diff --git a/changelog b/changelog index 160d461..d198089 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100615 tpd src/axiom-website/patches.html 20100615.03.tpd.patch +20100615 tpd src/input/Makefile rule-based hyper integration +20100615 tpd src/input/richhyper600-699.input rule-based hyper integration 20100615 tpd src/axiom-website/patches.html 20100615.02.tpd.patch 20100615 tpd src/input/Makefile rule-based hyper integration 20100615 tpd src/input/richhyper500-599.input rule-based hyper integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index cb7bd60..75e5541 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2900,6 +2900,8 @@ src/input/richhyper300-399.input rule-based hyper integration
src/input/richhyper400-499.input rule-based hyper integration
20100615.02.tpd.patch src/input/richhyper500-599.input rule-based hyper integration
+20100615.03.tpd.patch +src/input/richhyper600-699.input rule-based hyper integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 80f11ad..54c5739 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -381,6 +381,7 @@ REGRES= ackermann.regress \ richhyper300-399.regress \ richhyper400-499.regress \ richhyper500-599.regress \ + richhyper600-699.regress \ richrational.regress \ richtrig000-099.regress \ richtrig100-199.regress \ @@ -716,6 +717,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richhyper300-399.input \ ${OUT}/richhyper400-499.input \ ${OUT}/richhyper500-599.input \ + ${OUT}/richhyper600-699.input \ ${OUT}/richrational.input \ ${OUT}/richtrig000-099.input \ ${OUT}/richtrig100-199.input \ @@ -1080,6 +1082,7 @@ DOCFILES= \ ${DOC}/richhyper300-399.input.dvi \ ${DOC}/richhyper400-499.input.dvi \ ${DOC}/richhyper500-599.input.dvi \ + ${DOC}/richhyper600-699.input.dvi \ ${DOC}/richrational.input.dvi \ ${DOC}/richtrig000-099.input.dvi \ ${DOC}/richtrig100-199.input.dvi \ diff --git a/src/input/richhyper600-699.input.pamphlet b/src/input/richhyper600-699.input.pamphlet new file mode 100644 index 0000000..595a9ef --- /dev/null +++ b/src/input/richhyper600-699.input.pamphlet @@ -0,0 +1,25567 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richhyper600-699.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper600-699.output +)spool richhyper600-699.output +)set message auto off +)clear all + +--S 1 of 526 +t0600:= cosh(x)/(1+coth(x)) +--R +--R +--R cosh(x) +--R (1) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 1 + +--S 2 of 526 +r0600:= 1/3*cosh(x)^3-1/3*sinh(x)^3 +--R +--R +--R 3 3 +--R - sinh(x) + cosh(x) +--R (2) --------------------- +--R 3 +--R Type: Expression Integer +--E 2 + +--S 3 of 526 +a0600:= integrate(t0600,x) +--R +--R +--R 2 2 +--R sinh(x) + cosh(x)sinh(x) + cosh(x) +--R (3) ------------------------------------ +--R 3sinh(x) + 3cosh(x) +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 526 +m0600:= a0600-r0600 +--R +--R +--R (4) +--R 4 3 2 3 +--R sinh(x) + cosh(x)sinh(x) + sinh(x) + (- cosh(x) + cosh(x))sinh(x) +--R + +--R 4 2 +--R - cosh(x) + cosh(x) +--R / +--R 3sinh(x) + 3cosh(x) +--R Type: Expression Integer +--E 4 + +--S 5 of 526 +d0600:= D(m0600,x) +--R +--R +--R 3 3 +--R cosh(x)sinh(x) + (- cosh(x) + cosh(x))sinh(x) +--R (5) ----------------------------------------------- +--R sinh(x) + cosh(x) +--R Type: Expression Integer +--E 5 + +--S 6 of 526 +t0601:= cosh(x)^2/(1+coth(x)) +--R +--R +--R 2 +--R cosh(x) +--R (6) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 6 + +--S 7 of 526 +r0601:= 1/8*x+1/4*cosh(x)^4+1/8*cosh(x)*sinh(x)-1/4*cosh(x)^3*sinh(x) +--R +--R +--R 3 4 +--R (- 2cosh(x) + cosh(x))sinh(x) + 2cosh(x) + x +--R (7) ---------------------------------------------- +--R 8 +--R Type: Expression Integer +--E 7 + +--S 8 of 526 +a0601:= integrate(t0601,x) +--R +--R +--R (8) +--R 3 2 2 3 +--R sinh(x) + 9cosh(x)sinh(x) + (3cosh(x) + 4x - 2)sinh(x) + 3cosh(x) +--R + +--R (4x + 2)cosh(x) +--R / +--R 32sinh(x) + 32cosh(x) +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 526 +m0601:= a0601-r0601 +--R +--R +--R (9) +--R 3 3 2 2 +--R sinh(x) + (8cosh(x) + 5cosh(x))sinh(x) + (- cosh(x) - 2)sinh(x) +--R + +--R 5 3 +--R - 8cosh(x) + 3cosh(x) + 2cosh(x) +--R / +--R 32sinh(x) + 32cosh(x) +--R Type: Expression Integer +--E 9 + +--S 10 of 526 +d0601:= D(m0601,x) +--R +--R +--R (10) +--R 2 3 3 2 +--R (6cosh(x) + 1)sinh(x) + (- 2cosh(x) - cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (- 6cosh(x) + 5cosh(x) + 1)sinh(x) + 2cosh(x) - cosh(x) - cosh(x) +--R / +--R 8sinh(x) + 8cosh(x) +--R Type: Expression Integer +--E 10 + +--S 11 of 526 +t0602:= cosh(x)^3/(1+coth(x)) +--R +--R +--R 3 +--R cosh(x) +--R (11) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 11 + +--S 12 of 526 +r0602:= 1/5*cosh(x)^5-1/3*sinh(x)^3-1/5*sinh(x)^5 +--R +--R +--R 5 3 5 +--R - 3sinh(x) - 5sinh(x) + 3cosh(x) +--R (12) ----------------------------------- +--R 15 +--R Type: Expression Integer +--E 12 + +--S 13 of 526 +a0602:= integrate(t0602,x) +--R +--R +--R (13) +--R 4 3 2 2 +--R sinh(x) + cosh(x)sinh(x) + (6cosh(x) + 5)sinh(x) +--R + +--R 3 4 2 +--R (cosh(x) + 5cosh(x))sinh(x) + cosh(x) + 5cosh(x) +--R / +--R 30sinh(x) + 30cosh(x) +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 526 +m0602:= a0602-r0602 +--R +--R +--R (14) +--R 6 5 4 3 +--R 6sinh(x) + 6cosh(x)sinh(x) + 11sinh(x) + 11cosh(x)sinh(x) +--R + +--R 2 2 5 3 +--R (6cosh(x) + 5)sinh(x) + (- 6cosh(x) + cosh(x) + 5cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 6cosh(x) + cosh(x) + 5cosh(x) +--R / +--R 30sinh(x) + 30cosh(x) +--R Type: Expression Integer +--E 14 + +--S 15 of 526 +d0602:= D(m0602,x) +--R +--R +--R (15) +--R 5 2 4 3 +--R 2cosh(x)sinh(x) + 2cosh(x) sinh(x) + 3cosh(x)sinh(x) +--R + +--R 4 2 2 +--R (- 2cosh(x) + 2cosh(x) )sinh(x) +--R + +--R 5 3 +--R (- 2cosh(x) + cosh(x) + cosh(x))sinh(x) +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Expression Integer +--E 15 + +--S 16 of 526 +t0603:= cosh(x)^4/(1+coth(x)) +--R +--R +--R 4 +--R cosh(x) +--R (16) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 16 + +--S 17 of 526 +r0603:= 1/16*x+1/6*cosh(x)^6+1/16*cosh(x)*sinh(x)+1/24*cosh(x)^3*sinh(x)-_ + 1/6*cosh(x)^5*sinh(x) +--R +--R +--R 5 3 6 +--R (- 8cosh(x) + 2cosh(x) + 3cosh(x))sinh(x) + 8cosh(x) + 3x +--R (17) ------------------------------------------------------------ +--R 48 +--R Type: Expression Integer +--E 17 + +--S 18 of 526 +a0603:= integrate(t0603,x) +--R +--R +--R (18) +--R 5 4 2 3 +--R sinh(x) + 25cosh(x)sinh(x) + (10cosh(x) + 9)sinh(x) +--R + +--R 3 2 +--R (50cosh(x) + 81cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (5cosh(x) + 27cosh(x) + 24x - 12)sinh(x) + 5cosh(x) + 27cosh(x) +--R + +--R (24x + 12)cosh(x) +--R / +--R 384sinh(x) + 384cosh(x) +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 526 +m0603:= a0603-r0603 +--R +--R +--R (19) +--R 5 4 2 3 +--R sinh(x) + 25cosh(x)sinh(x) + (10cosh(x) + 9)sinh(x) +--R + +--R 5 3 2 +--R (64cosh(x) + 34cosh(x) + 57cosh(x))sinh(x) +--R + +--R 4 2 7 5 +--R (- 11cosh(x) + 3cosh(x) - 12)sinh(x) - 64cosh(x) + 5cosh(x) +--R + +--R 3 +--R 27cosh(x) + 12cosh(x) +--R / +--R 384sinh(x) + 384cosh(x) +--R Type: Expression Integer +--E 19 + +--S 20 of 526 +d0603:= D(m0603,x) +--R +--R +--R (20) +--R 5 4 2 3 +--R 3sinh(x) + (40cosh(x) + 24cosh(x) + 6)sinh(x) +--R + +--R 5 3 2 +--R (- 8cosh(x) - 6cosh(x) - 3cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (- 40cosh(x) + 13cosh(x) + 24cosh(x) + 3)sinh(x) + 8cosh(x) +--R + +--R 5 3 +--R - 2cosh(x) - 3cosh(x) - 3cosh(x) +--R / +--R 48sinh(x) + 48cosh(x) +--R Type: Expression Integer +--E 20 + +--S 21 of 526 +t0604:= tanh(x)/(a+b*coth(x)) +--R +--R +--R tanh(x) +--R (21) ------------- +--R b coth(x) + a +--R Type: Expression Integer +--E 21 + +--S 22 of 526 +r0604:= (-a*b*x+log(cosh(x))*a^2-log(cosh(x))*b^2+_ + b^2*log(b*cosh(x)+a*sinh(x)))/a/(a^2-b^2) +--R +--R +--R 2 2 2 +--R - b log(a sinh(x) + b cosh(x)) + (b - a )log(cosh(x)) + a b x +--R (22) -------------------------------------------------------------- +--R 2 3 +--R a b - a +--R Type: Expression Integer +--E 22 + +--S 23 of 526 +a0604:= integrate(t0604,x) +--R +--R +--R (23) +--R 2 2 2cosh(x) 2 - 2a sinh(x) - 2b cosh(x) +--R (b - a )log(- -----------------) - b log(-------------------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R + +--R 2 +--R (a b + a )x +--R / +--R 2 3 +--R a b - a +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 526 +m0604:= a0604-r0604 +--R +--R +--R (24) +--R 2 2 2 +--R b log(a sinh(x) + b cosh(x)) + (- b + a )log(cosh(x)) +--R + +--R 2 2 2cosh(x) 2 - 2a sinh(x) - 2b cosh(x) 2 +--R (b - a )log(- -----------------) - b log(-------------------------) + a x +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R / +--R 2 3 +--R a b - a +--R Type: Expression Integer +--E 24 + +--S 25 of 526 +d0604:= D(m0604,x) +--R +--R +--R (25) 0 +--R Type: Expression Integer +--E 25 + +--S 26 of 526 +t0605:= tanh(x)^2/(a+b*coth(x)) +--R +--R +--R 2 +--R tanh(x) +--R (26) ------------- +--R b coth(x) + a +--R Type: Expression Integer +--E 26 + +--S 27 of 526 +r0605:= a*x/(a^2-b^2)-b*log(cosh(x))/a^2-_ + b^3*log(b*cosh(x)+a*sinh(x))/a^2/(a^2-b^2)-tanh(x)/a +--R +--R +--R (27) +--R 3 3 2 +--R b log(a sinh(x) + b cosh(x)) + (- b + a b)log(cosh(x)) +--R + +--R 2 3 3 +--R (- a b + a )tanh(x) - a x +--R / +--R 2 2 4 +--R a b - a +--R Type: Expression Integer +--E 27 + +--S 28 of 526 +a0605:= integrate(t0605,x) +--R +--R +--R (28) +--R 3 2 2 3 2 +--R (- b + a b)sinh(x) + (- 2b + 2a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 +--R (- b + a b)cosh(x) - b + a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 2 3 +--R (- a b - a )x sinh(x) + (- 2a b - 2a )x cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- a b - a )x cosh(x) + (- a b - a )x + 2a b - 2a +--R / +--R 2 2 4 2 2 2 4 2 2 4 2 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) + (a b - a )cosh(x) +--R + +--R 2 2 4 +--R a b - a +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 526 +m0605:= a0605-r0605 +--R +--R +--R (29) +--R 3 2 3 3 2 3 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b ) +--R * +--R log(a sinh(x) + b cosh(x)) +--R + +--R 3 2 2 3 2 3 2 2 +--R (b - a b)sinh(x) + (2b - 2a b)cosh(x)sinh(x) + (b - a b)cosh(x) +--R + +--R 3 2 +--R b - a b +--R * +--R log(cosh(x)) +--R + +--R 3 2 2 3 2 +--R (- b + a b)sinh(x) + (- 2b + 2a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 +--R (- b + a b)cosh(x) - b + a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )cosh(x) + a b - a +--R * +--R tanh(x) +--R + +--R 2 2 2 2 2 2 2 +--R - a b x sinh(x) - 2a b x cosh(x)sinh(x) - a b x cosh(x) - a b x + 2a b +--R + +--R 3 +--R - 2a +--R / +--R 2 2 4 2 2 2 4 2 2 4 2 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) + (a b - a )cosh(x) +--R + +--R 2 2 4 +--R a b - a +--R Type: Expression Integer +--E 29 + +--S 30 of 526 +d0605:= D(m0605,x) +--R +--R +--R (30) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) - 4cosh(x))sinh(x) - cosh(x) - 2cosh(x) - 1 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R / +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression Integer +--E 30 + +--S 31 of 526 +t0606:= tanh(x)^3/(a+b*coth(x)) +--R +--R +--R 3 +--R tanh(x) +--R (31) ------------- +--R b coth(x) + a +--R Type: Expression Integer +--E 31 + +--S 32 of 526 +r0606:= -b*x/a^2-b^3*x/a^4-b^5*x/a^4/(a^2-b^2)+log(cosh(x))/a+_ + b^2*log(cosh(x))/a^3+b^4*log(b*cosh(x)+a*sinh(x))/a^3/(a^2-b^2)+_ + b*tanh(x)/a^2-1/2*tanh(x)^2/a +--R +--R +--R (32) +--R 4 4 4 +--R - 2b log(a sinh(x) + b cosh(x)) + (2b - 2a )log(cosh(x)) +--R + +--R 2 2 4 2 3 3 3 +--R (- a b + a )tanh(x) + (2a b - 2a b)tanh(x) + 2a b x +--R / +--R 3 2 5 +--R 2a b - 2a +--R Type: Expression Integer +--E 32 + +--S 33 of 526 +a0606:= integrate(t0606,x) +--R +--R +--R (33) +--R 4 4 4 4 4 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 4 4 2 4 4 2 +--R ((6b - 6a )cosh(x) + 2b - 2a )sinh(x) +--R + +--R 4 4 3 4 4 4 4 4 +--R ((4b - 4a )cosh(x) + (4b - 4a )cosh(x))sinh(x) + (b - a )cosh(x) +--R + +--R 4 4 2 4 4 +--R (2b - 2a )cosh(x) + b - a +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 4 4 3 4 2 4 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) - 2b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (- 4b cosh(x) - 4b cosh(x))sinh(x) - b cosh(x) - 2b cosh(x) - b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 4 4 3 4 3 +--R (a b + a )x sinh(x) + (4a b + 4a )x cosh(x)sinh(x) +--R + +--R 3 4 2 3 4 3 2 2 3 4 +--R ((6a b + 6a )x cosh(x) + (2a b + 2a )x - 2a b + 2a b + 2a b - 2a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 +--R (4a b + 4a )x cosh(x) +--R + +--R 3 4 3 2 2 3 4 +--R ((4a b + 4a )x - 4a b + 4a b + 4a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 +--R (a b + a )x cosh(x) +--R + +--R 3 4 3 2 2 3 4 2 3 4 +--R ((2a b + 2a )x - 2a b + 2a b + 2a b - 2a )cosh(x) + (a b + a )x +--R + +--R 3 3 +--R - 2a b + 2a b +--R / +--R 3 2 5 4 3 2 5 3 +--R (a b - a )sinh(x) + (4a b - 4a )cosh(x)sinh(x) +--R + +--R 3 2 5 2 3 2 5 2 +--R ((6a b - 6a )cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 3 2 5 3 3 2 5 +--R ((4a b - 4a )cosh(x) + (4a b - 4a )cosh(x))sinh(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R (a b - a )cosh(x) + (2a b - 2a )cosh(x) + a b - a +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 526 +m0606:= a0606-r0606 +--R +--R +--R (34) +--R 4 4 4 3 4 2 4 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) + 4b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (8b cosh(x) + 8b cosh(x))sinh(x) + 2b cosh(x) + 4b cosh(x) + 2b +--R * +--R log(a sinh(x) + b cosh(x)) +--R + +--R 4 4 4 4 4 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 4 4 2 4 4 2 +--R ((- 12b + 12a )cosh(x) - 4b + 4a )sinh(x) +--R + +--R 4 4 3 4 4 +--R ((- 8b + 8a )cosh(x) + (- 8b + 8a )cosh(x))sinh(x) +--R + +--R 4 4 4 4 4 2 4 4 +--R (- 2b + 2a )cosh(x) + (- 4b + 4a )cosh(x) - 2b + 2a +--R * +--R log(cosh(x)) +--R + +--R 4 4 4 4 4 3 +--R (2b - 2a )sinh(x) + (8b - 8a )cosh(x)sinh(x) +--R + +--R 4 4 2 4 4 2 +--R ((12b - 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 4 4 3 4 4 +--R ((8b - 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 4 4 4 4 4 2 4 4 +--R (2b - 2a )cosh(x) + (4b - 4a )cosh(x) + 2b - 2a +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 4 4 3 4 2 4 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) - 4b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) - 2b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 4 2 2 4 3 +--R (a b - a )sinh(x) + (4a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 4 2 2 2 4 2 +--R ((6a b - 6a )cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 2 4 3 2 2 4 +--R ((4a b - 4a )cosh(x) + (4a b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 +--R (a b - a )cosh(x) + (2a b - 2a )cosh(x) + a b - a +--R * +--R 2 +--R tanh(x) +--R + +--R 3 3 4 3 3 3 +--R (- 2a b + 2a b)sinh(x) + (- 8a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 2 +--R ((- 12a b + 12a b)cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 3 3 3 3 3 +--R ((- 8a b + 8a b)cosh(x) + (- 8a b + 8a b)cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 3 3 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a b)cosh(x) - 2a b + 2a b +--R * +--R tanh(x) +--R + +--R 4 4 4 3 +--R 2a x sinh(x) + 8a x cosh(x)sinh(x) +--R + +--R 4 2 4 3 2 2 3 4 2 +--R (12a x cosh(x) + 4a x - 4a b + 4a b + 4a b - 4a )sinh(x) +--R + +--R 4 3 4 3 2 2 3 4 +--R (8a x cosh(x) + (8a x - 8a b + 8a b + 8a b - 8a )cosh(x))sinh(x) +--R + +--R 4 4 4 3 2 2 3 4 2 4 +--R 2a x cosh(x) + (4a x - 4a b + 4a b + 4a b - 4a )cosh(x) + 2a x +--R + +--R 3 3 +--R - 4a b + 4a b +--R / +--R 3 2 5 4 3 2 5 3 +--R (2a b - 2a )sinh(x) + (8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 5 2 3 2 5 2 +--R ((12a b - 12a )cosh(x) + 4a b - 4a )sinh(x) +--R + +--R 3 2 5 3 3 2 5 +--R ((8a b - 8a )cosh(x) + (8a b - 8a )cosh(x))sinh(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R (2a b - 2a )cosh(x) + (4a b - 4a )cosh(x) + 2a b - 2a +--R Type: Expression Integer +--E 34 + +--S 35 of 526 +d0606:= D(m0606,x) +--R +--R +--R (35) +--R 6 5 2 4 +--R - a sinh(x) - 6a cosh(x)sinh(x) + (- 15a cosh(x) - 3a)sinh(x) +--R + +--R 3 3 +--R (- 20a cosh(x) - 12a cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 15a cosh(x) - 18a cosh(x) - 3a)sinh(x) +--R + +--R 5 3 6 +--R (- 6a cosh(x) - 12a cosh(x) - 6a cosh(x))sinh(x) - a cosh(x) +--R + +--R 4 2 +--R - 3a cosh(x) - 3a cosh(x) - a +--R * +--R 3 +--R tanh(x) +--R + +--R 6 5 2 4 +--R b sinh(x) + 6b cosh(x)sinh(x) + (15b cosh(x) + 3b)sinh(x) +--R + +--R 3 3 +--R (20b cosh(x) + 12b cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) + 18b cosh(x) + 3b)sinh(x) +--R + +--R 5 3 6 +--R (6b cosh(x) + 12b cosh(x) + 6b cosh(x))sinh(x) + b cosh(x) +--R + +--R 4 2 +--R 3b cosh(x) + 3b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 6 5 2 4 +--R a sinh(x) + 6a cosh(x)sinh(x) + (15a cosh(x) + 3a)sinh(x) +--R + +--R 3 3 +--R (20a cosh(x) + 12a cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15a cosh(x) + 18a cosh(x) + 3a)sinh(x) +--R + +--R 5 3 6 +--R (6a cosh(x) + 12a cosh(x) + 6a cosh(x))sinh(x) + a cosh(x) +--R + +--R 4 2 +--R 3a cosh(x) + 3a cosh(x) + a +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R - b sinh(x) - 6b cosh(x)sinh(x) + (- 15b cosh(x) + b - 4a)sinh(x) +--R + +--R 3 3 +--R (- 20b cosh(x) + (4b - 16a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 15b cosh(x) + (6b - 24a)cosh(x) + b + 4a)sinh(x) +--R + +--R 5 3 +--R (- 6b cosh(x) + (4b - 16a)cosh(x) + (2b + 8a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - b cosh(x) + (b - 4a)cosh(x) + (b + 4a)cosh(x) - b +--R / +--R 2 6 2 5 2 2 2 4 +--R a sinh(x) + 6a cosh(x)sinh(x) + (15a cosh(x) + 3a )sinh(x) +--R + +--R 2 3 2 3 +--R (20a cosh(x) + 12a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (15a cosh(x) + 18a cosh(x) + 3a )sinh(x) +--R + +--R 2 5 2 3 2 2 6 +--R (6a cosh(x) + 12a cosh(x) + 6a cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 4 2 2 2 +--R 3a cosh(x) + 3a cosh(x) + a +--R Type: Expression Integer +--E 35 + +--S 36 of 526 +t0607:= tanh(x)^4/(a+b*coth(x)) +--R +--R +--R 4 +--R tanh(x) +--R (36) ------------- +--R b coth(x) + a +--R Type: Expression Integer +--E 36 + +--S 37 of 526 +r0607:= x/a+b^2*x/a^3+b^4*x/a^5+b^6*x/a^5/(a^2-b^2)-b*log(cosh(x))/a^2-_ + b^3*log(cosh(x))/a^4-b^5*log(b*cosh(x)+a*sinh(x))/a^4/(a^2-b^2)-_ + tanh(x)/a-b^2*tanh(x)/a^3+1/2*b*tanh(x)^2/a^2-1/3*tanh(x)^3/a +--R +--R +--R (37) +--R 5 5 4 +--R 6b log(a sinh(x) + b cosh(x)) + (- 6b + 6a b)log(cosh(x)) +--R + +--R 3 2 5 3 2 3 4 2 4 5 +--R (- 2a b + 2a )tanh(x) + (3a b - 3a b)tanh(x) + (- 6a b + 6a )tanh(x) +--R + +--R 5 +--R - 6a x +--R / +--R 4 2 6 +--R 6a b - 6a +--R Type: Expression Integer +--E 37 + +--S 38 of 526 +a0607:= integrate(t0607,x) +--R +--R +--R (38) +--R 5 4 6 5 4 5 +--R (- 3b + 3a b)sinh(x) + (- 18b + 18a b)cosh(x)sinh(x) +--R + +--R 5 4 2 5 4 4 +--R ((- 45b + 45a b)cosh(x) - 9b + 9a b)sinh(x) +--R + +--R 5 4 3 5 4 3 +--R ((- 60b + 60a b)cosh(x) + (- 36b + 36a b)cosh(x))sinh(x) +--R + +--R 5 4 4 5 4 2 5 4 +--R ((- 45b + 45a b)cosh(x) + (- 54b + 54a b)cosh(x) - 9b + 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 5 4 3 +--R (- 18b + 18a b)cosh(x) + (- 36b + 36a b)cosh(x) +--R + +--R 5 4 +--R (- 18b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 6 5 4 4 +--R (- 3b + 3a b)cosh(x) + (- 9b + 9a b)cosh(x) +--R + +--R 5 4 2 5 4 +--R (- 9b + 9a b)cosh(x) - 3b + 3a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 5 6 5 5 5 2 5 4 +--R 3b sinh(x) + 18b cosh(x)sinh(x) + (45b cosh(x) + 9b )sinh(x) +--R + +--R 5 3 5 3 +--R (60b cosh(x) + 36b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (45b cosh(x) + 54b cosh(x) + 9b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (18b cosh(x) + 36b cosh(x) + 18b cosh(x))sinh(x) + 3b cosh(x) +--R + +--R 5 4 5 2 5 +--R 9b cosh(x) + 9b cosh(x) + 3b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 4 5 6 4 5 5 +--R (- 3a b - 3a )x sinh(x) + (- 18a b - 18a )x cosh(x)sinh(x) +--R + +--R 4 5 2 4 5 4 2 3 3 2 +--R (- 45a b - 45a )x cosh(x) + (- 9a b - 9a )x + 6a b - 6a b + 6a b +--R + +--R 4 5 +--R 6a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 +--R (- 60a b - 60a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 +--R ((- 36a b - 36a )x + 24a b - 24a b + 24a b + 24a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 4 +--R (- 45a b - 45a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 2 +--R ((- 54a b - 54a )x + 36a b - 36a b + 36a b + 36a b - 72a )cosh(x) +--R + +--R 4 5 4 2 3 4 5 +--R (- 9a b - 9a )x + 12a b - 6a b + 6a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 5 +--R (- 18a b - 18a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 3 +--R ((- 36a b - 36a )x + 24a b - 24a b + 24a b + 24a b - 48a )cosh(x) +--R + +--R 4 5 4 2 3 4 5 +--R ((- 18a b - 18a )x + 24a b - 12a b + 12a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 5 6 +--R (- 3a b - 3a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 4 +--R ((- 9a b - 9a )x + 6a b - 6a b + 6a b + 6a b - 12a )cosh(x) +--R + +--R 4 5 4 2 3 4 5 2 +--R ((- 9a b - 9a )x + 12a b - 6a b + 6a b - 12a )cosh(x) +--R + +--R 4 5 4 3 2 5 +--R (- 3a b - 3a )x + 6a b + 2a b - 8a +--R / +--R 4 2 6 6 4 2 6 5 +--R (3a b - 3a )sinh(x) + (18a b - 18a )cosh(x)sinh(x) +--R + +--R 4 2 6 2 4 2 6 4 +--R ((45a b - 45a )cosh(x) + 9a b - 9a )sinh(x) +--R + +--R 4 2 6 3 4 2 6 3 +--R ((60a b - 60a )cosh(x) + (36a b - 36a )cosh(x))sinh(x) +--R + +--R 4 2 6 4 4 2 6 2 4 2 6 2 +--R ((45a b - 45a )cosh(x) + (54a b - 54a )cosh(x) + 9a b - 9a )sinh(x) +--R + +--R 4 2 6 5 4 2 6 3 +--R (18a b - 18a )cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 4 2 6 +--R (18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 6 6 4 2 6 4 4 2 6 2 +--R (3a b - 3a )cosh(x) + (9a b - 9a )cosh(x) + (9a b - 9a )cosh(x) +--R + +--R 4 2 6 +--R 3a b - 3a +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 526 +m0607:= a0607-r0607 +--R +--R +--R (39) +--R 5 6 5 5 5 2 5 4 +--R - 6b sinh(x) - 36b cosh(x)sinh(x) + (- 90b cosh(x) - 18b )sinh(x) +--R + +--R 5 3 5 3 +--R (- 120b cosh(x) - 72b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (- 90b cosh(x) - 108b cosh(x) - 18b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (- 36b cosh(x) - 72b cosh(x) - 36b cosh(x))sinh(x) - 6b cosh(x) +--R + +--R 5 4 5 2 5 +--R - 18b cosh(x) - 18b cosh(x) - 6b +--R * +--R log(a sinh(x) + b cosh(x)) +--R + +--R 5 4 6 5 4 5 +--R (6b - 6a b)sinh(x) + (36b - 36a b)cosh(x)sinh(x) +--R + +--R 5 4 2 5 4 4 +--R ((90b - 90a b)cosh(x) + 18b - 18a b)sinh(x) +--R + +--R 5 4 3 5 4 3 +--R ((120b - 120a b)cosh(x) + (72b - 72a b)cosh(x))sinh(x) +--R + +--R 5 4 4 5 4 2 5 4 +--R ((90b - 90a b)cosh(x) + (108b - 108a b)cosh(x) + 18b - 18a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 5 4 3 +--R (36b - 36a b)cosh(x) + (72b - 72a b)cosh(x) +--R + +--R 5 4 +--R (36b - 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 6 5 4 4 +--R (6b - 6a b)cosh(x) + (18b - 18a b)cosh(x) +--R + +--R 5 4 2 5 4 +--R (18b - 18a b)cosh(x) + 6b - 6a b +--R * +--R log(cosh(x)) +--R + +--R 5 4 6 5 4 5 +--R (- 6b + 6a b)sinh(x) + (- 36b + 36a b)cosh(x)sinh(x) +--R + +--R 5 4 2 5 4 4 +--R ((- 90b + 90a b)cosh(x) - 18b + 18a b)sinh(x) +--R + +--R 5 4 3 5 4 3 +--R ((- 120b + 120a b)cosh(x) + (- 72b + 72a b)cosh(x))sinh(x) +--R + +--R 5 4 4 5 4 2 5 +--R (- 90b + 90a b)cosh(x) + (- 108b + 108a b)cosh(x) - 18b +--R + +--R 4 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 5 4 3 +--R (- 36b + 36a b)cosh(x) + (- 72b + 72a b)cosh(x) +--R + +--R 5 4 +--R (- 36b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 6 5 4 4 +--R (- 6b + 6a b)cosh(x) + (- 18b + 18a b)cosh(x) +--R + +--R 5 4 2 5 4 +--R (- 18b + 18a b)cosh(x) - 6b + 6a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 5 6 5 5 5 2 5 4 +--R 6b sinh(x) + 36b cosh(x)sinh(x) + (90b cosh(x) + 18b )sinh(x) +--R + +--R 5 3 5 3 +--R (120b cosh(x) + 72b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (90b cosh(x) + 108b cosh(x) + 18b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (36b cosh(x) + 72b cosh(x) + 36b cosh(x))sinh(x) + 6b cosh(x) +--R + +--R 5 4 5 2 5 +--R 18b cosh(x) + 18b cosh(x) + 6b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (2a b - 2a )sinh(x) + (12a b - 12a )cosh(x)sinh(x) +--R + +--R 3 2 5 2 3 2 5 4 +--R ((30a b - 30a )cosh(x) + 6a b - 6a )sinh(x) +--R + +--R 3 2 5 3 3 2 5 3 +--R ((40a b - 40a )cosh(x) + (24a b - 24a )cosh(x))sinh(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R ((30a b - 30a )cosh(x) + (36a b - 36a )cosh(x) + 6a b - 6a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 5 3 2 5 3 +--R (12a b - 12a )cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 2 5 +--R (12a b - 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 5 6 3 2 5 4 3 2 5 2 +--R (2a b - 2a )cosh(x) + (6a b - 6a )cosh(x) + (6a b - 6a )cosh(x) +--R + +--R 3 2 5 +--R 2a b - 2a +--R * +--R 3 +--R tanh(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 3a b + 3a b)sinh(x) + (- 18a b + 18a b)cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R ((- 45a b + 45a b)cosh(x) - 9a b + 9a b)sinh(x) +--R + +--R 2 3 4 3 2 3 4 3 +--R ((- 60a b + 60a b)cosh(x) + (- 36a b + 36a b)cosh(x))sinh(x) +--R + +--R 2 3 4 4 2 3 4 2 2 3 +--R (- 45a b + 45a b)cosh(x) + (- 54a b + 54a b)cosh(x) - 9a b +--R + +--R 4 +--R 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 5 2 3 4 3 +--R (- 18a b + 18a b)cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 4 +--R (- 18a b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 6 2 3 4 4 +--R (- 3a b + 3a b)cosh(x) + (- 9a b + 9a b)cosh(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 9a b + 9a b)cosh(x) - 3a b + 3a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 5 6 4 5 5 +--R (6a b - 6a )sinh(x) + (36a b - 36a )cosh(x)sinh(x) +--R + +--R 4 5 2 4 5 4 +--R ((90a b - 90a )cosh(x) + 18a b - 18a )sinh(x) +--R + +--R 4 5 3 4 5 3 +--R ((120a b - 120a )cosh(x) + (72a b - 72a )cosh(x))sinh(x) +--R + +--R 4 5 4 4 5 2 4 +--R (90a b - 90a )cosh(x) + (108a b - 108a )cosh(x) + 18a b +--R + +--R 5 +--R - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 5 4 5 3 +--R (36a b - 36a )cosh(x) + (72a b - 72a )cosh(x) +--R + +--R 4 5 +--R (36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 5 6 4 5 4 +--R (6a b - 6a )cosh(x) + (18a b - 18a )cosh(x) +--R + +--R 4 5 2 4 5 +--R (18a b - 18a )cosh(x) + 6a b - 6a +--R * +--R tanh(x) +--R + +--R 4 6 4 5 +--R - 6a b x sinh(x) - 36a b x cosh(x)sinh(x) +--R + +--R 4 2 4 4 2 3 3 2 4 +--R - 90a b x cosh(x) - 18a b x + 12a b - 12a b + 12a b + 12a b +--R + +--R 5 +--R - 24a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 +--R - 120a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 +--R (- 72a b x + 48a b - 48a b + 48a b + 48a b - 96a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 +--R - 90a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 2 +--R (- 108a b x + 72a b - 72a b + 72a b + 72a b - 144a )cosh(x) +--R + +--R 4 4 2 3 4 5 +--R - 18a b x + 24a b - 12a b + 12a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 +--R - 36a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 3 +--R (- 72a b x + 48a b - 48a b + 48a b + 48a b - 96a )cosh(x) +--R + +--R 4 4 2 3 4 5 +--R (- 36a b x + 48a b - 24a b + 24a b - 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 6 +--R - 6a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 4 +--R (- 18a b x + 12a b - 12a b + 12a b + 12a b - 24a )cosh(x) +--R + +--R 4 4 2 3 4 5 2 4 4 +--R (- 18a b x + 24a b - 12a b + 12a b - 24a )cosh(x) - 6a b x + 12a b +--R + +--R 3 2 5 +--R 4a b - 16a +--R / +--R 4 2 6 6 4 2 6 5 +--R (6a b - 6a )sinh(x) + (36a b - 36a )cosh(x)sinh(x) +--R + +--R 4 2 6 2 4 2 6 4 +--R ((90a b - 90a )cosh(x) + 18a b - 18a )sinh(x) +--R + +--R 4 2 6 3 4 2 6 3 +--R ((120a b - 120a )cosh(x) + (72a b - 72a )cosh(x))sinh(x) +--R + +--R 4 2 6 4 4 2 6 2 4 2 6 +--R ((90a b - 90a )cosh(x) + (108a b - 108a )cosh(x) + 18a b - 18a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 6 5 4 2 6 3 +--R (36a b - 36a )cosh(x) + (72a b - 72a )cosh(x) +--R + +--R 4 2 6 +--R (36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 6 6 4 2 6 4 4 2 6 2 +--R (6a b - 6a )cosh(x) + (18a b - 18a )cosh(x) + (18a b - 18a )cosh(x) +--R + +--R 4 2 6 +--R 6a b - 6a +--R Type: Expression Integer +--E 39 + +--S 40 of 526 +d0607:= D(m0607,x) +--R +--R +--R (40) +--R 2 8 2 7 2 2 2 6 +--R - a sinh(x) - 8a cosh(x)sinh(x) + (- 28a cosh(x) - 4a )sinh(x) +--R + +--R 2 3 2 5 +--R (- 56a cosh(x) - 24a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- 70a cosh(x) - 60a cosh(x) - 6a )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (- 56a cosh(x) - 80a cosh(x) - 24a cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 28a cosh(x) - 60a cosh(x) - 36a cosh(x) - 4a )sinh(x) +--R + +--R 2 7 2 5 2 3 2 +--R (- 8a cosh(x) - 24a cosh(x) - 24a cosh(x) - 8a cosh(x))sinh(x) +--R + +--R 2 8 2 6 2 4 2 2 2 +--R - a cosh(x) - 4a cosh(x) - 6a cosh(x) - 4a cosh(x) - a +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R a b sinh(x) + 8a b cosh(x)sinh(x) + (28a b cosh(x) + 4a b)sinh(x) +--R + +--R 3 5 +--R (56a b cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70a b cosh(x) + 60a b cosh(x) + 6a b)sinh(x) +--R + +--R 5 3 3 +--R (56a b cosh(x) + 80a b cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28a b cosh(x) + 60a b cosh(x) + 36a b cosh(x) + 4a b)sinh(x) +--R + +--R 7 5 3 +--R (8a b cosh(x) + 24a b cosh(x) + 24a b cosh(x) + 8a b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R a b cosh(x) + 4a b cosh(x) + 6a b cosh(x) + 4a b cosh(x) + a b +--R * +--R 3 +--R tanh(x) +--R + +--R 2 8 2 7 2 2 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) - 4b )sinh(x) +--R + +--R 2 3 2 5 +--R (- 56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- 70b cosh(x) - 60b cosh(x) - 6b )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (- 56b cosh(x) - 80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 28b cosh(x) - 60b cosh(x) - 36b cosh(x) - 4b )sinh(x) +--R + +--R 2 7 2 5 2 3 2 +--R (- 8b cosh(x) - 24b cosh(x) - 24b cosh(x) - 8b cosh(x))sinh(x) +--R + +--R 2 8 2 6 2 4 2 2 2 +--R - b cosh(x) - 4b cosh(x) - 6b cosh(x) - 4b cosh(x) - b +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R - a b sinh(x) - 8a b cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 28a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 5 +--R (- 56a b cosh(x) - 24a b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70a b cosh(x) - 60a b cosh(x) - 6a b)sinh(x) +--R + +--R 5 3 3 +--R (- 56a b cosh(x) - 80a b cosh(x) - 24a b cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28a b cosh(x) - 60a b cosh(x) - 36a b cosh(x) - 4a b)sinh(x) +--R + +--R 7 5 3 +--R (- 8a b cosh(x) - 24a b cosh(x) - 24a b cosh(x) - 8a b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - a b cosh(x) - 4a b cosh(x) - 6a b cosh(x) - 4a b cosh(x) - a b +--R * +--R tanh(x) +--R + +--R 2 2 8 2 2 7 +--R (b + a )sinh(x) + (8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((28b + 28a )cosh(x) + 4a b - 4a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((56b + 56a )cosh(x) + (24a b - 24a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 4 +--R ((70b + 70a )cosh(x) + (60a b - 60a )cosh(x) - 2b + 6a )sinh(x) +--R + +--R 2 2 5 2 3 +--R (56b + 56a )cosh(x) + (80a b - 80a )cosh(x) +--R + +--R 2 2 +--R (- 8b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 4 +--R (28b + 28a )cosh(x) + (60a b - 60a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b + 36a )cosh(x) - 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 2 2 3 +--R (8b + 8a )cosh(x) + (24a b - 24a )cosh(x) + (- 8b + 24a )cosh(x) +--R + +--R 2 +--R (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 6 2 2 4 +--R (b + a )cosh(x) + (4a b - 4a )cosh(x) + (- 2b + 6a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 4a b - 4a )cosh(x) + b + a +--R / +--R 3 8 3 7 3 2 3 6 +--R a sinh(x) + 8a cosh(x)sinh(x) + (28a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 5 +--R (56a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 4 +--R (70a cosh(x) + 60a cosh(x) + 6a )sinh(x) +--R + +--R 3 5 3 3 3 3 +--R (56a cosh(x) + 80a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 3 6 3 4 3 2 3 2 +--R (28a cosh(x) + 60a cosh(x) + 36a cosh(x) + 4a )sinh(x) +--R + +--R 3 7 3 5 3 3 3 +--R (8a cosh(x) + 24a cosh(x) + 24a cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 3 8 3 6 3 4 3 2 3 +--R a cosh(x) + 4a cosh(x) + 6a cosh(x) + 4a cosh(x) + a +--R Type: Expression Integer +--E 40 + +--S 41 of 526 +t0608:= tanh(x)/(1+coth(x)) +--R +--R +--R tanh(x) +--R (41) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 41 + +--S 42 of 526 +r0608:= -1/2*x+log(cosh(x))-1/(2+2*tanh(x)) +--R +--R +--R (2tanh(x) + 2)log(cosh(x)) - x tanh(x) - x - 1 +--R (42) ---------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression Integer +--E 42 + +--S 43 of 526 +a0608:= integrate(t0608,x) +--R +--R +--R (43) +--R 2 2 2cosh(x) +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 6x sinh(x) - 12x cosh(x)sinh(x) - 6x cosh(x) - 1 +--R / +--R 2 2 +--R 4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 526 +m0608:= a0608-r0608 +--R +--R +--R (44) +--R 2 2 2 +--R (- 4sinh(x) - 8cosh(x)sinh(x) - 4cosh(x) )tanh(x) - 4sinh(x) +--R + +--R 2 +--R - 8cosh(x)sinh(x) - 4cosh(x) +--R * +--R log(cosh(x)) +--R + +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 4x sinh(x) - 8x cosh(x)sinh(x) - 4x cosh(x) - 1)tanh(x) +--R + +--R 2 2 +--R (- 4x + 2)sinh(x) + (- 8x + 4)cosh(x)sinh(x) + (- 4x + 2)cosh(x) - 1 +--R / +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Expression Integer +--E 44 + +--S 45 of 526 +d0608:= D(m0608,x) +--R +--R +--R (45) +--R 2 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)tanh(x) - sinh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R / +--R 2 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )tanh(x) + 2sinh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 2cosh(x) +--R Type: Expression Integer +--E 45 + +--S 46 of 526 +t0609:= tanh(x)^2/(1+coth(x)) +--R +--R +--R 2 +--R tanh(x) +--R (46) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 46 + +--S 47 of 526 +r0609:= 3/2*x-log(cosh(x))-tanh(x)+1/(2+2*tanh(x)) +--R +--R +--R 2 +--R (- 2tanh(x) - 2)log(cosh(x)) - 2tanh(x) + (3x - 2)tanh(x) + 3x + 1 +--R (47) ------------------------------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression Integer +--E 47 + +--S 48 of 526 +a0609:= integrate(t0609,x) +--R +--R +--R (48) +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) - 8cosh(x))sinh(x) - 4cosh(x) - 4cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R 10x sinh(x) + 40x cosh(x)sinh(x) + (60x cosh(x) + 10x + 9)sinh(x) +--R + +--R 3 4 +--R (40x cosh(x) + (20x + 18)cosh(x))sinh(x) + 10x cosh(x) +--R + +--R 2 +--R (10x + 9)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 526 +m0609:= a0609-r0609 +--R +--R +--R (49) +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R log(cosh(x)) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) - 8cosh(x))sinh(x) - 4cosh(x) - 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) - 8cosh(x))sinh(x) - 4cosh(x) - 4cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R (4x + 4)sinh(x) + (16x + 16)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((24x + 24)cosh(x) + 4x + 13)sinh(x) +--R + +--R 3 4 +--R ((16x + 16)cosh(x) + (8x + 26)cosh(x))sinh(x) + (4x + 4)cosh(x) +--R + +--R 2 +--R (4x + 13)cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 4 3 +--R (4x - 2)sinh(x) + (16x - 8)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((24x - 12)cosh(x) + 4x + 7)sinh(x) +--R + +--R 3 4 +--R ((16x - 8)cosh(x) + (8x + 14)cosh(x))sinh(x) + (4x - 2)cosh(x) +--R + +--R 2 +--R (4x + 7)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R Type: Expression Integer +--E 49 + +--S 50 of 526 +d0609:= D(m0609,x) +--R +--R +--R (50) +--R 6 5 2 4 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 30cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (- 40cosh(x) - 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 30cosh(x) - 24cosh(x) - 2)sinh(x) +--R + +--R 5 3 6 4 +--R (- 12cosh(x) - 16cosh(x) - 4cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R - 2cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 30cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (- 40cosh(x) - 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 30cosh(x) - 24cosh(x) - 2)sinh(x) +--R + +--R 5 3 6 4 +--R (- 12cosh(x) - 16cosh(x) - 4cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R - 2cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 7)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 28cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 42cosh(x) - 1)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 28cosh(x) - 2cosh(x))sinh(x) + cosh(x) - 7cosh(x) +--R + +--R 2 +--R - cosh(x) - 1 +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 3sinh(x) + 18cosh(x)sinh(x) + (45cosh(x) - 3)sinh(x) +--R + +--R 3 3 4 2 2 +--R (60cosh(x) - 12cosh(x))sinh(x) + (45cosh(x) - 18cosh(x) + 1)sinh(x) +--R + +--R 5 3 6 4 +--R (18cosh(x) - 12cosh(x) + 2cosh(x))sinh(x) + 3cosh(x) - 3cosh(x) +--R + +--R 2 +--R cosh(x) - 1 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) + 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 4)sinh(x) +--R + +--R 3 3 4 2 2 +--R (40cosh(x) + 16cosh(x))sinh(x) + (30cosh(x) + 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R Type: Expression Integer +--E 50 + +--S 51 of 526 +t0610:= tanh(x)^3/(1+coth(x)) +--R +--R +--R 3 +--R tanh(x) +--R (51) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 51 + +--S 52 of 526 +r0610:= -3/2*x+2*log(cosh(x))+tanh(x)-1/2*tanh(x)^2-1/(2+2*tanh(x)) +--R +--R +--R (52) +--R 3 2 +--R (4tanh(x) + 4)log(cosh(x)) - tanh(x) + tanh(x) + (- 3x + 2)tanh(x) - 3x - 1 +--R ----------------------------------------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression Integer +--E 52 + +--S 53 of 526 +a0610:= integrate(t0610,x) +--R +--R +--R (53) +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) + 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (48cosh(x) + 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) + 16cosh(x) +--R + +--R 2 +--R 8cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 6 5 +--R - 14x sinh(x) - 84x cosh(x)sinh(x) +--R + +--R 2 4 +--R (- 210x cosh(x) - 28x - 1)sinh(x) +--R + +--R 3 3 +--R (- 280x cosh(x) + (- 112x - 4)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 210x cosh(x) + (- 168x - 6)cosh(x) - 14x - 10)sinh(x) +--R + +--R 5 3 +--R (- 84x cosh(x) + (- 112x - 4)cosh(x) + (- 28x - 20)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 14x cosh(x) + (- 28x - 1)cosh(x) + (- 14x - 10)cosh(x) - 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) + 8)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) + 32cosh(x))sinh(x) + (60cosh(x) + 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) + 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 526 +m0610:= a0610-r0610 +--R +--R +--R (54) +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) - 96cosh(x) - 8)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) - 64cosh(x) - 16cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R - 16cosh(x) - 8cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) - 96cosh(x) - 8)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) - 64cosh(x) - 16cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R - 16cosh(x) - 8cosh(x) +--R * +--R log(cosh(x)) +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) + 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 +--R (48cosh(x) + 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) +--R + +--R 4 2 +--R 16cosh(x) + 8cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) + 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (48cosh(x) + 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) + 16cosh(x) +--R + +--R 2 +--R 8cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) + 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 30cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (- 40cosh(x) - 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 30cosh(x) - 24cosh(x) - 2)sinh(x) +--R + +--R 5 3 6 4 +--R (- 12cosh(x) - 16cosh(x) - 4cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R - 2cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 6 5 +--R (- 8x - 4)sinh(x) + (- 48x - 24)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((- 120x - 60)cosh(x) - 16x - 9)sinh(x) +--R + +--R 3 3 +--R ((- 160x - 80)cosh(x) + (- 64x - 36)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((- 120x - 60)cosh(x) + (- 96x - 54)cosh(x) - 8x - 14)sinh(x) +--R + +--R 5 3 +--R ((- 48x - 24)cosh(x) + (- 64x - 36)cosh(x) + (- 16x - 28)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (- 8x - 4)cosh(x) + (- 16x - 9)cosh(x) + (- 8x - 14)cosh(x) - 1 +--R * +--R tanh(x) +--R + +--R 6 5 +--R (- 8x + 2)sinh(x) + (- 48x + 12)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((- 