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R 450a x - 6750a x + 24750a x - 38250a x + 27000a x - 7200a +--R Type: Union(Expression Integer,...) +--E 508 + +--S 509 of 510 +m0099:= a0099-r0099 +--R +--R +--R (340) +--R 9 7 5 3 - x - 1 +--R (- 600x + 3900x - 9045x + 9300x - 3600x)log(-------) +--R x - 1 +--R + +--R 9 7 5 3 10 +--R (1200x - 7800x + 18090x - 18600x + 7200x)atanh(x) + 298x +--R + +--R 8 6 4 2 +--R - 4470x + 16390x - 25330x + 17880x - 4768 +--R * +--R +----------+ +--R | 2 +-+ +--R \|- a x + a \|a +--R + +--R 11 9 7 5 3 +--R (- 120a x + 1860a x - 7485a x + 13245a x - 11100a x + 3600a x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 11 9 7 5 3 +--R (240a x - 3720a x + 14970a x - 26490a x + 22200a x - 7200a x) +--R * +--R atanh(x) +--R + +--R 10 8 6 4 2 +--R - 1490a x + 10430a x - 27118a x + 33674a x - 20264a x + 4768a +--R / +--R 4 10 4 8 4 6 4 4 4 2 4 +-+ +--R (2250a x - 15750a x + 40950a x - 50850a x + 30600a x - 7200a )\|a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R (- 450a x + 6750a x - 24750a x + 38250a x - 27000a x + 7200a ) +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R Type: Expression Integer +--E 509 + +--S 510 of 510 +d0099:= D(m0099,x) +--R +--R +--R - x - 1 +--R - log(-------) + 2atanh(x) +--R x - 1 +--R (341) ------------------------------------------ +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (2a x - 6a x + 6a x - 2a )\|- a x + a +--R Type: Expression Integer +--E 510 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}