120x + 30)cosh(x) - 16x + 3)sinh(x) +--R + +--R 3 3 +--R ((- 160x + 40)cosh(x) + (- 64x + 12)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((- 120x + 30)cosh(x) + (- 96x + 18)cosh(x) - 8x - 8)sinh(x) +--R + +--R 5 3 +--R ((- 48x + 12)cosh(x) + (- 64x + 12)cosh(x) + (- 16x - 16)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (- 8x + 2)cosh(x) + (- 16x + 3)cosh(x) + (- 8x - 8)cosh(x) - 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) + 8)sinh(x) +--R + +--R 3 3 +--R (80cosh(x) + 32cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (60cosh(x) + 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) + 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) + 8)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) + 32cosh(x))sinh(x) + (60cosh(x) + 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) + 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R Type: Expression Integer +--E 54 + +--S 55 of 526 +d0610:= D(m0610,x) +--R +--R +--R (55) +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) - 6)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) - 90cosh(x) - 6)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) - 120cosh(x) - 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) - 90cosh(x) - 36cosh(x) - 2)sinh(x) +--R + +--R 7 5 3 +--R (- 16cosh(x) - 36cosh(x) - 24cosh(x) - 4cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 2cosh(x) - 6cosh(x) - 6cosh(x) - 2cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 4sinh(x) + 32cosh(x)sinh(x) + (112cosh(x) + 12)sinh(x) +--R + +--R 3 5 +--R (224cosh(x) + 72cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (280cosh(x) + 180cosh(x) + 12)sinh(x) +--R + +--R 5 3 3 +--R (224cosh(x) + 240cosh(x) + 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (112cosh(x) + 180cosh(x) + 72cosh(x) + 4)sinh(x) +--R + +--R 7 5 3 8 +--R (32cosh(x) + 72cosh(x) + 48cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) +--R + +--R 6 4 2 +--R 12cosh(x) + 12cosh(x) + 4cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R sinh(x) + 8cosh(x)sinh(x) + (28cosh(x) + 4)sinh(x) +--R + +--R 3 5 +--R (56cosh(x) + 24cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70cosh(x) + 60cosh(x) + 22)sinh(x) +--R + +--R 5 3 3 +--R (56cosh(x) + 80cosh(x) + 88cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28cosh(x) + 60cosh(x) + 132cosh(x) + 4)sinh(x) +--R + +--R 7 5 3 8 +--R (8cosh(x) + 24cosh(x) + 88cosh(x) + 8cosh(x))sinh(x) + cosh(x) +--R + +--R 6 4 2 +--R 4cosh(x) + 22cosh(x) + 4cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 3sinh(x) - 24cosh(x)sinh(x) + (- 84cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (- 168cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 210cosh(x) - 120cosh(x) + 10)sinh(x) +--R + +--R 5 3 3 +--R (- 168cosh(x) - 160cosh(x) + 40cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 84cosh(x) - 120cosh(x) + 60cosh(x) )sinh(x) +--R + +--R 7 5 3 8 6 +--R (- 24cosh(x) - 48cosh(x) + 40cosh(x) )sinh(x) - 3cosh(x) - 8cosh(x) +--R + +--R 4 +--R 10cosh(x) + 1 +--R / +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) + 6)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) + 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) + 90cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) + 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) + 90cosh(x) + 36cosh(x) + 2)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) + 36cosh(x) + 24cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R 6cosh(x) + 6cosh(x) + 2cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) + 6)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) + 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) + 90cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) + 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) + 90cosh(x) + 36cosh(x) + 2)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) + 36cosh(x) + 24cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R 6cosh(x) + 6cosh(x) + 2cosh(x) +--R Type: Expression Integer +--E 55 + +--S 56 of 526 +t0611:= tanh(x)^4/(1+coth(x)) +--R +--R +--R 4 +--R tanh(x) +--R (56) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 56 + +--S 57 of 526 +r0611:= 5/2*x-2*log(cosh(x))-2*tanh(x)+1/2*tanh(x)^2-1/3*tanh(x)^3+_ + 1/(2+2*tanh(x)) +--R +--R +--R (57) +--R 4 3 2 +--R (- 12tanh(x) - 12)log(cosh(x)) - 2tanh(x) + tanh(x) - 9tanh(x) +--R + +--R (15x - 12)tanh(x) + 15x + 3 +--R / +--R 6tanh(x) + 6 +--R Type: Expression Integer +--E 57 + +--S 58 of 526 +a0611:= integrate(t0611,x) +--R +--R +--R (58) +--R 8 7 2 6 +--R - 24sinh(x) - 192cosh(x)sinh(x) + (- 672cosh(x) - 72)sinh(x) +--R + +--R 3 5 +--R (- 1344cosh(x) - 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 1680cosh(x) - 1080cosh(x) - 72)sinh(x) +--R + +--R 5 3 3 +--R (- 1344cosh(x) - 1440cosh(x) - 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 672cosh(x) - 1080cosh(x) - 432cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 +--R (- 192cosh(x) - 432cosh(x) - 288cosh(x) - 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 24cosh(x) - 72cosh(x) - 72cosh(x) - 24cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 8 7 +--R 54x sinh(x) + 432x cosh(x)sinh(x) +--R + +--R 2 6 +--R (1512x cosh(x) + 162x + 51)sinh(x) +--R + +--R 3 5 +--R (3024x cosh(x) + (972x + 306)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (3780x cosh(x) + (2430x + 765)cosh(x) + 162x + 81)sinh(x) +--R + +--R 5 3 3 +--R (3024x cosh(x) + (3240x + 1020)cosh(x) + (648x + 324)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 1512x cosh(x) + (2430x + 765)cosh(x) + (972x + 486)cosh(x) + 54x +--R + +--R 65 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R 432x cosh(x) + (972x + 306)cosh(x) + (648x + 324)cosh(x) +--R + +--R (108x + 130)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 +--R 54x cosh(x) + (162x + 51)cosh(x) + (162x + 81)cosh(x) +--R + +--R 2 +--R (54x + 65)cosh(x) + 3 +--R / +--R 8 7 2 6 +--R 12sinh(x) + 96cosh(x)sinh(x) + (336cosh(x) + 36)sinh(x) +--R + +--R 3 5 +--R (672cosh(x) + 216cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (840cosh(x) + 540cosh(x) + 36)sinh(x) +--R + +--R 5 3 3 +--R (672cosh(x) + 720cosh(x) + 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (336cosh(x) + 540cosh(x) + 216cosh(x) + 12)sinh(x) +--R + +--R 7 5 3 8 +--R (96cosh(x) + 216cosh(x) + 144cosh(x) + 24cosh(x))sinh(x) + 12cosh(x) +--R + +--R 6 4 2 +--R 36cosh(x) + 36cosh(x) + 12cosh(x) +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 526 +m0611:= a0611-r0611 +--R +--R +--R (59) +--R 8 7 2 6 +--R 24sinh(x) + 192cosh(x)sinh(x) + (672cosh(x) + 72)sinh(x) +--R + +--R 3 5 +--R (1344cosh(x) + 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1680cosh(x) + 1080cosh(x) + 72)sinh(x) +--R + +--R 5 3 3 +--R (1344cosh(x) + 1440cosh(x) + 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (672cosh(x) + 1080cosh(x) + 432cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 +--R (192cosh(x) + 432cosh(x) + 288cosh(x) + 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 24cosh(x) + 72cosh(x) + 72cosh(x) + 24cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R 24sinh(x) + 192cosh(x)sinh(x) + (672cosh(x) + 72)sinh(x) +--R + +--R 3 5 +--R (1344cosh(x) + 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1680cosh(x) + 1080cosh(x) + 72)sinh(x) +--R + +--R 5 3 3 +--R (1344cosh(x) + 1440cosh(x) + 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (672cosh(x) + 1080cosh(x) + 432cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 +--R (192cosh(x) + 432cosh(x) + 288cosh(x) + 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 24cosh(x) + 72cosh(x) + 72cosh(x) + 24cosh(x) +--R * +--R log(cosh(x)) +--R + +--R 8 7 2 6 +--R - 24sinh(x) - 192cosh(x)sinh(x) + (- 672cosh(x) - 72)sinh(x) +--R + +--R 3 5 +--R (- 1344cosh(x) - 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 1680cosh(x) - 1080cosh(x) - 72)sinh(x) +--R + +--R 5 3 3 +--R (- 1344cosh(x) - 1440cosh(x) - 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 672cosh(x) - 1080cosh(x) - 432cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 +--R (- 192cosh(x) - 432cosh(x) - 288cosh(x) - 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 24cosh(x) - 72cosh(x) - 72cosh(x) - 24cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 24sinh(x) - 192cosh(x)sinh(x) + (- 672cosh(x) - 72)sinh(x) +--R + +--R 3 5 +--R (- 1344cosh(x) - 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 1680cosh(x) - 1080cosh(x) - 72)sinh(x) +--R + +--R 5 3 3 +--R (- 1344cosh(x) - 1440cosh(x) - 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 672cosh(x) - 1080cosh(x) - 432cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 +--R (- 192cosh(x) - 432cosh(x) - 288cosh(x) - 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 24cosh(x) - 72cosh(x) - 72cosh(x) - 24cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 8 7 2 6 +--R 4sinh(x) + 32cosh(x)sinh(x) + (112cosh(x) + 12)sinh(x) +--R + +--R 3 5 +--R (224cosh(x) + 72cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (280cosh(x) + 180cosh(x) + 12)sinh(x) +--R + +--R 5 3 3 +--R (224cosh(x) + 240cosh(x) + 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (112cosh(x) + 180cosh(x) + 72cosh(x) + 4)sinh(x) +--R + +--R 7 5 3 8 +--R (32cosh(x) + 72cosh(x) + 48cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) +--R + +--R 6 4 2 +--R 12cosh(x) + 12cosh(x) + 4cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) - 6)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) - 90cosh(x) - 6)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) - 120cosh(x) - 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) - 90cosh(x) - 36cosh(x) - 2)sinh(x) +--R + +--R 7 5 3 +--R (- 16cosh(x) - 36cosh(x) - 24cosh(x) - 4cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 2cosh(x) - 6cosh(x) - 6cosh(x) - 2cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 18sinh(x) + 144cosh(x)sinh(x) + (504cosh(x) + 54)sinh(x) +--R + +--R 3 5 +--R (1008cosh(x) + 324cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1260cosh(x) + 810cosh(x) + 54)sinh(x) +--R + +--R 5 3 3 +--R (1008cosh(x) + 1080cosh(x) + 216cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (504cosh(x) + 810cosh(x) + 324cosh(x) + 18)sinh(x) +--R + +--R 7 5 3 +--R (144cosh(x) + 324cosh(x) + 216cosh(x) + 36cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 18cosh(x) + 54cosh(x) + 54cosh(x) + 18cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R (24x + 24)sinh(x) + (192x + 192)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((672x + 672)cosh(x) + 72x + 123)sinh(x) +--R + +--R 3 5 +--R ((1344x + 1344)cosh(x) + (432x + 738)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R ((1680x + 1680)cosh(x) + (1080x + 1845)cosh(x) + 72x + 153)sinh(x) +--R + +--R 5 3 +--R (1344x + 1344)cosh(x) + (1440x + 2460)cosh(x) +--R + +--R (288x + 612)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 +--R (672x + 672)cosh(x) + (1080x + 1845)cosh(x) +--R + +--R 2 +--R (432x + 918)cosh(x) + 24x + 89 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 +--R (192x + 192)cosh(x) + (432x + 738)cosh(x) +--R + +--R 3 +--R (288x + 612)cosh(x) + (48x + 178)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 +--R (24x + 24)cosh(x) + (72x + 123)cosh(x) + (72x + 153)cosh(x) +--R + +--R 2 +--R (24x + 89)cosh(x) + 3 +--R * +--R tanh(x) +--R + +--R 8 7 +--R (24x - 6)sinh(x) + (192x - 48)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((672x - 168)cosh(x) + 72x + 33)sinh(x) +--R + +--R 3 5 +--R ((1344x - 336)cosh(x) + (432x + 198)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R ((1680x - 420)cosh(x) + (1080x + 495)cosh(x) + 72x + 63)sinh(x) +--R + +--R 5 3 +--R ((1344x - 336)cosh(x) + (1440x + 660)cosh(x) + (288x + 252)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 +--R (672x - 168)cosh(x) + (1080x + 495)cosh(x) + (432x + 378)cosh(x) +--R + +--R 24x + 59 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R (192x - 48)cosh(x) + (432x + 198)cosh(x) + (288x + 252)cosh(x) +--R + +--R (48x + 118)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 +--R (24x - 6)cosh(x) + (72x + 33)cosh(x) + (72x + 63)cosh(x) +--R + +--R 2 +--R (24x + 59)cosh(x) + 3 +--R / +--R 8 7 2 6 +--R 12sinh(x) + 96cosh(x)sinh(x) + (336cosh(x) + 36)sinh(x) +--R + +--R 3 5 +--R (672cosh(x) + 216cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (840cosh(x) + 540cosh(x) + 36)sinh(x) +--R + +--R 5 3 3 +--R (672cosh(x) + 720cosh(x) + 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (336cosh(x) + 540cosh(x) + 216cosh(x) + 12)sinh(x) +--R + +--R 7 5 3 +--R (96cosh(x) + 216cosh(x) + 144cosh(x) + 24cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 12cosh(x) + 36cosh(x) + 36cosh(x) + 12cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R 12sinh(x) + 96cosh(x)sinh(x) + (336cosh(x) + 36)sinh(x) +--R + +--R 3 5 +--R (672cosh(x) + 216cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (840cosh(x) + 540cosh(x) + 36)sinh(x) +--R + +--R 5 3 3 +--R (672cosh(x) + 720cosh(x) + 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (336cosh(x) + 540cosh(x) + 216cosh(x) + 12)sinh(x) +--R + +--R 7 5 3 8 +--R (96cosh(x) + 216cosh(x) + 144cosh(x) + 24cosh(x))sinh(x) + 12cosh(x) +--R + +--R 6 4 2 +--R 36cosh(x) + 36cosh(x) + 12cosh(x) +--R Type: Expression Integer +--E 59 + +--S 60 of 526 +d0611:= D(m0611,x) +--R +--R +--R (60) +--R 10 9 2 8 +--R - 2sinh(x) - 20cosh(x)sinh(x) + (- 90cosh(x) - 8)sinh(x) +--R + +--R 3 7 +--R (- 240cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (- 420cosh(x) - 224cosh(x) - 12)sinh(x) +--R + +--R 5 3 5 +--R (- 504cosh(x) - 448cosh(x) - 72cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 420cosh(x) - 560cosh(x) - 180cosh(x) - 8)sinh(x) +--R + +--R 7 5 3 3 +--R (- 240cosh(x) - 448cosh(x) - 240cosh(x) - 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 90cosh(x) - 224cosh(x) - 180cosh(x) - 48cosh(x) - 2)sinh(x) +--R + +--R 9 7 5 3 +--R (- 20cosh(x) - 64cosh(x) - 72cosh(x) - 32cosh(x) - 4cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 2cosh(x) - 8cosh(x) - 12cosh(x) - 8cosh(x) - 2cosh(x) +--R * +--R 5 +--R tanh(x) +--R + +--R 10 9 2 8 +--R - 4sinh(x) - 40cosh(x)sinh(x) + (- 180cosh(x) - 16)sinh(x) +--R + +--R 3 7 +--R (- 480cosh(x) - 128cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (- 840cosh(x) - 448cosh(x) - 24)sinh(x) +--R + +--R 5 3 5 +--R (- 1008cosh(x) - 896cosh(x) - 144cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 840cosh(x) - 1120cosh(x) - 360cosh(x) - 16)sinh(x) +--R + +--R 7 5 3 3 +--R (- 480cosh(x) - 896cosh(x) - 480cosh(x) - 64cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 180cosh(x) - 448cosh(x) - 360cosh(x) - 96cosh(x) - 4)sinh(x) +--R + +--R 9 7 5 3 +--R (- 40cosh(x) - 128cosh(x) - 144cosh(x) - 64cosh(x) - 8cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 4cosh(x) - 16cosh(x) - 24cosh(x) - 16cosh(x) - 4cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 10 9 2 8 +--R sinh(x) + 10cosh(x)sinh(x) + (45cosh(x) - 13)sinh(x) +--R + +--R 3 7 +--R (120cosh(x) - 104cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (210cosh(x) - 364cosh(x) - 14)sinh(x) +--R + +--R 5 3 5 +--R (252cosh(x) - 728cosh(x) - 84cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (210cosh(x) - 910cosh(x) - 210cosh(x) - 34)sinh(x) +--R + +--R 7 5 3 3 +--R (120cosh(x) - 728cosh(x) - 280cosh(x) - 136cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (45cosh(x) - 364cosh(x) - 210cosh(x) - 204cosh(x) - 3)sinh(x) +--R + +--R 9 7 5 3 +--R (10cosh(x) - 104cosh(x) - 84cosh(x) - 136cosh(x) - 6cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) - 13cosh(x) - 14cosh(x) - 34cosh(x) - 3cosh(x) - 1 +--R * +--R tanh(x) +--R + +--R 10 9 2 8 +--R 5sinh(x) + 50cosh(x)sinh(x) + (225cosh(x) + 3)sinh(x) +--R + +--R 3 7 +--R (600cosh(x) + 24cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (1050cosh(x) + 84cosh(x) + 10)sinh(x) +--R + +--R 5 3 5 +--R (1260cosh(x) + 168cosh(x) + 60cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (1050cosh(x) + 210cosh(x) + 150cosh(x) - 18)sinh(x) +--R + +--R 7 5 3 3 +--R (600cosh(x) + 168cosh(x) + 200cosh(x) - 72cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (225cosh(x) + 84cosh(x) + 150cosh(x) - 108cosh(x) + 1)sinh(x) +--R + +--R 9 7 5 3 +--R (50cosh(x) + 24cosh(x) + 60cosh(x) - 72cosh(x) + 2cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R 5cosh(x) + 3cosh(x) + 10cosh(x) - 18cosh(x) + cosh(x) - 1 +--R / +--R 10 9 2 8 +--R 2sinh(x) + 20cosh(x)sinh(x) + (90cosh(x) + 8)sinh(x) +--R + +--R 3 7 +--R (240cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (420cosh(x) + 224cosh(x) + 12)sinh(x) +--R + +--R 5 3 5 +--R (504cosh(x) + 448cosh(x) + 72cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (420cosh(x) + 560cosh(x) + 180cosh(x) + 8)sinh(x) +--R + +--R 7 5 3 3 +--R (240cosh(x) + 448cosh(x) + 240cosh(x) + 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (90cosh(x) + 224cosh(x) + 180cosh(x) + 48cosh(x) + 2)sinh(x) +--R + +--R 9 7 5 3 +--R (20cosh(x) + 64cosh(x) + 72cosh(x) + 32cosh(x) + 4cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R 2cosh(x) + 8cosh(x) + 12cosh(x) + 8cosh(x) + 2cosh(x) +--R * +--R tanh(x) +--R + +--R 10 9 2 8 +--R 2sinh(x) + 20cosh(x)sinh(x) + (90cosh(x) + 8)sinh(x) +--R + +--R 3 7 +--R (240cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (420cosh(x) + 224cosh(x) + 12)sinh(x) +--R + +--R 5 3 5 +--R (504cosh(x) + 448cosh(x) + 72cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (420cosh(x) + 560cosh(x) + 180cosh(x) + 8)sinh(x) +--R + +--R 7 5 3 3 +--R (240cosh(x) + 448cosh(x) + 240cosh(x) + 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (90cosh(x) + 224cosh(x) + 180cosh(x) + 48cosh(x) + 2)sinh(x) +--R + +--R 9 7 5 3 +--R (20cosh(x) + 64cosh(x) + 72cosh(x) + 32cosh(x) + 4cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R 2cosh(x) + 8cosh(x) + 12cosh(x) + 8cosh(x) + 2cosh(x) +--R Type: Expression Integer +--E 60 + +--S 61 of 526 +t0612:= coth(x)/(a+b*coth(x)) +--R +--R +--R coth(x) +--R (61) ------------- +--R b coth(x) + a +--R Type: Expression Integer +--E 61 + +--S 62 of 526 +r0612:= (-b*x+a*log(b*cosh(x)+a*sinh(x)))/(a^2-b^2) +--R +--R +--R - a log(a sinh(x) + b cosh(x)) + b x +--R (62) ------------------------------------ +--R 2 2 +--R b - a +--R Type: Expression Integer +--E 62 + +--S 63 of 526 +a0612:= integrate(t0612,x) +--R +--R +--R - 2a sinh(x) - 2b cosh(x) +--R - a log(-------------------------) + (b + a)x +--R sinh(x) - cosh(x) +--R (63) --------------------------------------------- +--R 2 2 +--R b - a +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 526 +m0612:= a0612-r0612 +--R +--R +--R - 2a sinh(x) - 2b cosh(x) +--R a log(a sinh(x) + b cosh(x)) - a log(-------------------------) + a x +--R sinh(x) - cosh(x) +--R (64) --------------------------------------------------------------------- +--R 2 2 +--R b - a +--R Type: Expression Integer +--E 64 + +--S 65 of 526 +d0612:= D(m0612,x) +--R +--R +--R (65) 0 +--R Type: Expression Integer +--E 65 + +--S 66 of 526 +t0613:= coth(x)/(1+coth(x)) +--R +--R +--R coth(x) +--R (66) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 66 + +--S 67 of 526 +r0613:= 1/2*x-1/(2+2*tanh(x)) +--R +--R +--R x tanh(x) + x - 1 +--R (67) ----------------- +--R 2tanh(x) + 2 +--R Type: Expression Integer +--E 67 + +--S 68 of 526 +a0613:= integrate(t0613,x) +--R +--R +--R (2x + 1)sinh(x) + (2x - 1)cosh(x) +--R (68) --------------------------------- +--R 4sinh(x) + 4cosh(x) +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 526 +m0613:= a0613-r0613 +--R +--R +--R (sinh(x) - cosh(x))tanh(x) + 3sinh(x) + cosh(x) +--R (69) -------------------------------------------------- +--R (4sinh(x) + 4cosh(x))tanh(x) + 4sinh(x) + 4cosh(x) +--R Type: Expression Integer +--E 69 + +--S 70 of 526 +d0613:= D(m0613,x) +--R +--R +--R cosh(x)tanh(x) - sinh(x) +--R (70) ---------------------------------------------- +--R (sinh(x) + cosh(x))tanh(x) + sinh(x) + cosh(x) +--R Type: Expression Integer +--E 70 + +--S 71 of 526 +t0614:= coth(x)^2/(1+coth(x)) +--R +--R +--R 2 +--R coth(x) +--R (71) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 71 + +--S 72 of 526 +r0614:= -1/2*x+log(sinh(x))+1/(2+2*tanh(x)) +--R +--R +--R (2tanh(x) + 2)log(sinh(x)) - x tanh(x) - x + 1 +--R (72) ---------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression Integer +--E 72 + +--S 73 of 526 +a0614:= integrate(t0614,x) +--R +--R +--R (73) +--R 2 2 2sinh(x) +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 6x sinh(x) - 12x cosh(x)sinh(x) - 6x cosh(x) + 1 +--R / +--R 2 2 +--R 4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 526 +m0614:= a0614-r0614 +--R +--R +--R (74) +--R 2 2 2 +--R (- 4sinh(x) - 8cosh(x)sinh(x) - 4cosh(x) )tanh(x) - 4sinh(x) +--R + +--R 2 +--R - 8cosh(x)sinh(x) - 4cosh(x) +--R * +--R log(sinh(x)) +--R + +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 4x sinh(x) - 8x cosh(x)sinh(x) - 4x cosh(x) + 1)tanh(x) +--R + +--R 2 2 +--R (- 4x - 2)sinh(x) + (- 8x - 4)cosh(x)sinh(x) + (- 4x - 2)cosh(x) + 1 +--R / +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Expression Integer +--E 74 + +--S 75 of 526 +d0614:= D(m0614,x) +--R +--R +--R (75) +--R 2 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)tanh(x) + sinh(x) +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 2 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )tanh(x) + 2sinh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 2cosh(x) +--R Type: Expression Integer +--E 75 + +--S 76 of 526 +t0615:= coth(x)^3/(1+coth(x)) +--R +--R +--R 3 +--R coth(x) +--R (76) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 76 + +--S 77 of 526 +r0615:= 3/2*x-coth(x)-log(sinh(x))-1/(2+2*tanh(x)) +--R +--R +--R (77) +--R (- 2tanh(x) - 2)log(sinh(x)) + (- 2coth(x) + 3x)tanh(x) - 2coth(x) + 3x - 1 +--R --------------------------------------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression Integer +--E 77 + +--S 78 of 526 +a0615:= integrate(t0615,x) +--R +--R +--R (78) +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 8cosh(x))sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R 10x sinh(x) + 40x cosh(x)sinh(x) + (60x cosh(x) - 10x - 9)sinh(x) +--R + +--R 3 4 +--R (40x cosh(x) + (- 20x - 18)cosh(x))sinh(x) + 10x cosh(x) +--R + +--R 2 +--R (- 10x - 9)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 526 +m0615:= a0615-r0615 +--R +--R +--R (79) +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R log(sinh(x)) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 8cosh(x))sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 8cosh(x))sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 +--R (4coth(x) + 4x)sinh(x) + (16cosh(x)coth(x) + 16x cosh(x))sinh(x) +--R + +--R 2 2 2 +--R ((24cosh(x) - 4)coth(x) + 24x cosh(x) - 4x - 9)sinh(x) +--R + +--R 3 3 +--R (16cosh(x) - 8cosh(x))coth(x) + 16x cosh(x) +--R + +--R (- 8x - 18)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 4 2 +--R (4cosh(x) - 4cosh(x) )coth(x) + 4x cosh(x) + (- 4x - 9)cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 4 +--R (4coth(x) + 4x + 2)sinh(x) +--R + +--R 3 +--R (16cosh(x)coth(x) + (16x + 8)cosh(x))sinh(x) +--R + +--R 2 2 2 +--R ((24cosh(x) - 4)coth(x) + (24x + 12)cosh(x) - 4x - 11)sinh(x) +--R + +--R 3 3 +--R (16cosh(x) - 8cosh(x))coth(x) + (16x + 8)cosh(x) +--R + +--R (- 8x - 22)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 4 2 +--R (4cosh(x) - 4cosh(x) )coth(x) + (4x + 2)cosh(x) + (- 4x - 11)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R Type: Expression Integer +--E 79 + +--S 80 of 526 +d0615:= D(m0615,x) +--R +--R +--R (80) +--R 2 6 2 5 +--R (- 2coth(x) + 3)sinh(x) + (- 12cosh(x)coth(x) + 18cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30cosh(x) + 4)coth(x) + 45cosh(x) + 3)sinh(x) +--R + +--R 3 2 3 3 +--R ((- 40cosh(x) + 16cosh(x))coth(x) + 60cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (- 30cosh(x) + 24cosh(x) - 2)coth(x) + 45cosh(x) + 18cosh(x) +--R + +--R 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 12cosh(x) + 16cosh(x) - 4cosh(x))coth(x) + 18cosh(x) +--R + +--R 3 +--R 12cosh(x) + 2cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (- 2cosh(x) + 4cosh(x) - 2cosh(x) )coth(x) + 3cosh(x) + 3cosh(x) +--R + +--R 2 +--R cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 2 6 2 5 +--R (- 2coth(x) + 1)sinh(x) + (- 12cosh(x)coth(x) + 6cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30cosh(x) + 4)coth(x) + 15cosh(x) + 7)sinh(x) +--R + +--R 3 2 3 3 +--R ((- 40cosh(x) + 16cosh(x))coth(x) + 20cosh(x) + 28cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R ((- 30cosh(x) + 24cosh(x) - 2)coth(x) + 15cosh(x) + 42cosh(x) - 1) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 12cosh(x) + 16cosh(x) - 4cosh(x))coth(x) + 6cosh(x) +--R + +--R 3 +--R 28cosh(x) - 2cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (- 2cosh(x) + 4cosh(x) - 2cosh(x) )coth(x) + cosh(x) + 7cosh(x) +--R + +--R 2 +--R - cosh(x) + 1 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) - 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) - 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) - 4)sinh(x) +--R + +--R 3 3 4 2 2 +--R (40cosh(x) - 16cosh(x))sinh(x) + (30cosh(x) - 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R Type: Expression Integer +--E 80 + +--S 81 of 526 +t0616:= coth(x)^4/(1+coth(x)) +--R +--R +--R 4 +--R coth(x) +--R (81) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 81 + +--S 82 of 526 +r0616:= -3/2*x+coth(x)-1/2*coth(x)^2+2*log(sinh(x))+1/(2+2*tanh(x)) +--R +--R +--R (82) +--R 2 +--R (4tanh(x) + 4)log(sinh(x)) + (- coth(x) + 2coth(x) - 3x)tanh(x) +--R + +--R 2 +--R - coth(x) + 2coth(x) - 3x + 1 +--R / +--R 2tanh(x) + 2 +--R Type: Expression Integer +--E 82 + +--S 83 of 526 +a0616:= integrate(t0616,x) +--R +--R +--R (83) +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) - 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (48cosh(x) - 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) - 16cosh(x) +--R + +--R 2 +--R 8cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 6 5 +--R - 14x sinh(x) - 84x cosh(x)sinh(x) +--R + +--R 2 4 +--R (- 210x cosh(x) + 28x + 1)sinh(x) +--R + +--R 3 3 +--R (- 280x cosh(x) + (112x + 4)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 210x cosh(x) + (168x + 6)cosh(x) - 14x - 10)sinh(x) +--R + +--R 5 3 +--R (- 84x cosh(x) + (112x + 4)cosh(x) + (- 28x - 20)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 14x cosh(x) + (28x + 1)cosh(x) + (- 14x - 10)cosh(x) + 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) - 8)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) - 32cosh(x))sinh(x) + (60cosh(x) - 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) - 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 526 +m0616:= a0616-r0616 +--R +--R +--R (84) +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) + 96cosh(x) - 8)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) + 64cosh(x) - 16cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R 16cosh(x) - 8cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) + 96cosh(x) - 8)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) + 64cosh(x) - 16cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R 16cosh(x) - 8cosh(x) +--R * +--R log(sinh(x)) +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) - 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 +--R (48cosh(x) - 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) +--R + +--R 4 2 +--R - 16cosh(x) + 8cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) - 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (48cosh(x) - 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) - 16cosh(x) +--R + +--R 2 +--R 8cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 6 +--R (2coth(x) - 4coth(x) - 8x)sinh(x) +--R + +--R 2 5 +--R (12cosh(x)coth(x) - 24cosh(x)coth(x) - 48x cosh(x))sinh(x) +--R + +--R 2 2 2 +--R (30cosh(x) - 4)coth(x) + (- 60cosh(x) + 8)coth(x) +--R + +--R 2 +--R - 120x cosh(x) + 16x + 1 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (40cosh(x) - 16cosh(x))coth(x) +--R + +--R 3 3 +--R (- 80cosh(x) + 32cosh(x))coth(x) - 160x cosh(x) +--R + +--R (64x + 4)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) - 24cosh(x) + 2)coth(x) +--R + +--R 4 2 4 +--R (- 60cosh(x) + 48cosh(x) - 4)coth(x) - 120x cosh(x) +--R + +--R 2 +--R (96x + 6)cosh(x) - 8x - 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))coth(x) +--R + +--R 5 3 5 +--R (- 24cosh(x) + 32cosh(x) - 8cosh(x))coth(x) - 48x cosh(x) +--R + +--R 3 +--R (64x + 4)cosh(x) + (- 16x - 20)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (2cosh(x) - 4cosh(x) + 2cosh(x) )coth(x) +--R + +--R 6 4 2 6 +--R (- 4cosh(x) + 8cosh(x) - 4cosh(x) )coth(x) - 8x cosh(x) +--R + +--R 4 2 +--R (16x + 1)cosh(x) + (- 8x - 10)cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 2 6 +--R (2coth(x) - 4coth(x) - 8x - 2)sinh(x) +--R + +--R 2 5 +--R (12cosh(x)coth(x) - 24cosh(x)coth(x) + (- 48x - 12)cosh(x))sinh(x) +--R + +--R 2 2 2 +--R (30cosh(x) - 4)coth(x) + (- 60cosh(x) + 8)coth(x) +--R + +--R 2 +--R (- 120x - 30)cosh(x) + 16x + 5 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 +--R (40cosh(x) - 16cosh(x))coth(x) + (- 80cosh(x) + 32cosh(x))coth(x) +--R + +--R 3 +--R (- 160x - 40)cosh(x) + (64x + 20)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) - 24cosh(x) + 2)coth(x) +--R + +--R 4 2 4 +--R (- 60cosh(x) + 48cosh(x) - 4)coth(x) + (- 120x - 30)cosh(x) +--R + +--R 2 +--R (96x + 30)cosh(x) - 8x - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))coth(x) +--R + +--R 5 3 5 +--R (- 24cosh(x) + 32cosh(x) - 8cosh(x))coth(x) + (- 48x - 12)cosh(x) +--R + +--R 3 +--R (64x + 20)cosh(x) + (- 16x - 24)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (2cosh(x) - 4cosh(x) + 2cosh(x) )coth(x) +--R + +--R 6 4 2 6 +--R (- 4cosh(x) + 8cosh(x) - 4cosh(x) )coth(x) + (- 8x - 2)cosh(x) +--R + +--R 4 2 +--R (16x + 5)cosh(x) + (- 8x - 12)cosh(x) + 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) - 8)sinh(x) +--R + +--R 3 3 +--R (80cosh(x) - 32cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (60cosh(x) - 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) - 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) - 8)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) - 32cosh(x))sinh(x) + (60cosh(x) - 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) - 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R Type: Expression Integer +--E 84 + +--S 85 of 526 +d0616:= D(m0616,x) +--R +--R +--R (85) +--R 3 2 8 +--R (- 2coth(x) + 2coth(x) + 2coth(x) - 3)sinh(x) +--R + +--R 3 2 +--R - 16cosh(x)coth(x) + 16cosh(x)coth(x) + 16cosh(x)coth(x) +--R + +--R - 24cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 56cosh(x) + 6)coth(x) + (56cosh(x) - 6)coth(x) +--R + +--R 2 2 +--R (56cosh(x) - 6)coth(x) - 84cosh(x) + 8 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 +--R (- 112cosh(x) + 36cosh(x))coth(x) +--R + +--R 3 2 +--R (112cosh(x) - 36cosh(x))coth(x) +--R + +--R 3 3 +--R (112cosh(x) - 36cosh(x))coth(x) - 168cosh(x) + 48cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 +--R (- 140cosh(x) + 90cosh(x) - 6)coth(x) +--R + +--R 4 2 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) +--R + +--R 4 2 4 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) - 210cosh(x) + 120cosh(x) +--R + +--R 10 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) + 120cosh(x) - 24cosh(x))coth(x) +--R + +--R 5 3 2 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) +--R + +--R 5 3 5 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) - 168cosh(x) +--R + +--R 3 +--R 160cosh(x) + 40cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- 56cosh(x) + 90cosh(x) - 36cosh(x) + 2)coth(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) +--R + +--R 6 4 2 6 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) - 84cosh(x) +--R + +--R 4 2 +--R 120cosh(x) + 60cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 3 +--R (- 16cosh(x) + 36cosh(x) - 24cosh(x) + 4cosh(x))coth(x) +--R + +--R 7 5 3 2 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) +--R + +--R 7 5 3 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) +--R + +--R 7 5 3 +--R - 24cosh(x) + 48cosh(x) + 40cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (- 2cosh(x) + 6cosh(x) - 6cosh(x) + 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 2 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 8 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) - 3cosh(x) +--R + +--R 6 4 +--R 8cosh(x) + 10cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 3 2 8 +--R (- 2coth(x) + 2coth(x) + 2coth(x) - 1)sinh(x) +--R + +--R 3 2 +--R (- 16cosh(x)coth(x) + 16cosh(x)coth(x) + 16cosh(x)coth(x) - 8cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 56cosh(x) + 6)coth(x) + (56cosh(x) - 6)coth(x) +--R + +--R 2 2 +--R (56cosh(x) - 6)coth(x) - 28cosh(x) + 2 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 +--R (- 112cosh(x) + 36cosh(x))coth(x) +--R + +--R 3 2 3 +--R (112cosh(x) - 36cosh(x))coth(x) + (112cosh(x) - 36cosh(x))coth(x) +--R + +--R 3 +--R - 56cosh(x) + 12cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 +--R (- 140cosh(x) + 90cosh(x) - 6)coth(x) +--R + +--R 4 2 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) +--R + +--R 4 2 4 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) - 70cosh(x) + 30cosh(x) + 16 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) + 120cosh(x) - 24cosh(x))coth(x) +--R + +--R 5 3 2 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) +--R + +--R 5 3 5 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) - 56cosh(x) +--R + +--R 3 +--R 40cosh(x) + 64cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- 56cosh(x) + 90cosh(x) - 36cosh(x) + 2)coth(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) +--R + +--R 6 4 2 6 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) - 28cosh(x) +--R + +--R 4 2 +--R 30cosh(x) + 96cosh(x) - 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 3 +--R (- 16cosh(x) + 36cosh(x) - 24cosh(x) + 4cosh(x))coth(x) +--R + +--R 7 5 3 2 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) +--R + +--R 7 5 3 7 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) - 8cosh(x) +--R + +--R 5 3 +--R 12cosh(x) + 64cosh(x) - 4cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (- 2cosh(x) + 6cosh(x) - 6cosh(x) + 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 2 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 8 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) - cosh(x) +--R + +--R 6 4 2 +--R 2cosh(x) + 16cosh(x) - 2cosh(x) + 1 +--R / +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) - 6)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) - 90cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 6cosh(x) + 6cosh(x) - 2cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) - 6)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) - 90cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 6cosh(x) + 6cosh(x) - 2cosh(x) +--R Type: Expression Integer +--E 85 + +--S 86 of 526 +t0617:= sech(x)^2/(a+b*coth(x)) +--R +--R +--R 2 +--R sech(x) +--R (86) ------------- +--R b coth(x) + a +--R Type: Expression Integer +--E 86 + +--S 87 of 526 +r0617:= -b*log(b+a*tanh(x))/a^2+tanh(x)/a +--R +--R +--R - b log(a tanh(x) + b) + a tanh(x) +--R (87) ---------------------------------- +--R 2 +--R a +--R Type: Expression Integer +--E 87 + +--S 88 of 526 +a0617:= integrate(t0617,x) +--R +--R +--R (88) +--R 2 2 2cosh(x) +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R - 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 526 +m0617:= a0617-r0617 +--R +--R +--R (89) +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b)log(a tanh(x) + b) +--R + +--R 2 2 2cosh(x) +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a)tanh(x) - 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Expression Integer +--E 89 + +--S 90 of 526 +d0617:= D(m0617,x) +--R +--R +--R (90) +--R 2 5 2 2 4 +--R a cosh(x)sinh(x) + (a b + 4a )cosh(x) sinh(x) +--R + +--R 2 3 2 3 +--R ((4a b + 6a )cosh(x) + 2a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R ((6a b + 4a )cosh(x) + (2a b + 4a )cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((4a b + a )cosh(x) + (4a b + 2a )cosh(x) + a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 6 2 5 +--R a b sinh(x) + (4a b - a )cosh(x)sinh(x) +--R + +--R 2 2 4 +--R ((4a b - 4a )cosh(x) + 2a b)sinh(x) +--R + +--R 2 3 2 3 +--R ((- 4a b - 6a )cosh(x) + (4a b + 2a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R ((- 11a b - 4a )cosh(x) + (2a b + 4a )cosh(x) + a b)sinh(x) +--R + +--R 2 5 2 3 2 +--R ((- 8a b - a )cosh(x) + 2a cosh(x) - a cosh(x))sinh(x) +--R + +--R 6 2 +--R - 2a b cosh(x) - 2a b cosh(x) +--R * +--R tanh(x) +--R + +--R 2 6 2 5 2 2 2 4 +--R b sinh(x) + 4b cosh(x)sinh(x) + (5b cosh(x) + 2b )sinh(x) +--R + +--R 2 3 +--R (4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 5b cosh(x) + (4b + 8a b)cosh(x) + b )sinh(x) +--R + +--R 2 5 2 3 2 6 2 4 +--R (- 4b cosh(x) + (4b + 4a b)cosh(x) )sinh(x) - b cosh(x) + 2b cosh(x) +--R + +--R 2 2 +--R - b cosh(x) +--R / +--R 3 5 2 3 2 4 +--R a cosh(x)sinh(x) + (a b + 4a )cosh(x) sinh(x) +--R + +--R 2 3 3 3 3 +--R ((4a b + 6a )cosh(x) + 2a cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R ((6a b + 4a )cosh(x) + (2a b + 4a )cosh(x) )sinh(x) +--R + +--R 2 3 5 2 3 3 3 +--R ((4a b + a )cosh(x) + (4a b + 2a )cosh(x) + a cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) +--R * +--R tanh(x) +--R + +--R 2 5 2 2 2 4 +--R a b cosh(x)sinh(x) + (a b + 4a b)cosh(x) sinh(x) +--R + +--R 2 2 3 2 3 +--R ((4a b + 6a b)cosh(x) + 2a b cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R ((6a b + 4a b)cosh(x) + (2a b + 4a b)cosh(x) )sinh(x) +--R + +--R 2 2 5 2 2 3 2 +--R ((4a b + a b)cosh(x) + (4a b + 2a b)cosh(x) + a b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) +--R Type: Expression Integer +--E 90 + +--S 91 of 526 +t0618:= sech(x)^3/(a+b*coth(x)) +--R +--R +--R 3 +--R sech(x) +--R (91) ------------- +--R b coth(x) + a +--R Type: Expression Integer +--E 91 + +--S 92 of 526 +r0618:= atan(tanh(1/2*x))/a-2*b^2*atan(tanh(1/2*x))/a^3+_ + 2*b*(a^2-b^2)^(1/2)*atanh((a+b*tanh(1/2*x))/(a^2-b^2)^(1/2))/a^3+_ + 2*tanh(1/2*x)/a/(1+tanh(1/2*x)^2)^2-2*b/a^2/(1+tanh(1/2*x)^2)-_ + tanh(1/2*x)/a/(1+tanh(1/2*x)^2) +--R +--R +--R (92) +--R x +--R +---------+ b tanh(-) + a +--R x 4 x 2 | 2 2 2 +--R (2b tanh(-) + 4b tanh(-) + 2b)\|- b + a atanh(-------------) +--R 2 2 +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 x 4 2 2 x 2 2 2 x +--R ((- 2b + a )tanh(-) + (- 4b + 2a )tanh(-) - 2b + a )atan(tanh(-)) +--R 2 2 2 +--R + +--R 2 x 3 x 2 2 x +--R - a tanh(-) - 2a b tanh(-) + a tanh(-) - 2a b +--R 2 2 2 +--R / +--R 3 x 4 3 x 2 3 +--R a tanh(-) + 2a tanh(-) + a +--R 2 2 +--R Type: Expression Integer +--E 92 + +--S 93 of 526 +a0618:= integrate(t0618,x) +--R +--R +--R (93) +--R [ +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- b + a + (b + a)sinh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b + a +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R (- 2a b + a )sinh(x) + (- 6a b + 3a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 +--R ((- 6a b + 3a )cosh(x) - 2a b - a )sinh(x) + (- 2a b + a )cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R , +--R +--R 4 3 2 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) - 2b +--R * +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 \|b - a +--R \|b - a atan(-------------------------------) +--R (b + a)sinh(x) + (b + a)cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R (- 2a b + a )sinh(x) + (- 6a b + 3a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 +--R ((- 6a b + 3a )cosh(x) - 2a b - a )sinh(x) + (- 2a b + a )cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 93 + +--S 94 of 526 +m0618a:= a0618.1-r0618 +--R +--R +--R (94) +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) + 4b)sinh(x) +--R + +--R 3 4 2 +--R (8b cosh(x) + 8b cosh(x))sinh(x) + 2b cosh(x) + 4b cosh(x) + 2b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- b + a + (b + a)sinh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b + a +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) + b +--R + +--R - a +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) +--R + +--R - 2b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - 4b sinh(x) - 16b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 24b cosh(x) - 8b)sinh(x) +--R + +--R 3 4 2 +--R (- 16b cosh(x) - 16b cosh(x))sinh(x) - 4b cosh(x) - 8b cosh(x) +--R + +--R - 4b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) - 2b +--R * +--R x +--R +---------+ b tanh(-) + a +--R | 2 2 2 +--R \|- b + a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 2 2 3 +--R (2b - a )sinh(x) + (8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 6a )cosh(x) + 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 4a )cosh(x) + (8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - a )cosh(x) + (4b - 2a )cosh(x) + 2b - a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (4b - 2a )sinh(x) + (16b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b - 12a )cosh(x) + 8b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b - 8a )cosh(x) + (16b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b - 2a )cosh(x) + (8b - 4a )cosh(x) + 4b - 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (2b - a )sinh(x) + (8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 6a )cosh(x) + 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 4a )cosh(x) + (8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - a )cosh(x) + (4b - 2a )cosh(x) + 2b - a +--R * +--R x +--R atan(tanh(-)) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 4b + 2a )sinh(x) + (- 16b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 24b + 12a )cosh(x) - 8b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 16b + 8a )cosh(x) + (- 16b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 4b + 2a )cosh(x) + (- 8b + 4a )cosh(x) - 4b + 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R (- 2a b + a )sinh(x) + (- 6a b + 3a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 +--R ((- 6a b + 3a )cosh(x) - 2a b - a )sinh(x) + (- 2a b + a )cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 2 2 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 2 3 2 2 4 2 2 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2a b sinh(x) + (8a b cosh(x) - 4a b + 2a )sinh(x) +--R + +--R 2 2 2 +--R (12a b cosh(x) + (- 12a b + 6a )cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 +--R 8a b cosh(x) + (- 12a b + 6a )cosh(x) + 8a b cosh(x) - 4a b +--R + +--R 2 +--R - 2a +--R * +--R sinh(x) +--R + +--R 4 2 3 2 +--R 2a b cosh(x) + (- 4a b + 2a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R (- 4a b - 2a )cosh(x) + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 2 2 2 2 +--R - a sinh(x) - 4a cosh(x)sinh(x) + (- 6a cosh(x) - 2a )sinh(x) +--R + +--R 2 3 2 2 4 2 2 2 +--R (- 4a cosh(x) - 4a cosh(x))sinh(x) - a cosh(x) - 2a cosh(x) - a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2a b sinh(x) + (8a b cosh(x) - 2a b + a )sinh(x) +--R + +--R 2 2 2 +--R (12a b cosh(x) + (- 6a b + 3a )cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 2 +--R (8a b cosh(x) + (- 6a b + 3a )cosh(x) + 8a b cosh(x) - 2a b - a ) +--R * +--R sinh(x) +--R + +--R 4 2 3 2 +--R 2a b cosh(x) + (- 2a b + a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) + 2a b +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression Integer +--E 94 + +--S 95 of 526 +d0618a:= D(m0618a,x) +--R +--R +--R (95) +--R 5 4 2 3 +--R 8b sinh(x) + 40b cosh(x)sinh(x) + (80b cosh(x) - 8b)sinh(x) +--R + +--R 3 2 +--R (80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (40b cosh(x) - 24b cosh(x) )sinh(x) + 8b cosh(x) - 8b cosh(x) +--R * +--R x 8 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (2b + 2a)sinh(x) + (16b + 16a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((56b + 56a)cosh(x) + 8b + 4a)sinh(x) +--R + +--R 3 5 +--R ((112b + 112a)cosh(x) + (48b + 24a)cosh(x) + 16a)sinh(x) +--R + +--R 4 2 +--R ((140b + 140a)cosh(x) + (120b + 60a)cosh(x) + 80a cosh(x) + 12b) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (112b + 112a)cosh(x) + (160b + 80a)cosh(x) + 160a cosh(x) +--R + +--R 48b cosh(x) - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (56b + 56a)cosh(x) + (120b + 60a)cosh(x) + 160a cosh(x) +--R + +--R 2 +--R 72b cosh(x) - 48a cosh(x) + 8b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (16b + 16a)cosh(x) + (48b + 24a)cosh(x) + 80a cosh(x) +--R + +--R 3 2 +--R 48b cosh(x) - 48a cosh(x) + (16b - 8a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 4 +--R (2b + 2a)cosh(x) + (8b + 4a)cosh(x) + 16a cosh(x) + 12b cosh(x) +--R + +--R 3 2 +--R - 16a cosh(x) + (8b - 4a)cosh(x) + 2b - 2a +--R * +--R x 7 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 32b sinh(x) + 160b cosh(x)sinh(x) + (320b cosh(x) - 32b)sinh(x) +--R + +--R 3 2 +--R (320b cosh(x) - 96b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (160b cosh(x) - 96b cosh(x) )sinh(x) + 32b cosh(x) - 32b cosh(x) +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (- 6b - 6a)sinh(x) + (- 48b - 48a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((- 168b - 168a)cosh(x) - 24b - 12a)sinh(x) +--R + +--R 3 5 +--R ((- 336b - 336a)cosh(x) + (- 144b - 72a)cosh(x) + 48a)sinh(x) +--R + +--R 4 2 +--R (- 420b - 420a)cosh(x) + (- 360b - 180a)cosh(x) + 240a cosh(x) +--R + +--R - 36b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 336b - 336a)cosh(x) + (- 480b - 240a)cosh(x) + 480a cosh(x) +--R + +--R - 144b cosh(x) - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (- 168b - 168a)cosh(x) + (- 360b - 180a)cosh(x) + 480a cosh(x) +--R + +--R 2 +--R - 216b cosh(x) - 144a cosh(x) - 24b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (- 48b - 48a)cosh(x) + (- 144b - 72a)cosh(x) + 240a cosh(x) +--R + +--R 3 2 +--R - 144b cosh(x) - 144a cosh(x) + (- 48b + 24a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 +--R (- 6b - 6a)cosh(x) + (- 24b - 12a)cosh(x) + 48a cosh(x) +--R + +--R 4 3 2 +--R - 36b cosh(x) - 48a cosh(x) + (- 24b + 12a)cosh(x) - 6b + 6a +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 48b sinh(x) + 240b cosh(x)sinh(x) + (480b cosh(x) - 48b)sinh(x) +--R + +--R 3 2 +--R (480b cosh(x) - 144b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (240b cosh(x) - 144b cosh(x) )sinh(x) + 48b cosh(x) - 48b cosh(x) +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (6b + 6a)sinh(x) + (48b + 48a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((168b + 168a)cosh(x) + 24b + 12a)sinh(x) +--R + +--R 3 5 +--R ((336b + 336a)cosh(x) + (144b + 72a)cosh(x) + 48a)sinh(x) +--R + +--R 4 2 +--R (420b + 420a)cosh(x) + (360b + 180a)cosh(x) + 240a cosh(x) +--R + +--R 36b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (336b + 336a)cosh(x) + (480b + 240a)cosh(x) + 480a cosh(x) +--R + +--R 144b cosh(x) - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (168b + 168a)cosh(x) + (360b + 180a)cosh(x) + 480a cosh(x) +--R + +--R 2 +--R 216b cosh(x) - 144a cosh(x) + 24b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (48b + 48a)cosh(x) + (144b + 72a)cosh(x) + 240a cosh(x) +--R + +--R 3 2 +--R 144b cosh(x) - 144a cosh(x) + (48b - 24a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 4 +--R (6b + 6a)cosh(x) + (24b + 12a)cosh(x) + 48a cosh(x) + 36b cosh(x) +--R + +--R 3 2 +--R - 48a cosh(x) + (24b - 12a)cosh(x) + 6b - 6a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 32b sinh(x) + 160b cosh(x)sinh(x) + (320b cosh(x) - 32b)sinh(x) +--R + +--R 3 2 +--R (320b cosh(x) - 96b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (160b cosh(x) - 96b cosh(x) )sinh(x) + 32b cosh(x) - 32b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (- 2b - 2a)sinh(x) + (- 16b - 16a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((- 56b - 56a)cosh(x) - 8b - 4a)sinh(x) +--R + +--R 3 5 +--R ((- 112b - 112a)cosh(x) + (- 48b - 24a)cosh(x) + 16a)sinh(x) +--R + +--R 4 2 +--R (- 140b - 140a)cosh(x) + (- 120b - 60a)cosh(x) + 80a cosh(x) +--R + +--R - 12b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 112b - 112a)cosh(x) + (- 160b - 80a)cosh(x) + 160a cosh(x) +--R + +--R - 48b cosh(x) - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (- 56b - 56a)cosh(x) + (- 120b - 60a)cosh(x) + 160a cosh(x) +--R + +--R 2 +--R - 72b cosh(x) - 48a cosh(x) - 8b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (- 16b - 16a)cosh(x) + (- 48b - 24a)cosh(x) + 80a cosh(x) +--R + +--R 3 2 +--R - 48b cosh(x) - 48a cosh(x) + (- 16b + 8a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 +--R (- 2b - 2a)cosh(x) + (- 8b - 4a)cosh(x) + 16a cosh(x) +--R + +--R 4 3 2 +--R - 12b cosh(x) - 16a cosh(x) + (- 8b + 4a)cosh(x) - 2b + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 8b sinh(x) + 40b cosh(x)sinh(x) + (80b cosh(x) - 8b)sinh(x) +--R + +--R 3 2 +--R (80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (40b cosh(x) - 24b cosh(x) )sinh(x) + 8b cosh(x) - 8b cosh(x) +--R / +--R 2 8 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b + 28a b)cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((56b + 56a b)cosh(x) + (24b + 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((70b + 70a b)cosh(x) + (60b + 30a b)cosh(x) + 6b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((56b + 56a b)cosh(x) + (80b + 40a b)cosh(x) + 24b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (28b + 28a b)cosh(x) + (60b + 30a b)cosh(x) + 36b cosh(x) +--R + +--R 2 +--R 4b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (8b + 8a b)cosh(x) + (24b + 12a b)cosh(x) + 24b cosh(x) +--R + +--R 2 +--R (8b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (b + a b)cosh(x) + (4b + 2a b)cosh(x) + 6b cosh(x) +--R + +--R 2 2 2 +--R (4b - 2a b)cosh(x) + b - a b +--R * +--R x 8 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (2a b + 2a )sinh(x) + (16a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((56a b + 56a )cosh(x) + 8a b + 4a )sinh(x) +--R + +--R 2 3 2 5 +--R ((112a b + 112a )cosh(x) + (48a b + 24a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((140a b + 140a )cosh(x) + (120a b + 60a )cosh(x) + 12a b)sinh(x) +--R + +--R 2 5 2 3 +--R (112a b + 112a )cosh(x) + (160a b + 80a )cosh(x) +--R + +--R 48a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 +--R (56a b + 56a )cosh(x) + (120a b + 60a )cosh(x) + 72a b cosh(x) +--R + +--R 2 +--R 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 3 +--R (16a b + 16a )cosh(x) + (48a b + 24a )cosh(x) + 48a b cosh(x) +--R + +--R 2 +--R (16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (2a b + 2a )cosh(x) + (8a b + 4a )cosh(x) + 12a b cosh(x) +--R + +--R 2 2 2 +--R (8a b - 4a )cosh(x) + 2a b - 2a +--R * +--R x 7 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (4b + 4a b)sinh(x) + (32b + 32a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((112b + 112a b)cosh(x) + 16b + 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((224b + 224a b)cosh(x) + (96b + 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((280b + 280a b)cosh(x) + (240b + 120a b)cosh(x) + 24b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((224b + 224a b)cosh(x) + (320b + 160a b)cosh(x) + 96b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (112b + 112a b)cosh(x) + (240b + 120a b)cosh(x) +--R + +--R 2 2 2 +--R 144b cosh(x) + 16b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (32b + 32a b)cosh(x) + (96b + 48a b)cosh(x) + 96b cosh(x) +--R + +--R 2 +--R (32b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (4b + 4a b)cosh(x) + (16b + 8a b)cosh(x) + 24b cosh(x) +--R + +--R 2 2 2 +--R (16b - 8a b)cosh(x) + 4b - 4a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6a b + 6a )sinh(x) + (48a b + 48a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168a b + 168a )cosh(x) + 24a b + 12a )sinh(x) +--R + +--R 2 3 2 5 +--R ((336a b + 336a )cosh(x) + (144a b + 72a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((420a b + 420a )cosh(x) + (360a b + 180a )cosh(x) + 36a b)sinh(x) +--R + +--R 2 5 2 3 +--R (336a b + 336a )cosh(x) + (480a b + 240a )cosh(x) +--R + +--R 144a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168a b + 168a )cosh(x) + (360a b + 180a )cosh(x) +--R + +--R 2 2 +--R 216a b cosh(x) + 24a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (48a b + 48a )cosh(x) + (144a b + 72a )cosh(x) +--R + +--R 3 2 +--R 144a b cosh(x) + (48a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (6a b + 6a )cosh(x) + (24a b + 12a )cosh(x) + 36a b cosh(x) +--R + +--R 2 2 2 +--R (24a b - 12a )cosh(x) + 6a b - 6a +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6b + 6a b)sinh(x) + (48b + 48a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168b + 168a b)cosh(x) + 24b + 12a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((336b + 336a b)cosh(x) + (144b + 72a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((420b + 420a b)cosh(x) + (360b + 180a b)cosh(x) + 36b )sinh(x) +--R + +--R 2 5 2 3 +--R (336b + 336a b)cosh(x) + (480b + 240a b)cosh(x) +--R + +--R 2 +--R 144b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168b + 168a b)cosh(x) + (360b + 180a b)cosh(x) +--R + +--R 2 2 2 +--R 216b cosh(x) + 24b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (48b + 48a b)cosh(x) + (144b + 72a b)cosh(x) + 144b cosh(x) +--R + +--R 2 +--R (48b - 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (6b + 6a b)cosh(x) + (24b + 12a b)cosh(x) + 36b cosh(x) +--R + +--R 2 2 2 +--R (24b - 12a b)cosh(x) + 6b - 6a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6a b + 6a )sinh(x) + (48a b + 48a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168a b + 168a )cosh(x) + 24a b + 12a )sinh(x) +--R + +--R 2 3 2 5 +--R ((336a b + 336a )cosh(x) + (144a b + 72a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((420a b + 420a )cosh(x) + (360a b + 180a )cosh(x) + 36a b)sinh(x) +--R + +--R 2 5 2 3 +--R (336a b + 336a )cosh(x) + (480a b + 240a )cosh(x) +--R + +--R 144a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168a b + 168a )cosh(x) + (360a b + 180a )cosh(x) +--R + +--R 2 2 +--R 216a b cosh(x) + 24a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (48a b + 48a )cosh(x) + (144a b + 72a )cosh(x) +--R + +--R 3 2 +--R 144a b cosh(x) + (48a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (6a b + 6a )cosh(x) + (24a b + 12a )cosh(x) + 36a b cosh(x) +--R + +--R 2 2 2 +--R (24a b - 12a )cosh(x) + 6a b - 6a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (4b + 4a b)sinh(x) + (32b + 32a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((112b + 112a b)cosh(x) + 16b + 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((224b + 224a b)cosh(x) + (96b + 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((280b + 280a b)cosh(x) + (240b + 120a b)cosh(x) + 24b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((224b + 224a b)cosh(x) + (320b + 160a b)cosh(x) + 96b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (112b + 112a b)cosh(x) + (240b + 120a b)cosh(x) +--R + +--R 2 2 2 +--R 144b cosh(x) + 16b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (32b + 32a b)cosh(x) + (96b + 48a b)cosh(x) + 96b cosh(x) +--R + +--R 2 +--R (32b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (4b + 4a b)cosh(x) + (16b + 8a b)cosh(x) + 24b cosh(x) +--R + +--R 2 2 2 +--R (16b - 8a b)cosh(x) + 4b - 4a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (2a b + 2a )sinh(x) + (16a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((56a b + 56a )cosh(x) + 8a b + 4a )sinh(x) +--R + +--R 2 3 2 5 +--R ((112a b + 112a )cosh(x) + (48a b + 24a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((140a b + 140a )cosh(x) + (120a b + 60a )cosh(x) + 12a b)sinh(x) +--R + +--R 2 5 2 3 +--R (112a b + 112a )cosh(x) + (160a b + 80a )cosh(x) +--R + +--R 48a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 +--R (56a b + 56a )cosh(x) + (120a b + 60a )cosh(x) + 72a b cosh(x) +--R + +--R 2 +--R 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 3 +--R (16a b + 16a )cosh(x) + (48a b + 24a )cosh(x) + 48a b cosh(x) +--R + +--R 2 +--R (16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (2a b + 2a )cosh(x) + (8a b + 4a )cosh(x) + 12a b cosh(x) +--R + +--R 2 2 2 +--R (8a b - 4a )cosh(x) + 2a b - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b + 28a b)cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((56b + 56a b)cosh(x) + (24b + 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((70b + 70a b)cosh(x) + (60b + 30a b)cosh(x) + 6b )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R ((56b + 56a b)cosh(x) + (80b + 40a b)cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (28b + 28a b)cosh(x) + (60b + 30a b)cosh(x) + 36b cosh(x) + 4b +--R + +--R - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (8b + 8a b)cosh(x) + (24b + 12a b)cosh(x) + 24b cosh(x) +--R + +--R 2 +--R (8b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (b + a b)cosh(x) + (4b + 2a b)cosh(x) + 6b cosh(x) +--R + +--R 2 2 2 +--R (4b - 2a b)cosh(x) + b - a b +--R Type: Expression Integer +--E 95 + +--S 96 of 526 +m0618b:= a0618.2-r0618 +--R +--R +--R (96) +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) +--R + +--R - 2b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - 4b sinh(x) - 16b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 24b cosh(x) - 8b)sinh(x) +--R + +--R 3 4 2 +--R (- 16b cosh(x) - 16b cosh(x))sinh(x) - 4b cosh(x) - 8b cosh(x) +--R + +--R - 4b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) - 2b +--R * +--R x +--R +---------+ b tanh(-) + a +--R | 2 2 2 +--R \|- b + a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) +--R + +--R - 2b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - 4b sinh(x) - 16b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 24b cosh(x) - 8b)sinh(x) +--R + +--R 3 4 2 +--R (- 16b cosh(x) - 16b cosh(x))sinh(x) - 4b cosh(x) - 8b cosh(x) +--R + +--R - 4b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) - 2b +--R * +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 \|b - a +--R \|b - a atan(-------------------------------) +--R (b + a)sinh(x) + (b + a)cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (2b - a )sinh(x) + (8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 6a )cosh(x) + 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 4a )cosh(x) + (8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - a )cosh(x) + (4b - 2a )cosh(x) + 2b - a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (4b - 2a )sinh(x) + (16b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b - 12a )cosh(x) + 8b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b - 8a )cosh(x) + (16b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b - 2a )cosh(x) + (8b - 4a )cosh(x) + 4b - 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (2b - a )sinh(x) + (8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 6a )cosh(x) + 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 4a )cosh(x) + (8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - a )cosh(x) + (4b - 2a )cosh(x) + 2b - a +--R * +--R x +--R atan(tanh(-)) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 4b + 2a )sinh(x) + (- 16b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 24b + 12a )cosh(x) - 8b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 16b + 8a )cosh(x) + (- 16b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 4b + 2a )cosh(x) + (- 8b + 4a )cosh(x) - 4b + 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R (- 2a b + a )sinh(x) + (- 6a b + 3a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 +--R ((- 6a b + 3a )cosh(x) - 2a b - a )sinh(x) + (- 2a b + a )cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 2 2 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 2 3 2 2 4 2 2 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2a b sinh(x) + (8a b cosh(x) - 4a b + 2a )sinh(x) +--R + +--R 2 2 2 +--R (12a b cosh(x) + (- 12a b + 6a )cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 +--R 8a b cosh(x) + (- 12a b + 6a )cosh(x) + 8a b cosh(x) - 4a b +--R + +--R 2 +--R - 2a +--R * +--R sinh(x) +--R + +--R 4 2 3 2 +--R 2a b cosh(x) + (- 4a b + 2a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R (- 4a b - 2a )cosh(x) + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 2 2 2 2 +--R - a sinh(x) - 4a cosh(x)sinh(x) + (- 6a cosh(x) - 2a )sinh(x) +--R + +--R 2 3 2 2 4 2 2 2 +--R (- 4a cosh(x) - 4a cosh(x))sinh(x) - a cosh(x) - 2a cosh(x) - a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2a b sinh(x) + (8a b cosh(x) - 2a b + a )sinh(x) +--R + +--R 2 2 2 +--R (12a b cosh(x) + (- 6a b + 3a )cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 2 +--R (8a b cosh(x) + (- 6a b + 3a )cosh(x) + 8a b cosh(x) - 2a b - a ) +--R * +--R sinh(x) +--R + +--R 4 2 3 2 +--R 2a b cosh(x) + (- 2a b + a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) + 2a b +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression Integer +--E 96 + +--S 97 of 526 +d0618b:= D(m0618b,x) +--R +--R +--R (97) +--R 5 4 2 3 +--R 8b sinh(x) + 40b cosh(x)sinh(x) + (80b cosh(x) - 8b)sinh(x) +--R + +--R 3 2 +--R (80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (40b cosh(x) - 24b cosh(x) )sinh(x) + 8b cosh(x) - 8b cosh(x) +--R * +--R x 8 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (2b + 2a)sinh(x) + (16b + 16a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((56b + 56a)cosh(x) + 8b + 4a)sinh(x) +--R + +--R 3 5 +--R ((112b + 112a)cosh(x) + (48b + 24a)cosh(x) + 16a)sinh(x) +--R + +--R 4 2 +--R ((140b + 140a)cosh(x) + (120b + 60a)cosh(x) + 80a cosh(x) + 12b) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (112b + 112a)cosh(x) + (160b + 80a)cosh(x) + 160a cosh(x) +--R + +--R 48b cosh(x) - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (56b + 56a)cosh(x) + (120b + 60a)cosh(x) + 160a cosh(x) +--R + +--R 2 +--R 72b cosh(x) - 48a cosh(x) + 8b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (16b + 16a)cosh(x) + (48b + 24a)cosh(x) + 80a cosh(x) +--R + +--R 3 2 +--R 48b cosh(x) - 48a cosh(x) + (16b - 8a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 4 +--R (2b + 2a)cosh(x) + (8b + 4a)cosh(x) + 16a cosh(x) + 12b cosh(x) +--R + +--R 3 2 +--R - 16a cosh(x) + (8b - 4a)cosh(x) + 2b - 2a +--R * +--R x 7 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 32b sinh(x) + 160b cosh(x)sinh(x) + (320b cosh(x) - 32b)sinh(x) +--R + +--R 3 2 +--R (320b cosh(x) - 96b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (160b cosh(x) - 96b cosh(x) )sinh(x) + 32b cosh(x) - 32b cosh(x) +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (- 6b - 6a)sinh(x) + (- 48b - 48a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((- 168b - 168a)cosh(x) - 24b - 12a)sinh(x) +--R + +--R 3 5 +--R ((- 336b - 336a)cosh(x) + (- 144b - 72a)cosh(x) + 48a)sinh(x) +--R + +--R 4 2 +--R (- 420b - 420a)cosh(x) + (- 360b - 180a)cosh(x) + 240a cosh(x) +--R + +--R - 36b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 336b - 336a)cosh(x) + (- 480b - 240a)cosh(x) + 480a cosh(x) +--R + +--R - 144b cosh(x) - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (- 168b - 168a)cosh(x) + (- 360b - 180a)cosh(x) + 480a cosh(x) +--R + +--R 2 +--R - 216b cosh(x) - 144a cosh(x) - 24b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (- 48b - 48a)cosh(x) + (- 144b - 72a)cosh(x) + 240a cosh(x) +--R + +--R 3 2 +--R - 144b cosh(x) - 144a cosh(x) + (- 48b + 24a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 +--R (- 6b - 6a)cosh(x) + (- 24b - 12a)cosh(x) + 48a cosh(x) +--R + +--R 4 3 2 +--R - 36b cosh(x) - 48a cosh(x) + (- 24b + 12a)cosh(x) - 6b + 6a +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 48b sinh(x) + 240b cosh(x)sinh(x) + (480b cosh(x) - 48b)sinh(x) +--R + +--R 3 2 +--R (480b cosh(x) - 144b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (240b cosh(x) - 144b cosh(x) )sinh(x) + 48b cosh(x) - 48b cosh(x) +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (6b + 6a)sinh(x) + (48b + 48a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((168b + 168a)cosh(x) + 24b + 12a)sinh(x) +--R + +--R 3 5 +--R ((336b + 336a)cosh(x) + (144b + 72a)cosh(x) + 48a)sinh(x) +--R + +--R 4 2 +--R (420b + 420a)cosh(x) + (360b + 180a)cosh(x) + 240a cosh(x) +--R + +--R 36b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (336b + 336a)cosh(x) + (480b + 240a)cosh(x) + 480a cosh(x) +--R + +--R 144b cosh(x) - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (168b + 168a)cosh(x) + (360b + 180a)cosh(x) + 480a cosh(x) +--R + +--R 2 +--R 216b cosh(x) - 144a cosh(x) + 24b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (48b + 48a)cosh(x) + (144b + 72a)cosh(x) + 240a cosh(x) +--R + +--R 3 2 +--R 144b cosh(x) - 144a cosh(x) + (48b - 24a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 4 +--R (6b + 6a)cosh(x) + (24b + 12a)cosh(x) + 48a cosh(x) + 36b cosh(x) +--R + +--R 3 2 +--R - 48a cosh(x) + (24b - 12a)cosh(x) + 6b - 6a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 32b sinh(x) + 160b cosh(x)sinh(x) + (320b cosh(x) - 32b)sinh(x) +--R + +--R 3 2 +--R (320b cosh(x) - 96b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (160b cosh(x) - 96b cosh(x) )sinh(x) + 32b cosh(x) - 32b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (- 2b - 2a)sinh(x) + (- 16b - 16a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((- 56b - 56a)cosh(x) - 8b - 4a)sinh(x) +--R + +--R 3 5 +--R ((- 112b - 112a)cosh(x) + (- 48b - 24a)cosh(x) + 16a)sinh(x) +--R + +--R 4 2 +--R (- 140b - 140a)cosh(x) + (- 120b - 60a)cosh(x) + 80a cosh(x) +--R + +--R - 12b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 112b - 112a)cosh(x) + (- 160b - 80a)cosh(x) + 160a cosh(x) +--R + +--R - 48b cosh(x) - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (- 56b - 56a)cosh(x) + (- 120b - 60a)cosh(x) + 160a cosh(x) +--R + +--R 2 +--R - 72b cosh(x) - 48a cosh(x) - 8b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (- 16b - 16a)cosh(x) + (- 48b - 24a)cosh(x) + 80a cosh(x) +--R + +--R 3 2 +--R - 48b cosh(x) - 48a cosh(x) + (- 16b + 8a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 +--R (- 2b - 2a)cosh(x) + (- 8b - 4a)cosh(x) + 16a cosh(x) +--R + +--R 4 3 2 +--R - 12b cosh(x) - 16a cosh(x) + (- 8b + 4a)cosh(x) - 2b + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 8b sinh(x) + 40b cosh(x)sinh(x) + (80b cosh(x) - 8b)sinh(x) +--R + +--R 3 2 +--R (80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (40b cosh(x) - 24b cosh(x) )sinh(x) + 8b cosh(x) - 8b cosh(x) +--R / +--R 2 8 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b + 28a b)cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((56b + 56a b)cosh(x) + (24b + 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((70b + 70a b)cosh(x) + (60b + 30a b)cosh(x) + 6b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((56b + 56a b)cosh(x) + (80b + 40a b)cosh(x) + 24b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (28b + 28a b)cosh(x) + (60b + 30a b)cosh(x) + 36b cosh(x) +--R + +--R 2 +--R 4b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (8b + 8a b)cosh(x) + (24b + 12a b)cosh(x) + 24b cosh(x) +--R + +--R 2 +--R (8b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (b + a b)cosh(x) + (4b + 2a b)cosh(x) + 6b cosh(x) +--R + +--R 2 2 2 +--R (4b - 2a b)cosh(x) + b - a b +--R * +--R x 8 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (2a b + 2a )sinh(x) + (16a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((56a b + 56a )cosh(x) + 8a b + 4a )sinh(x) +--R + +--R 2 3 2 5 +--R ((112a b + 112a )cosh(x) + (48a b + 24a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((140a b + 140a )cosh(x) + (120a b + 60a )cosh(x) + 12a b)sinh(x) +--R + +--R 2 5 2 3 +--R (112a b + 112a )cosh(x) + (160a b + 80a )cosh(x) +--R + +--R 48a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 +--R (56a b + 56a )cosh(x) + (120a b + 60a )cosh(x) + 72a b cosh(x) +--R + +--R 2 +--R 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 3 +--R (16a b + 16a )cosh(x) + (48a b + 24a )cosh(x) + 48a b cosh(x) +--R + +--R 2 +--R (16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (2a b + 2a )cosh(x) + (8a b + 4a )cosh(x) + 12a b cosh(x) +--R + +--R 2 2 2 +--R (8a b - 4a )cosh(x) + 2a b - 2a +--R * +--R x 7 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (4b + 4a b)sinh(x) + (32b + 32a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((112b + 112a b)cosh(x) + 16b + 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((224b + 224a b)cosh(x) + (96b + 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((280b + 280a b)cosh(x) + (240b + 120a b)cosh(x) + 24b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((224b + 224a b)cosh(x) + (320b + 160a b)cosh(x) + 96b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (112b + 112a b)cosh(x) + (240b + 120a b)cosh(x) +--R + +--R 2 2 2 +--R 144b cosh(x) + 16b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (32b + 32a b)cosh(x) + (96b + 48a b)cosh(x) + 96b cosh(x) +--R + +--R 2 +--R (32b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (4b + 4a b)cosh(x) + (16b + 8a b)cosh(x) + 24b cosh(x) +--R + +--R 2 2 2 +--R (16b - 8a b)cosh(x) + 4b - 4a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6a b + 6a )sinh(x) + (48a b + 48a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168a b + 168a )cosh(x) + 24a b + 12a )sinh(x) +--R + +--R 2 3 2 5 +--R ((336a b + 336a )cosh(x) + (144a b + 72a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((420a b + 420a )cosh(x) + (360a b + 180a )cosh(x) + 36a b)sinh(x) +--R + +--R 2 5 2 3 +--R (336a b + 336a )cosh(x) + (480a b + 240a )cosh(x) +--R + +--R 144a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168a b + 168a )cosh(x) + (360a b + 180a )cosh(x) +--R + +--R 2 2 +--R 216a b cosh(x) + 24a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (48a b + 48a )cosh(x) + (144a b + 72a )cosh(x) +--R + +--R 3 2 +--R 144a b cosh(x) + (48a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (6a b + 6a )cosh(x) + (24a b + 12a )cosh(x) + 36a b cosh(x) +--R + +--R 2 2 2 +--R (24a b - 12a )cosh(x) + 6a b - 6a +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6b + 6a b)sinh(x) + (48b + 48a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168b + 168a b)cosh(x) + 24b + 12a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((336b + 336a b)cosh(x) + (144b + 72a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((420b + 420a b)cosh(x) + (360b + 180a b)cosh(x) + 36b )sinh(x) +--R + +--R 2 5 2 3 +--R (336b + 336a b)cosh(x) + (480b + 240a b)cosh(x) +--R + +--R 2 +--R 144b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168b + 168a b)cosh(x) + (360b + 180a b)cosh(x) +--R + +--R 2 2 2 +--R 216b cosh(x) + 24b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (48b + 48a b)cosh(x) + (144b + 72a b)cosh(x) + 144b cosh(x) +--R + +--R 2 +--R (48b - 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (6b + 6a b)cosh(x) + (24b + 12a b)cosh(x) + 36b cosh(x) +--R + +--R 2 2 2 +--R (24b - 12a b)cosh(x) + 6b - 6a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6a b + 6a )sinh(x) + (48a b + 48a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168a b + 168a )cosh(x) + 24a b + 12a )sinh(x) +--R + +--R 2 3 2 5 +--R ((336a b + 336a )cosh(x) + (144a b + 72a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((420a b + 420a )cosh(x) + (360a b + 180a )cosh(x) + 36a b)sinh(x) +--R + +--R 2 5 2 3 +--R (336a b + 336a )cosh(x) + (480a b + 240a )cosh(x) +--R + +--R 144a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168a b + 168a )cosh(x) + (360a b + 180a )cosh(x) +--R + +--R 2 2 +--R 216a b cosh(x) + 24a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (48a b + 48a )cosh(x) + (144a b + 72a )cosh(x) +--R + +--R 3 2 +--R 144a b cosh(x) + (48a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (6a b + 6a )cosh(x) + (24a b + 12a )cosh(x) + 36a b cosh(x) +--R + +--R 2 2 2 +--R (24a b - 12a )cosh(x) + 6a b - 6a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (4b + 4a b)sinh(x) + (32b + 32a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((112b + 112a b)cosh(x) + 16b + 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((224b + 224a b)cosh(x) + (96b + 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((280b + 280a b)cosh(x) + (240b + 120a b)cosh(x) + 24b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((224b + 224a b)cosh(x) + (320b + 160a b)cosh(x) + 96b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (112b + 112a b)cosh(x) + (240b + 120a b)cosh(x) +--R + +--R 2 2 2 +--R 144b cosh(x) + 16b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (32b + 32a b)cosh(x) + (96b + 48a b)cosh(x) + 96b cosh(x) +--R + +--R 2 +--R (32b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (4b + 4a b)cosh(x) + (16b + 8a b)cosh(x) + 24b cosh(x) +--R + +--R 2 2 2 +--R (16b - 8a b)cosh(x) + 4b - 4a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (2a b + 2a )sinh(x) + (16a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((56a b + 56a )cosh(x) + 8a b + 4a )sinh(x) +--R + +--R 2 3 2 5 +--R ((112a b + 112a )cosh(x) + (48a b + 24a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((140a b + 140a )cosh(x) + (120a b + 60a )cosh(x) + 12a b)sinh(x) +--R + +--R 2 5 2 3 +--R (112a b + 112a )cosh(x) + (160a b + 80a )cosh(x) +--R + +--R 48a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 +--R (56a b + 56a )cosh(x) + (120a b + 60a )cosh(x) + 72a b cosh(x) +--R + +--R 2 +--R 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 3 +--R (16a b + 16a )cosh(x) + (48a b + 24a )cosh(x) + 48a b cosh(x) +--R + +--R 2 +--R (16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (2a b + 2a )cosh(x) + (8a b + 4a )cosh(x) + 12a b cosh(x) +--R + +--R 2 2 2 +--R (8a b - 4a )cosh(x) + 2a b - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b + 28a b)cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((56b + 56a b)cosh(x) + (24b + 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((70b + 70a b)cosh(x) + (60b + 30a b)cosh(x) + 6b )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R ((56b + 56a b)cosh(x) + (80b + 40a b)cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (28b + 28a b)cosh(x) + (60b + 30a b)cosh(x) + 36b cosh(x) + 4b +--R + +--R - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (8b + 8a b)cosh(x) + (24b + 12a b)cosh(x) + 24b cosh(x) +--R + +--R 2 +--R (8b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (b + a b)cosh(x) + (4b + 2a b)cosh(x) + 6b cosh(x) +--R + +--R 2 2 2 +--R (4b - 2a b)cosh(x) + b - a b +--R Type: Expression Integer +--E 97 + +--S 98 of 526 +t0619:= sech(x)^4/(a+b*coth(x)) +--R +--R +--R 4 +--R sech(x) +--R (98) ------------- +--R b coth(x) + a +--R Type: Expression Integer +--E 98 + +--S 99 of 526 +r0619:= -b*(a^2-b^2)*log(b+a*tanh(x))/a^4+(a^2-b^2)*tanh(x)/a^3+_ + 1/2*b*tanh(x)^2/a^2-1/3*tanh(x)^3/a +--R +--R +--R (99) +--R 3 2 3 3 2 2 +--R (6b - 6a b)log(a tanh(x) + b) - 2a tanh(x) + 3a b tanh(x) +--R + +--R 2 3 +--R (- 6a b + 6a )tanh(x) +--R / +--R 4 +--R 6a +--R Type: Expression Integer +--E 99 + +--S 100 of 526 +a0619:= integrate(t0619,x) +--R +--R +--R (100) +--R 3 2 6 3 2 5 +--R (- 3b + 3a b)sinh(x) + (- 18b + 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 45b + 45a b)cosh(x) - 9b + 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 60b + 60a b)cosh(x) + (- 36b + 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((- 45b + 45a b)cosh(x) + (- 54b + 54a b)cosh(x) - 9b + 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 18b + 18a b)cosh(x) + (- 36b + 36a b)cosh(x) +--R + +--R 3 2 +--R (- 18b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 3b + 3a b)cosh(x) + (- 9b + 9a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 9b + 9a b)cosh(x) - 3b + 3a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 6 3 2 5 +--R (3b - 3a b)sinh(x) + (18b - 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((45b - 45a b)cosh(x) + 9b - 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((60b - 60a b)cosh(x) + (36b - 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((45b - 45a b)cosh(x) + (54b - 54a b)cosh(x) + 9b - 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (18b - 18a b)cosh(x) + (36b - 36a b)cosh(x) +--R + +--R 3 2 +--R (18b - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R (3b - 3a b)cosh(x) + (9b - 9a b)cosh(x) + (9b - 9a b)cosh(x) +--R + +--R 3 2 +--R 3b - 3a b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (6a b - 6a b)sinh(x) + (24a b - 24a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((36a b - 36a b)cosh(x) + 12a b - 6a b - 12a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((24a b - 24a b)cosh(x) + (24a b - 12a b - 24a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 3 +--R (6a b - 6a b)cosh(x) + (12a b - 6a b - 12a )cosh(x) + 6a b - 4a +--R / +--R 4 6 4 5 4 2 4 4 +--R 3a sinh(x) + 18a cosh(x)sinh(x) + (45a cosh(x) + 9a )sinh(x) +--R + +--R 4 3 4 3 +--R (60a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45a cosh(x) + 54a cosh(x) + 9a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18a cosh(x) + 36a cosh(x) + 18a cosh(x))sinh(x) + 3a cosh(x) +--R + +--R 4 4 4 2 4 +--R 9a cosh(x) + 9a cosh(x) + 3a +--R Type: Union(Expression Integer,...) +--E 100 + +--S 101 of 526 +m0619:= a0619-r0619 +--R +--R +--R (101) +--R 3 2 6 3 2 5 +--R (- 6b + 6a b)sinh(x) + (- 36b + 36a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b + 90a b)cosh(x) - 18b + 18a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b + 120a b)cosh(x) + (- 72b + 72a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b + 90a b)cosh(x) + (- 108b + 108a b)cosh(x) - 18b +--R + +--R 2 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b + 36a b)cosh(x) + (- 72b + 72a b)cosh(x) +--R + +--R 3 2 +--R (- 36b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b + 6a b)cosh(x) + (- 18b + 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b + 18a b)cosh(x) - 6b + 6a b +--R * +--R log(a tanh(x) + b) +--R + +--R 3 2 6 3 2 5 +--R (- 6b + 6a b)sinh(x) + (- 36b + 36a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b + 90a b)cosh(x) - 18b + 18a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b + 120a b)cosh(x) + (- 72b + 72a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b + 90a b)cosh(x) + (- 108b + 108a b)cosh(x) - 18b +--R + +--R 2 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b + 36a b)cosh(x) + (- 72b + 72a b)cosh(x) +--R + +--R 3 2 +--R (- 36b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b + 6a b)cosh(x) + (- 18b + 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b + 18a b)cosh(x) - 6b + 6a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 6 3 2 5 +--R (6b - 6a b)sinh(x) + (36b - 36a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((90b - 90a b)cosh(x) + 18b - 18a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((120b - 120a b)cosh(x) + (72b - 72a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((90b - 90a b)cosh(x) + (108b - 108a b)cosh(x) + 18b - 18a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (36b - 36a b)cosh(x) + (72b - 72a b)cosh(x) +--R + +--R 3 2 +--R (36b - 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (6b - 6a b)cosh(x) + (18b - 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (18b - 18a b)cosh(x) + 6b - 6a b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 6 3 5 3 2 3 4 +--R 2a sinh(x) + 12a cosh(x)sinh(x) + (30a cosh(x) + 6a )sinh(x) +--R + +--R 3 3 3 3 +--R (40a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (30a cosh(x) + 36a cosh(x) + 6a )sinh(x) +--R + +--R 3 5 3 3 3 3 6 +--R (12a cosh(x) + 24a cosh(x) + 12a cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 3 4 3 2 3 +--R 6a cosh(x) + 6a cosh(x) + 2a +--R * +--R 3 +--R tanh(x) +--R + +--R 2 6 2 5 +--R - 3a b sinh(x) - 18a b cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R (- 45a b cosh(x) - 9a b)sinh(x) +--R + +--R 2 3 2 3 +--R (- 60a b cosh(x) - 36a b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 45a b cosh(x) - 54a b cosh(x) - 9a b)sinh(x) +--R + +--R 2 5 2 3 2 +--R (- 18a b cosh(x) - 36a b cosh(x) - 18a b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R - 3a b cosh(x) - 9a b cosh(x) - 9a b cosh(x) - 3a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 3 6 2 3 5 +--R (6a b - 6a )sinh(x) + (36a b - 36a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((90a b - 90a )cosh(x) + 18a b - 18a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((120a b - 120a )cosh(x) + (72a b - 72a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (90a b - 90a )cosh(x) + (108a b - 108a )cosh(x) + 18a b +--R + +--R 3 +--R - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (36a b - 36a )cosh(x) + (72a b - 72a )cosh(x) +--R + +--R 2 3 +--R (36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (6a b - 6a )cosh(x) + (18a b - 18a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (18a b - 18a )cosh(x) + 6a b - 6a +--R * +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (12a b - 12a b)sinh(x) + (48a b - 48a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((72a b - 72a b)cosh(x) + 24a b - 12a b - 24a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((48a b - 48a b)cosh(x) + (48a b - 24a b - 48a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 3 +--R (12a b - 12a b)cosh(x) + (24a b - 12a b - 24a )cosh(x) + 12a b - 8a +--R / +--R 4 6 4 5 4 2 4 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) + 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (120a cosh(x) + 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90a cosh(x) + 108a cosh(x) + 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36a cosh(x) + 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R 18a cosh(x) + 18a cosh(x) + 6a +--R Type: Expression Integer +--E 101 + +--S 102 of 526 +d0619:= D(m0619,x) +--R +--R +--R (102) +--R 4 9 3 4 2 8 +--R - a cosh(x)sinh(x) + (- a b - 8a )cosh(x) sinh(x) +--R + +--R 3 4 3 4 7 +--R ((- 8a b - 28a )cosh(x) - 4a cosh(x))sinh(x) +--R + +--R 3 4 4 3 4 2 6 +--R ((- 28a b - 56a )cosh(x) + (- 4a b - 24a )cosh(x) )sinh(x) +--R + +--R 3 4 5 3 4 3 4 +--R ((- 56a b - 70a )cosh(x) + (- 24a b - 60a )cosh(x) - 6a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 6 3 4 4 +--R (- 70a b - 56a )cosh(x) + (- 60a b - 80a )cosh(x) +--R + +--R 3 4 2 +--R (- 6a b - 24a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 7 3 4 5 +--R (- 56a b - 28a )cosh(x) + (- 80a b - 60a )cosh(x) +--R + +--R 3 4 3 4 +--R (- 24a b - 36a )cosh(x) - 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 8 3 4 6 +--R (- 28a b - 8a )cosh(x) + (- 60a b - 24a )cosh(x) +--R + +--R 3 4 4 3 4 2 +--R (- 36a b - 24a )cosh(x) + (- 4a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 9 3 4 7 +--R (- 8a b - a )cosh(x) + (- 24a b - 4a )cosh(x) +--R + +--R 3 4 5 3 4 3 4 +--R (- 24a b - 6a )cosh(x) + (- 8a b - 4a )cosh(x) - a cosh(x) +--R * +--R sinh(x) +--R + +--R 3 10 3 8 3 6 3 4 +--R - a b cosh(x) - 4a b cosh(x) - 6a b cosh(x) - 4a b cosh(x) +--R + +--R 3 2 +--R - a b cosh(x) +--R * +--R 5 +--R tanh(x) +--R + +--R 4 9 3 4 2 8 +--R 2a cosh(x)sinh(x) + (2a b + 16a )cosh(x) sinh(x) +--R + +--R 3 4 3 4 7 +--R ((16a b + 56a )cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 3 4 4 3 4 2 6 +--R ((56a b + 112a )cosh(x) + (8a b + 48a )cosh(x) )sinh(x) +--R + +--R 3 4 5 3 4 3 4 +--R ((112a b + 140a )cosh(x) + (48a b + 120a )cosh(x) + 12a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 6 3 4 4 +--R (140a b + 112a )cosh(x) + (120a b + 160a )cosh(x) +--R + +--R 3 4 2 +--R (12a b + 48a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 7 3 4 5 +--R (112a b + 56a )cosh(x) + (160a b + 120a )cosh(x) +--R + +--R 3 4 3 4 +--R (48a b + 72a )cosh(x) + 8a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 8 3 4 6 +--R (56a b + 16a )cosh(x) + (120a b + 48a )cosh(x) +--R + +--R 3 4 4 3 4 2 +--R (72a b + 48a )cosh(x) + (8a b + 16a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 9 3 4 7 +--R (16a b + 2a )cosh(x) + (48a b + 8a )cosh(x) +--R + +--R 3 4 5 3 4 3 4 +--R (48a b + 12a )cosh(x) + (16a b + 8a )cosh(x) + 2a cosh(x) +--R * +--R sinh(x) +--R + +--R 3 10 3 8 3 6 3 4 +--R 2a b cosh(x) + 8a b cosh(x) + 12a b cosh(x) + 8a b cosh(x) +--R + +--R 3 2 +--R 2a b cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 3 3 10 3 3 4 9 +--R (- a b + a b)sinh(x) + (- 8a b + 8a b - a )cosh(x)sinh(x) +--R + +--R 3 3 4 2 3 3 8 +--R ((- 27a b + 26a b - 8a )cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 3 3 4 3 +--R (- 48a b + 40a b - 28a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 24a b - 4a b + 28a b - 4a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 3 4 4 +--R (- 42a b + 14a b - 56a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (- 60a b - 20a b + 76a b - 24a )cosh(x) - 6a b + 6a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 5 +--R (- 56a b - 70a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 80a b - 36a b + 92a b - 60a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 24a b - 8a b + 24a b + 10a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 3 4 6 +--R (42a b - 112a b - 56a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 60a b - 20a b + 20a b - 80a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (- 38a b - 32a b + 40a b + 40a )cosh(x) - 4a b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 4 7 +--R (48a b - 104a b - 28a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 24a b + 20a b - 76a b - 60a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 32a b - 48a b + 40a b + 60a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 8a b - 4a b + 4a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 8 +--R (27a b - 55a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 6 +--R (- 4a b + 36a b - 92a b - 24a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 18a b - 32a b + 30a b + 40a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (- 4a b - 12a b - 12a b - 8a )cosh(x) - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 9 2 2 3 4 7 +--R (8a b - 16a b - a )cosh(x) + (20a b - 44a b - 4a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 8a b - 8a b + 16a b + 10a )cosh(x) +--R + +--R 2 2 3 4 3 4 +--R (- 12a b - 20a b - 4a )cosh(x) - a cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 10 2 2 3 8 +--R (a b - 2a b)cosh(x) + (4a b - 8a b)cosh(x) +--R + +--R 3 3 6 2 2 3 4 +--R (- 2a b + 4a b)cosh(x) + (- 4a b - 8a b)cosh(x) +--R + +--R 3 3 2 +--R (a b - 2a b)cosh(x) +--R * +--R tanh(x) +--R + +--R 4 2 2 10 4 2 2 9 +--R (- b + a b )sinh(x) + (- 8b + 8a b )cosh(x)sinh(x) +--R + +--R 4 2 2 2 4 2 2 8 +--R ((- 27b + 27a b )cosh(x) - 4b + 4a b )sinh(x) +--R + +--R 4 2 2 3 4 3 2 2 7 +--R ((- 48b + 48a b )cosh(x) + (- 24b - 4a b + 28a b )cosh(x))sinh(x) +--R + +--R 4 2 2 4 4 3 2 2 2 4 +--R (- 42b + 42a b )cosh(x) + (- 60b - 20a b + 80a b )cosh(x) - 6b +--R + +--R 2 2 +--R 6a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 +--R (- 80b - 36a b + 116a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 24b - 8a b + 24a b + 16a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 2 6 4 3 2 2 4 +--R (42b - 42a b )cosh(x) + (- 60b - 20a b + 80a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (- 38b - 32a b + 46a b + 64a b)cosh(x) - 4b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 7 4 3 2 2 5 +--R (48b - 48a b )cosh(x) + (- 24b + 20a b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 32b - 48a b + 64a b + 96a b)cosh(x) +--R + +--R 4 3 2 2 +--R (- 8b - 4a b + 4a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 8 4 3 2 2 6 +--R (27b - 27a b )cosh(x) + (- 4b + 36a b - 32a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 18b - 32a b + 66a b + 64a b)cosh(x) +--R + +--R 4 3 2 2 2 4 2 2 +--R (- 4b - 12a b - 8a b )cosh(x) - b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 9 3 2 2 7 +--R (8b - 8a b )cosh(x) + (20a b - 20a b )cosh(x) +--R + +--R 4 3 2 2 3 5 3 2 2 3 +--R (- 8b - 8a b + 40a b + 16a b)cosh(x) + (- 12a b - 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 10 3 2 2 8 4 2 2 6 +--R (b - a b )cosh(x) + (4a b - 4a b )cosh(x) + (- 2b + 10a b )cosh(x) +--R + +--R 3 2 2 4 4 2 2 2 +--R (- 4a b - 4a b )cosh(x) + (b - a b )cosh(x) +--R / +--R 5 9 4 5 2 8 +--R a cosh(x)sinh(x) + (a b + 8a )cosh(x) sinh(x) +--R + +--R 4 5 3 5 7 +--R ((8a b + 28a )cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 5 4 4 5 2 6 +--R ((28a b + 56a )cosh(x) + (4a b + 24a )cosh(x) )sinh(x) +--R + +--R 4 5 5 4 5 3 5 +--R ((56a b + 70a )cosh(x) + (24a b + 60a )cosh(x) + 6a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 5 6 4 5 4 +--R (70a b + 56a )cosh(x) + (60a b + 80a )cosh(x) +--R + +--R 4 5 2 +--R (6a b + 24a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 7 4 5 5 +--R (56a b + 28a )cosh(x) + (80a b + 60a )cosh(x) +--R + +--R 4 5 3 5 +--R (24a b + 36a )cosh(x) + 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 8 4 5 6 +--R (28a b + 8a )cosh(x) + (60a b + 24a )cosh(x) +--R + +--R 4 5 4 4 5 2 +--R (36a b + 24a )cosh(x) + (4a b + 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 9 4 5 7 +--R (8a b + a )cosh(x) + (24a b + 4a )cosh(x) +--R + +--R 4 5 5 4 5 3 5 +--R (24a b + 6a )cosh(x) + (8a b + 4a )cosh(x) + a cosh(x) +--R * +--R sinh(x) +--R + +--R 4 10 4 8 4 6 4 4 +--R a b cosh(x) + 4a b cosh(x) + 6a b cosh(x) + 4a b cosh(x) +--R + +--R 4 2 +--R a b cosh(x) +--R * +--R tanh(x) +--R + +--R 4 9 3 2 4 2 8 +--R a b cosh(x)sinh(x) + (a b + 8a b)cosh(x) sinh(x) +--R + +--R 3 2 4 3 4 7 +--R ((8a b + 28a b)cosh(x) + 4a b cosh(x))sinh(x) +--R + +--R 3 2 4 4 3 2 4 2 6 +--R ((28a b + 56a b)cosh(x) + (4a b + 24a b)cosh(x) )sinh(x) +--R + +--R 3 2 4 5 3 2 4 3 4 +--R ((56a b + 70a b)cosh(x) + (24a b + 60a b)cosh(x) + 6a b cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 6 3 2 4 4 +--R (70a b + 56a b)cosh(x) + (60a b + 80a b)cosh(x) +--R + +--R 3 2 4 2 +--R (6a b + 24a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 7 3 2 4 5 +--R (56a b + 28a b)cosh(x) + (80a b + 60a b)cosh(x) +--R + +--R 3 2 4 3 4 +--R (24a b + 36a b)cosh(x) + 4a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 8 3 2 4 6 +--R (28a b + 8a b)cosh(x) + (60a b + 24a b)cosh(x) +--R + +--R 3 2 4 4 3 2 4 2 +--R (36a b + 24a b)cosh(x) + (4a b + 8a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 9 3 2 4 7 +--R (8a b + a b)cosh(x) + (24a b + 4a b)cosh(x) +--R + +--R 3 2 4 5 3 2 4 3 4 +--R (24a b + 6a b)cosh(x) + (8a b + 4a b)cosh(x) + a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 10 3 2 8 3 2 6 3 2 4 +--R a b cosh(x) + 4a b cosh(x) + 6a b cosh(x) + 4a b cosh(x) +--R + +--R 3 2 2 +--R a b cosh(x) +--R Type: Expression Integer +--E 102 + +--S 103 of 526 +t0620:= sech(x)/(1+coth(x)) +--R +--R +--R sech(x) +--R (103) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 103 + +--S 104 of 526 +r0620:= atan(sinh(x))+cosh(x)-sinh(x) +--R +--R +--R (104) atan(sinh(x)) - sinh(x) + cosh(x) +--R Type: Expression Integer +--E 104 + +--S 105 of 526 +a0620:= integrate(t0620,x) +--R +--R +--R (2sinh(x) + 2cosh(x))atan(sinh(x) + cosh(x)) + 1 +--R (105) ------------------------------------------------ +--R sinh(x) + cosh(x) +--R Type: Union(Expression Integer,...) +--E 105 + +--S 106 of 526 +m0620:= a0620-r0620 +--R +--R +--R (106) +--R (2sinh(x) + 2cosh(x))atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R (- sinh(x) - cosh(x))atan(sinh(x)) + sinh(x) - cosh(x) + 1 +--R / +--R sinh(x) + cosh(x) +--R Type: Expression Integer +--E 106 + +--S 107 of 526 +d0620:= D(m0620,x) +--R +--R +--R (107) +--R 6 5 4 3 3 +--R - sinh(x) - 2cosh(x)sinh(x) - sinh(x) + (2cosh(x) - cosh(x))sinh(x) +--R + +--R 4 2 2 3 +--R (cosh(x) - cosh(x) - 1)sinh(x) + (- cosh(x) + cosh(x))sinh(x) +--R + +--R 2 +--R cosh(x) - 1 +--R / +--R 5 4 2 3 +--R sinh(x) + 3cosh(x)sinh(x) + (3cosh(x) + 2)sinh(x) +--R + +--R 3 2 2 3 +--R (cosh(x) + 4cosh(x))sinh(x) + (3cosh(x) + 1)sinh(x) + cosh(x) + cosh(x) +--R Type: Expression Integer +--E 107 + +--S 108 of 526 +t0621:= sech(x)^2/(1+coth(x)) +--R +--R +--R 2 +--R sech(x) +--R (108) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 108 + +--S 109 of 526 +r0621:= -log(1+tanh(x))+tanh(x) +--R +--R +--R (109) - log(tanh(x) + 1) + tanh(x) +--R Type: Expression Integer +--E 109 + +--S 110 of 526 +a0621:= integrate(t0621,x) +--R +--R +--R (110) +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 2x sinh(x) - 4x cosh(x)sinh(x) - 2x cosh(x) - 2x - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Union(Expression Integer,...) +--E 110 + +--S 111 of 526 +m0621:= a0621-r0621 +--R +--R +--R (111) +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(tanh(x) + 1) +--R + +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)tanh(x) - 2x sinh(x) +--R + +--R 2 +--R - 4x cosh(x)sinh(x) - 2x cosh(x) - 2x - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Expression Integer +--E 111 + +--S 112 of 526 +d0621:= D(m0621,x) +--R +--R +--R (112) +--R 4 2 3 3 2 +--R cosh(x)sinh(x) + 4cosh(x) sinh(x) + (6cosh(x) + 2cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (4cosh(x) + 4cosh(x) )sinh(x) + cosh(x) + 2cosh(x) + cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 4 2 3 +--R - cosh(x)sinh(x) - 4cosh(x) sinh(x) +--R + +--R 3 2 4 2 +--R (- 6cosh(x) - 2cosh(x))sinh(x) + (- 4cosh(x) - 4cosh(x) )sinh(x) +--R + +--R 5 3 +--R - cosh(x) - 2cosh(x) - cosh(x) +--R * +--R tanh(x) +--R + +--R 5 4 2 3 +--R sinh(x) + 3cosh(x)sinh(x) + (2cosh(x) + 2)sinh(x) +--R + +--R 3 2 4 2 +--R (- 2cosh(x) + 6cosh(x))sinh(x) + (- 3cosh(x) + 6cosh(x) + 1)sinh(x) +--R + +--R 5 3 +--R - cosh(x) + 2cosh(x) - cosh(x) +--R / +--R 4 2 3 3 2 +--R cosh(x)sinh(x) + 4cosh(x) sinh(x) + (6cosh(x) + 2cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (4cosh(x) + 4cosh(x) )sinh(x) + cosh(x) + 2cosh(x) + cosh(x) +--R Type: Expression Integer +--E 112 + +--S 113 of 526 +t0622:= sech(x)^3/(1+coth(x)) +--R +--R +--R 3 +--R sech(x) +--R (113) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 113 + +--S 114 of 526 +r0622:= -1/2*atan(sinh(x))-sech(x)+1/2*sech(x)*tanh(x) +--R +--R +--R - atan(sinh(x)) + sech(x)tanh(x) - 2sech(x) +--R (114) ------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 114 + +--S 115 of 526 +a0622:= integrate(t0622,x) +--R +--R +--R (115) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) - 4cosh(x))sinh(x) - cosh(x) - 2cosh(x) - 1 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 2 2 3 +--R - sinh(x) - 3cosh(x)sinh(x) + (- 3cosh(x) - 3)sinh(x) - cosh(x) +--R + +--R - 3cosh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Union(Expression Integer,...) +--E 115 + +--S 116 of 526 +m0622:= a0622-r0622 +--R +--R +--R (116) +--R 4 3 2 2 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 8cosh(x) - 8cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) - 2 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R * +--R atan(sinh(x)) +--R + +--R 4 3 +--R - sech(x)sinh(x) - 4cosh(x)sech(x)sinh(x) +--R + +--R 2 2 +--R (- 6cosh(x) - 2)sech(x)sinh(x) +--R + +--R 3 +--R (- 4cosh(x) - 4cosh(x))sech(x)sinh(x) +--R + +--R 4 2 +--R (- cosh(x) - 2cosh(x) - 1)sech(x) +--R * +--R tanh(x) +--R + +--R 4 3 +--R 2sech(x)sinh(x) + (8cosh(x)sech(x) - 2)sinh(x) +--R + +--R 2 2 +--R ((12cosh(x) + 4)sech(x) - 6cosh(x))sinh(x) +--R + +--R 3 2 +--R ((8cosh(x) + 8cosh(x))sech(x) - 6cosh(x) - 6)sinh(x) +--R + +--R 4 2 3 +--R (2cosh(x) + 4cosh(x) + 2)sech(x) - 2cosh(x) - 6cosh(x) +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) + 8cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) + 2 +--R Type: Expression Integer +--E 116 + +--S 117 of 526 +d0622:= D(m0622,x) +--R +--R +--R (117) +--R 8 7 +--R 2sech(x)sinh(x) + 12cosh(x)sech(x)sinh(x) +--R + +--R 2 6 +--R (30cosh(x) + 8)sech(x)sinh(x) +--R + +--R 3 5 +--R (40cosh(x) + 36cosh(x))sech(x)sinh(x) +--R + +--R 4 2 4 +--R (30cosh(x) + 66cosh(x) + 12)sech(x)sinh(x) +--R + +--R 5 3 3 +--R (12cosh(x) + 64cosh(x) + 36cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 2 +--R (2cosh(x) + 36cosh(x) + 42cosh(x) + 8)sech(x)sinh(x) +--R + +--R 5 3 +--R (12cosh(x) + 24cosh(x) + 12cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 +--R (2cosh(x) + 6cosh(x) + 6cosh(x) + 2)sech(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R - 2sech(x)sinh(x) - 12cosh(x)sech(x)sinh(x) +--R + +--R 2 6 +--R (- 30cosh(x) - 8)sech(x)sinh(x) +--R + +--R 3 5 +--R (- 40cosh(x) - 36cosh(x))sech(x)sinh(x) +--R + +--R 4 2 4 +--R (- 30cosh(x) - 66cosh(x) - 12)sech(x)sinh(x) +--R + +--R 5 3 3 +--R (- 12cosh(x) - 64cosh(x) - 36cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 2 +--R (- 2cosh(x) - 36cosh(x) - 42cosh(x) - 8)sech(x)sinh(x) +--R + +--R 5 3 +--R (- 12cosh(x) - 24cosh(x) - 12cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 +--R (- 2cosh(x) - 6cosh(x) - 6cosh(x) - 2)sech(x) +--R * +--R tanh(x) +--R + +--R 8 7 +--R - sech(x)sinh(x) - 6cosh(x)sech(x)sinh(x) +--R + +--R 2 6 +--R ((- 15cosh(x) - 4)sech(x) + cosh(x))sinh(x) +--R + +--R 3 2 5 +--R ((- 20cosh(x) - 18cosh(x))sech(x) + 6cosh(x) + 8)sinh(x) +--R + +--R 4 2 3 4 +--R ((- 15cosh(x) - 33cosh(x) - 6)sech(x) + 15cosh(x) + 27cosh(x))sinh(x) +--R + +--R 5 3 4 +--R (- 6cosh(x) - 32cosh(x) - 18cosh(x))sech(x) + 20cosh(x) +--R + +--R 2 +--R 36cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 5 +--R (- cosh(x) - 18cosh(x) - 21cosh(x) - 4)sech(x) + 15cosh(x) +--R + +--R 3 +--R 26cosh(x) + 19cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 4 +--R (- 6cosh(x) - 12cosh(x) - 6cosh(x))sech(x) + 6cosh(x) + 12cosh(x) +--R + +--R 2 +--R 30cosh(x) - 8 +--R * +--R sinh(x) +--R + +--R 6 4 2 7 5 +--R (- cosh(x) - 3cosh(x) - 3cosh(x) - 1)sech(x) + cosh(x) + 3cosh(x) +--R + +--R 3 +--R 11cosh(x) - 7cosh(x) +--R / +--R 8 7 2 6 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 8)sinh(x) +--R + +--R 3 5 4 2 4 +--R (40cosh(x) + 36cosh(x))sinh(x) + (30cosh(x) + 66cosh(x) + 12)sinh(x) +--R + +--R 5 3 3 +--R (12cosh(x) + 64cosh(x) + 36cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (2cosh(x) + 36cosh(x) + 42cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 24cosh(x) + 12cosh(x))sinh(x) + 2cosh(x) + 6cosh(x) +--R + +--R 2 +--R 6cosh(x) + 2 +--R Type: Expression Integer +--E 117 + +--S 118 of 526 +t0623:= sech(x)/(%i+2*coth(x)) +--R +--R +--R sech(x) +--R (118) ------------- +--R 2coth(x) + %i +--R Type: Expression Complex Integer +--E 118 + +--S 119 of 526 +r0623:= -%i*atan(sinh(x))+2/5*%i*atan(1/5*(%i*cosh(x)+_ + 2*sinh(x))*5^(1/2))*5^(1/2) +--R +--R +--R 2 +-+ 2 +-+ 1 +-+ +--R (119) - %i\|5 atan(- \|5 sinh(x) + - %i\|5 cosh(x)) - %i atan(sinh(x)) +--R 5 5 5 +--R Type: Expression Complex Fraction Integer +--E 119 + +--S 120 of 526 +a0623:= integrate(t0623,x) +--R +--R +--R (120) +--R +-+ +-+ +--R \|5 log(sinh(x) + cosh(x) + %i) - \|5 log(sinh(x) + cosh(x) - %i) +--R + +--R +-+ +-+ +--R - 2%i\|5 sinh(x) + \|5 cosh(x) - 5 +--R 2log(----------------------------------) +--R sinh(x) - 2%i cosh(x) +--R / +--R +-+ +--R \|5 +--R Type: Union(Expression Complex Integer,...) +--E 120 + +--S 121 of 526 +m0623:= a0623-r0623 +--R +--R +--R (121) +--R +-+ +-+ +--R \|5 log(sinh(x) + cosh(x) + %i) - \|5 log(sinh(x) + cosh(x) - %i) +--R + +--R +-+ +-+ +--R - 2%i\|5 sinh(x) + \|5 cosh(x) - 5 +--R 2log(----------------------------------) +--R sinh(x) - 2%i cosh(x) +--R + +--R 2 +-+ 1 +-+ +-+ +--R - 2%i atan(- \|5 sinh(x) + - %i\|5 cosh(x)) + %i\|5 atan(sinh(x)) +--R 5 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression Complex Fraction Integer +--E 121 + +--S 122 of 526 +d0623:= D(m0623,x) +--R +--R +--R (122) +--R 8 5 +-+ 7 +--R 5%i sinh(x) + ((- 5 + 10%i)cosh(x) + (- - 2%i)\|5 )sinh(x) +--R 2 +--R + +--R 5 2 1 +-+ 6 +--R ((- 10 - - %i)cosh(x) + (4 + - %i)\|5 cosh(x) - 5 + 15%i)sinh(x) +--R 4 4 +--R + +--R 25 3 1 +-+ 2 35 +--R - -- %i cosh(x) - - \|5 cosh(x) + (- -- + 25%i)cosh(x) +--R 2 2 2 +--R + +--R 15 9 +-+ +--R (-- - - %i)\|5 +--R 2 2 +--R * +--R 5 +--R sinh(x) +--R + +--R 4 5 5 +-+ 3 95 5 2 +--R (10 - 5%i)cosh(x) + (- - - - %i)\|5 cosh(x) + (- -- - - %i)cosh(x) +--R 4 4 4 4 +--R + +--R 21 3 +-+ 45 +--R (-- + - %i)\|5 cosh(x) - -- + 15%i +--R 4 2 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 5 5 +-+ 4 +--R (5 + - %i)cosh(x) + (- - + - %i)\|5 cosh(x) +--R 2 8 2 +--R + +--R 15 45 3 19 1 +-+ 2 +--R (- -- - -- %i)cosh(x) + (- -- + - %i)\|5 cosh(x) +--R 8 2 8 2 +--R + +--R 165 55 15 5 +-+ +--R (- --- + -- %i)cosh(x) + (-- - - %i)\|5 +--R 8 2 2 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 6 11 5 +-+ 5 75 35 4 +--R - %i cosh(x) + (- -- + - %i)\|5 cosh(x) + (-- - -- %i)cosh(x) +--R 4 4 4 4 4 +--R + +--R 3 9 +-+ 3 25 2 5 5 +-+ +--R (- - - %i)\|5 cosh(x) + (- -- + 5%i)cosh(x) + (- + - %i)\|5 cosh(x) +--R 2 4 2 4 2 +--R + +--R 25 +--R - -- + 5%i +--R 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 1 +-+ 6 75 5 +--R (- -- - - %i)\|5 cosh(x) + (-- + 5%i)cosh(x) +--R 8 2 8 +--R + +--R 3 1 +-+ 4 5 35 3 15 +-+ 2 +--R (- + - %i)\|5 cosh(x) + (- - - -- %i)cosh(x) - -- \|5 cosh(x) +--R 4 2 4 2 8 +--R + +--R 65 25 5 +-+ +--R (- -- + -- %i)cosh(x) + - \|5 +--R 8 2 2 +--R * +--R sinh(x) +--R + +--R 1 +-+ 7 5 6 1 +-+ 5 15 4 +--R - - %i\|5 cosh(x) + - %i cosh(x) + - %i\|5 cosh(x) - -- %i cosh(x) +--R 4 2 4 2 +--R + +--R 5 +-+ 3 2 5 +-+ +--R - - %i\|5 cosh(x) + 5%i cosh(x) + - %i\|5 cosh(x) +--R 4 4 +--R / +--R +-+ 8 1 +-+ 5 7 +--R \|5 sinh(x) + ((2 - - %i)\|5 cosh(x) - - %i)sinh(x) +--R 2 2 +--R + +--R 13 +-+ 2 5 13 +-+ 6 +--R ((-- - %i)\|5 cosh(x) + (- - - 5%i)cosh(x) + -- \|5 )sinh(x) +--R 4 2 4 +--R + +--R 9 7 +-+ 3 55 2 +--R (- + - %i)\|5 cosh(x) + (- 5 - -- %i)cosh(x) +--R 2 8 8 +--R + +--R 9 23 +-+ 65 +--R (- - -- %i)\|5 cosh(x) - -- %i +--R 2 8 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 11 +-+ 4 5 35 3 +--R (2 + -- %i)\|5 cosh(x) + (- - - -- %i)cosh(x) +--R 4 4 4 +--R + +--R 19 +-+ 2 45 45 7 +-+ +--R (8 - -- %i)\|5 cosh(x) + (- -- - -- %i)cosh(x) + - \|5 +--R 4 4 4 2 +--R * +--R 4 +--R sinh(x) +--R + +--R 1 11 +-+ 5 5 35 4 +--R (- - + -- %i)\|5 cosh(x) + (- - -- %i)cosh(x) +--R 2 8 2 8 +--R + +--R 3 +-+ 3 35 115 2 +--R (7 + - %i)\|5 cosh(x) + (- -- - --- %i)cosh(x) +--R 8 2 8 +--R + +--R 5 17 +-+ 35 +--R (- - -- %i)\|5 cosh(x) - -- %i +--R 2 4 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 +-+ 6 5 5 11 +-+ 4 +--R - - \|5 cosh(x) + - cosh(x) + (3 + -- %i)\|5 cosh(x) +--R 4 4 4 +--R + +--R 25 35 3 15 +-+ 2 +--R (- -- - -- %i)cosh(x) + (6 - -- %i)\|5 cosh(x) +--R 4 4 4 +--R + +--R 25 5 +-+ +--R (- 15 - -- %i)cosh(x) + - \|5 +--R 4 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 11 +-+ 5 5 35 4 +--R (- - + -- %i)\|5 cosh(x) + (- - -- %i)cosh(x) +--R 2 8 2 8 +--R + +--R 5 1 +-+ 3 25 15 2 15 +-+ +--R (- - - %i)\|5 cosh(x) + (- -- - -- %i)cosh(x) - -- %i\|5 cosh(x) +--R 2 2 2 2 8 +--R + +--R 25 +--R - -- %i +--R 8 +--R * +--R sinh(x) +--R + +--R 1 +-+ 6 5 5 +-+ 4 3 5 +-+ 2 +--R - - \|5 cosh(x) + - cosh(x) + \|5 cosh(x) - 5cosh(x) + - \|5 cosh(x) +--R 4 4 4 +--R + +--R 25 +--R - -- cosh(x) +--R 4 +--R Type: Expression Complex Fraction Integer +--E 122 + +--S 123 of 526 +t0624:= csch(x)^2/(a+b*coth(x)) +--R +--R +--R 2 +--R csch(x) +--R (123) ------------- +--R b coth(x) + a +--R Type: Expression Integer +--E 123 + +--S 124 of 526 +r0624:= -log(a+b*coth(x))/b +--R +--R +--R log(b coth(x) + a) +--R (124) - ------------------ +--R b +--R Type: Expression Integer +--E 124 + +--S 125 of 526 +a0624:= integrate(t0624,x) +--R +--R +--R 2sinh(x) - 2a sinh(x) - 2b cosh(x) +--R log(- -----------------) - log(-------------------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R (125) --------------------------------------------------------- +--R b +--R Type: Union(Expression Integer,...) +--E 125 + +--S 126 of 526 +m0624:= a0624-r0624 +--R +--R +--R (126) +--R 2sinh(x) +--R log(b coth(x) + a) + log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2a sinh(x) - 2b cosh(x) +--R - log(-------------------------) +--R sinh(x) - cosh(x) +--R / +--R b +--R Type: Expression Integer +--E 126 + +--S 127 of 526 +d0624:= D(m0624,x) +--R +--R +--R (127) +--R 2 2 +--R (- a coth(x) - b coth(x))sinh(x) +--R + +--R 2 2 2 +--R (- b cosh(x)coth(x) + b cosh(x))sinh(x) + b cosh(x) coth(x) + a cosh(x) +--R / +--R 2 2 2 +--R (a b coth(x) + a )sinh(x) + (b cosh(x)coth(x) + a b cosh(x))sinh(x) +--R Type: Expression Integer +--E 127 + +--S 128 of 526 +t0625:= csch(x)^3/(a+b*coth(x)) +--R +--R +--R 3 +--R csch(x) +--R (128) ------------- +--R b coth(x) + a +--R Type: Expression Integer +--E 128 + +--S 129 of 526 +r0625:= -(2*(a^2-b^2)^(1/2)*atanh(1/(a^2-b^2)^(1/2)*(a*sinh(x)+_ + b*cosh(x)-b)/sinh(x))*sinh(x)+b+_ + a*log((cosh(x)-1)/sinh(x))*sinh(x))/sinh(x)/b^2 +--R +--R +--R (129) +--R cosh(x) - 1 +--R - a sinh(x)log(-----------) +--R sinh(x) +--R + +--R +---------+ +--R | 2 2 a sinh(x) + b cosh(x) - b +--R - 2sinh(x)\|- b + a atanh(-------------------------) - b +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R / +--R 2 +--R b sinh(x) +--R Type: Expression Integer +--E 129 + +--S 130 of 526 +a0625:= integrate(t0625,x) +--R +--R +--R (130) +--R [ +--R 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 +--R (- 2sinh(x) - 2cosh(x))\|- b + a + (b + a)sinh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b + a +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R + +--R - 2b sinh(x) - 2b cosh(x) +--R / +--R 2 2 2 2 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b +--R , +--R +--R 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 2)\|b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R atan(-------------------------------) +--R (b + a)sinh(x) + (b + a)cosh(x) +--R + +--R - 2b sinh(x) - 2b cosh(x) +--R / +--R 2 2 2 2 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b +--R ] +--R Type: Union(List Expression Integer,...) +--E 130 + +--S 131 of 526 +m0625a:= a0625.1-r0625 +--R +--R +--R (131) +--R 3 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + (a cosh(x) - a)sinh(x)) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) + (- a cosh(x) + a)sinh(x)) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + (a cosh(x) - a)sinh(x)) +--R * +--R cosh(x) - 1 +--R log(-----------) +--R sinh(x) +--R + +--R +---------+ +--R 3 2 2 | 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + (cosh(x) - 1)sinh(x))\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 +--R (- 2sinh(x) - 2cosh(x))\|- b + a + (b + a)sinh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b + a +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) + b +--R + +--R - a +--R + +--R +---------+ +--R 3 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + (2cosh(x) - 2)sinh(x))\|- b + a +--R * +--R a sinh(x) + b cosh(x) - b +--R atanh(-------------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R + +--R 2 2 +--R - b sinh(x) + b cosh(x) - b +--R / +--R 2 3 2 2 2 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + (b cosh(x) - b )sinh(x) +--R Type: Expression Integer +--E 131 + +--S 132 of 526 +d0625a:= D(m0625a,x) +--R +--R +--R (132) +--R 2 11 2 2 2 10 +--R (a b + a )sinh(x) + ((2b + 8a b + 6a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 27a b + 15a )cosh(x) + (- 12b - 13a b - a )cosh(x) - 2a ) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 2 2 +--R (28b + 48a b + 20a )cosh(x) + (- 27b - 33a b - 6a )cosh(x) +--R + +--R 2 2 2 +--R (- 3b - 5a b - 6a )cosh(x) + 2b + 6a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 4 2 2 3 +--R (28b + 42a b + 14a )cosh(x) + (- 22b - 36a b - 14a )cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (- 14b - 20a b - 2a )cosh(x) + (16b + 24a b + 2a )cosh(x) - 8b +--R + +--R - 2a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 4 2 2 3 +--R (14b - 14a )cosh(x) + (- 22b - 20a b + 14a )cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (30b + 38a b + 6a )cosh(x) + (- 24b - 28a b - 6a )cosh(x) + 2b +--R + +--R 10a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 6 2 5 +--R (- 28b - 42a b - 14a )cosh(x) + (42b + 42a b)cosh(x) +--R + +--R 2 2 4 2 3 +--R (- 2b + 28a b + 30a )cosh(x) + (10b + 8a b)cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (- 42b - 74a b - 18a )cosh(x) + (28b + 38a b)cosh(x) - 8b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 7 2 2 6 +--R (- 28b - 48a b - 20a )cosh(x) + (28b + 42a b + 14a )cosh(x) +--R + +--R 2 2 5 2 2 4 +--R (40b + 90a b + 38a )cosh(x) + (- 28b - 62a b - 20a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 62b - 80a b - 24a )cosh(x) + (74b + 66a b + 6a )cosh(x) +--R + +--R 2 2 2 +--R (- 22b - 10a b + 6a )cosh(x) - 2b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 12b - 27a b - 15a )cosh(x) + (- 2b + 12a b + 14a )cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (62b + 100a b + 34a )cosh(x) + (- 44b - 88a b - 30a )cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 56b - 54a b - 24a )cosh(x) + (78b + 76a b + 18a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 26b - 20a b + 6a )cosh(x) - 2a cosh(x) + a b - a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 9 2 2 8 +--R (- 2b - 8a b - 6a )cosh(x) + (- 12b - 6a b + 6a )cosh(x) +--R + +--R 2 2 7 2 2 6 +--R (46b + 60a b + 18a )cosh(x) + (- 34b - 46a b - 18a )cosh(x) +--R + +--R 2 2 5 2 2 4 +--R (- 24b - 44a b - 18a )cosh(x) + (40b + 62a b + 18a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 18b - 12a b + 6a )cosh(x) + (6b - 10a b - 6a )cosh(x) +--R + +--R 2 +--R (- 2b + 4a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 10 2 2 9 +--R (- a b - a )cosh(x) + (- 6b - 5a b + a )cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (18b + 20a b + 4a )cosh(x) + (- 14b - 8a b - 4a )cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (- 6b - 30a b - 6a )cosh(x) + (14b + 30a b + 6a )cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 10b + 4a b + 4a )cosh(x) + (6b - 16a b - 4a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 7a b - a )cosh(x) + (- a b + a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 9 2 8 +--R (- b - a b)cosh(x) + (3b + 3a b)cosh(x) - 2b cosh(x) +--R + +--R 2 7 2 6 2 5 +--R (- 2b - 8a b)cosh(x) + (4b + 6a b)cosh(x) + (- 4b + 6a b)cosh(x) +--R + +--R 2 4 2 3 2 2 +--R (2b - 8a b)cosh(x) + 2b cosh(x) + (- 3b + 3a b)cosh(x) +--R + +--R 2 +--R (b - a b)cosh(x) +--R / +--R 3 2 3 2 10 +--R ((b + a b )cosh(x) - b - a b )sinh(x) +--R + +--R 3 2 2 2 3 2 2 2 +--R (6b + 8a b + 2a b)cosh(x) + (- 6b - 10a b - 4a b)cosh(x) + 2a b +--R + +--R 2 +--R 2a b +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (16b + 28a b + 12a b)cosh(x) + (- 18b - 42a b - 24a b)cosh(x) +--R + +--R 3 2 2 2 +--R (2b + 12a b + 12a b)cosh(x) + 2a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (26b + 56a b + 30a b)cosh(x) + (- 38b - 98a b - 60a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (14b + 34a b + 24a b)cosh(x) + (- 2b + 10a b + 12a b)cosh(x) +--R + +--R 2 2 +--R - 2a b - 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (30b + 70a b + 40a b)cosh(x) + (- 60b - 140a b - 80a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (38b + 56a b + 16a b)cosh(x) + (- 6b + 28a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b - 14a b - 24a b)cosh(x) + 2b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (26b + 56a b + 30a b)cosh(x) + (- 66b - 126a b - 60a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (52b + 54a b - 6a b)cosh(x) + (- 4b + 52a b + 72a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 14b - 44a b - 30a b)cosh(x) + (6b + 10a b - 12a b)cosh(x) +--R + +--R 2 2 +--R - 2a b + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 6 +--R (16b + 28a b + 12a b)cosh(x) + (- 46b - 70a b - 24a b)cosh(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (38b + 28a b - 12a b)cosh(x) + (4b + 58a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (- 20b - 60a b - 12a b)cosh(x) + (10b + 14a b - 24a b)cosh(x) +--R + +--R 3 2 2 2 +--R (- 2b + 4a b + 12a b)cosh(x) - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (6b + 8a b + 2a b)cosh(x) + (- 18b - 22a b - 4a b)cosh(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (14b + 6a b - 4a b)cosh(x) + (6b + 34a b + 12a b)cosh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 14b - 34a b )cosh(x) + (10b - 2a b - 12a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 6b + 18a b + 4a b)cosh(x) + (2b - 10a b + 4a b)cosh(x) +--R + +--R 2 2 +--R 2a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 9 3 2 8 3 7 +--R (b + a b )cosh(x) + (- 3b - 3a b )cosh(x) + 2b cosh(x) +--R + +--R 3 2 6 3 2 5 +--R (2b + 8a b )cosh(x) + (- 4b - 6a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 +--R (4b - 6a b )cosh(x) + (- 2b + 8a b )cosh(x) - 2b cosh(x) +--R + +--R 3 2 3 2 +--R (3b - 3a b )cosh(x) - b + a b +--R * +--R 2 +--R sinh(x) +--R Type: Expression Integer +--E 132 + +--S 133 of 526 +m0625b:= a0625.2-r0625 +--R +--R +--R (133) +--R 3 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + (a cosh(x) - a)sinh(x)) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) + (- a cosh(x) + a)sinh(x)) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + (a cosh(x) - a)sinh(x)) +--R * +--R cosh(x) - 1 +--R log(-----------) +--R sinh(x) +--R + +--R +---------+ +--R 3 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + (2cosh(x) - 2)sinh(x))\|- b + a +--R * +--R a sinh(x) + b cosh(x) - b +--R atanh(-------------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R + +--R +-------+ +--R 3 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + (2cosh(x) - 2)sinh(x))\|b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R atan(-------------------------------) +--R (b + a)sinh(x) + (b + a)cosh(x) +--R + +--R 2 2 +--R - b sinh(x) + b cosh(x) - b +--R / +--R 2 3 2 2 2 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + (b cosh(x) - b )sinh(x) +--R Type: Expression Integer +--E 133 + +--S 134 of 526 +d0625b:= D(m0625b,x) +--R +--R +--R (134) +--R 2 11 2 2 2 10 +--R (a b + a )sinh(x) + ((2b + 8a b + 6a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 27a b + 15a )cosh(x) + (- 12b - 13a b - a )cosh(x) - 2a ) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 2 2 +--R (28b + 48a b + 20a )cosh(x) + (- 27b - 33a b - 6a )cosh(x) +--R + +--R 2 2 2 +--R (- 3b - 5a b - 6a )cosh(x) + 2b + 6a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 4 2 2 3 +--R (28b + 42a b + 14a )cosh(x) + (- 22b - 36a b - 14a )cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (- 14b - 20a b - 2a )cosh(x) + (16b + 24a b + 2a )cosh(x) - 8b +--R + +--R - 2a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 4 2 2 3 +--R (14b - 14a )cosh(x) + (- 22b - 20a b + 14a )cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (30b + 38a b + 6a )cosh(x) + (- 24b - 28a b - 6a )cosh(x) + 2b +--R + +--R 10a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 6 2 5 +--R (- 28b - 42a b - 14a )cosh(x) + (42b + 42a b)cosh(x) +--R + +--R 2 2 4 2 3 +--R (- 2b + 28a b + 30a )cosh(x) + (10b + 8a b)cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (- 42b - 74a b - 18a )cosh(x) + (28b + 38a b)cosh(x) - 8b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 7 2 2 6 +--R (- 28b - 48a b - 20a )cosh(x) + (28b + 42a b + 14a )cosh(x) +--R + +--R 2 2 5 2 2 4 +--R (40b + 90a b + 38a )cosh(x) + (- 28b - 62a b - 20a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 62b - 80a b - 24a )cosh(x) + (74b + 66a b + 6a )cosh(x) +--R + +--R 2 2 2 +--R (- 22b - 10a b + 6a )cosh(x) - 2b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 12b - 27a b - 15a )cosh(x) + (- 2b + 12a b + 14a )cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (62b + 100a b + 34a )cosh(x) + (- 44b - 88a b - 30a )cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 56b - 54a b - 24a )cosh(x) + (78b + 76a b + 18a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 26b - 20a b + 6a )cosh(x) - 2a cosh(x) + a b - a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 9 2 2 8 +--R (- 2b - 8a b - 6a )cosh(x) + (- 12b - 6a b + 6a )cosh(x) +--R + +--R 2 2 7 2 2 6 +--R (46b + 60a b + 18a )cosh(x) + (- 34b - 46a b - 18a )cosh(x) +--R + +--R 2 2 5 2 2 4 +--R (- 24b - 44a b - 18a )cosh(x) + (40b + 62a b + 18a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 18b - 12a b + 6a )cosh(x) + (6b - 10a b - 6a )cosh(x) +--R + +--R 2 +--R (- 2b + 4a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 10 2 2 9 +--R (- a b - a )cosh(x) + (- 6b - 5a b + a )cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (18b + 20a b + 4a )cosh(x) + (- 14b - 8a b - 4a )cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (- 6b - 30a b - 6a )cosh(x) + (14b + 30a b + 6a )cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 10b + 4a b + 4a )cosh(x) + (6b - 16a b - 4a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 7a b - a )cosh(x) + (- a b + a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 9 2 8 +--R (- b - a b)cosh(x) + (3b + 3a b)cosh(x) - 2b cosh(x) +--R + +--R 2 7 2 6 2 5 +--R (- 2b - 8a b)cosh(x) + (4b + 6a b)cosh(x) + (- 4b + 6a b)cosh(x) +--R + +--R 2 4 2 3 2 2 +--R (2b - 8a b)cosh(x) + 2b cosh(x) + (- 3b + 3a b)cosh(x) +--R + +--R 2 +--R (b - a b)cosh(x) +--R / +--R 3 2 3 2 10 +--R ((b + a b )cosh(x) - b - a b )sinh(x) +--R + +--R 3 2 2 2 3 2 2 2 +--R (6b + 8a b + 2a b)cosh(x) + (- 6b - 10a b - 4a b)cosh(x) + 2a b +--R + +--R 2 +--R 2a b +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (16b + 28a b + 12a b)cosh(x) + (- 18b - 42a b - 24a b)cosh(x) +--R + +--R 3 2 2 2 +--R (2b + 12a b + 12a b)cosh(x) + 2a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (26b + 56a b + 30a b)cosh(x) + (- 38b - 98a b - 60a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (14b + 34a b + 24a b)cosh(x) + (- 2b + 10a b + 12a b)cosh(x) +--R + +--R 2 2 +--R - 2a b - 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (30b + 70a b + 40a b)cosh(x) + (- 60b - 140a b - 80a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (38b + 56a b + 16a b)cosh(x) + (- 6b + 28a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b - 14a b - 24a b)cosh(x) + 2b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (26b + 56a b + 30a b)cosh(x) + (- 66b - 126a b - 60a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (52b + 54a b - 6a b)cosh(x) + (- 4b + 52a b + 72a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 14b - 44a b - 30a b)cosh(x) + (6b + 10a b - 12a b)cosh(x) +--R + +--R 2 2 +--R - 2a b + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 6 +--R (16b + 28a b + 12a b)cosh(x) + (- 46b - 70a b - 24a b)cosh(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (38b + 28a b - 12a b)cosh(x) + (4b + 58a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (- 20b - 60a b - 12a b)cosh(x) + (10b + 14a b - 24a b)cosh(x) +--R + +--R 3 2 2 2 +--R (- 2b + 4a b + 12a b)cosh(x) - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (6b + 8a b + 2a b)cosh(x) + (- 18b - 22a b - 4a b)cosh(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (14b + 6a b - 4a b)cosh(x) + (6b + 34a b + 12a b)cosh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 14b - 34a b )cosh(x) + (10b - 2a b - 12a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 6b + 18a b + 4a b)cosh(x) + (2b - 10a b + 4a b)cosh(x) +--R + +--R 2 2 +--R 2a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 9 3 2 8 3 7 +--R (b + a b )cosh(x) + (- 3b - 3a b )cosh(x) + 2b cosh(x) +--R + +--R 3 2 6 3 2 5 +--R (2b + 8a b )cosh(x) + (- 4b - 6a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 +--R (4b - 6a b )cosh(x) + (- 2b + 8a b )cosh(x) - 2b cosh(x) +--R + +--R 3 2 3 2 +--R (3b - 3a b )cosh(x) - b + a b +--R * +--R 2 +--R sinh(x) +--R Type: Expression Integer +--E 134 + +--S 135 of 526 +t0626:= csch(x)^4/(a+b*coth(x)) +--R +--R +--R 4 +--R csch(x) +--R (135) ------------- +--R b coth(x) + a +--R Type: Expression Integer +--E 135 + +--S 136 of 526 +r0626:= a*coth(x)/b^2-1/2*coth(x)^2/b-(a^2-b^2)*log(a+b*coth(x))/b^3 +--R +--R +--R 2 2 2 2 +--R (2b - 2a )log(b coth(x) + a) - b coth(x) + 2a b coth(x) +--R (136) --------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression Integer +--E 136 + +--S 137 of 526 +a0626:= integrate(t0626,x) +--R +--R +--R (137) +--R 2 2 4 2 2 3 +--R (- b + a )sinh(x) + (- 4b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b + 6a )cosh(x) + 2b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b + 4a )cosh(x) + (4b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b + a )cosh(x) + (2b - 2a )cosh(x) - b + a +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b - 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b - 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b - a )cosh(x) + (- 2b + 2a )cosh(x) + b - a +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 +--R (- 2b + 2a b)sinh(x) + (- 4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 2b + 2a b)cosh(x) - 2a b +--R / +--R 3 4 3 3 3 2 3 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) - 2b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4b cosh(x) - 4b cosh(x))sinh(x) + b cosh(x) - 2b cosh(x) + b +--R Type: Union(Expression Integer,...) +--E 137 + +--S 138 of 526 +m0626:= a0626-r0626 +--R +--R +--R (138) +--R 2 2 4 2 2 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + (4b - 4a )cosh(x) - 2b + 2a +--R * +--R log(b coth(x) + a) +--R + +--R 2 2 4 2 2 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + (4b - 4a )cosh(x) - 2b + 2a +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (2b - 2a )sinh(x) + (8b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 12a )cosh(x) - 4b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 8a )cosh(x) + (- 8b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - 2a )cosh(x) + (- 4b + 4a )cosh(x) + 2b - 2a +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 +--R (b coth(x) - 2a b coth(x))sinh(x) +--R + +--R 2 2 3 +--R (4b cosh(x)coth(x) - 8a b cosh(x)coth(x))sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (6b cosh(x) - 2b )coth(x) + (- 12a b cosh(x) + 4a b)coth(x) - 4b +--R + +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4b cosh(x) - 4b cosh(x))coth(x) +--R + +--R 3 2 +--R (- 8a b cosh(x) + 8a b cosh(x))coth(x) + (- 8b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b cosh(x) - 2b cosh(x) + b )coth(x) +--R + +--R 4 2 2 2 +--R (- 2a b cosh(x) + 4a b cosh(x) - 2a b)coth(x) + (- 4b + 4a b)cosh(x) +--R + +--R - 4a b +--R / +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) - 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) - 8b cosh(x))sinh(x) + 2b cosh(x) - 4b cosh(x) + 2b +--R Type: Expression Integer +--E 138 + +--S 139 of 526 +d0626:= D(m0626,x) +--R +--R +--R (139) +--R 2 4 2 2 3 2 3 8 +--R (- a b coth(x) + 2a b coth(x) + (b - a b)coth(x) - a )sinh(x) +--R + +--R 3 2 4 3 2 2 +--R (- b - 6a b )cosh(x)coth(x) + (2b + 12a b )cosh(x)coth(x) +--R + +--R 3 2 3 3 +--R (6b - 6a b)cosh(x)coth(x) + (- b - 6a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 2 4 +--R ((- 6b - 15a b )cosh(x) + 3a b )coth(x) +--R + +--R 3 2 2 2 2 +--R ((12b + 30a b )cosh(x) - 6a b )coth(x) +--R + +--R 3 2 2 3 2 2 +--R ((14b - 14a b)cosh(x) - 3b + 4a b - a b)coth(x) +--R + +--R 3 2 3 2 2 3 +--R (- 6b - a b - 14a )cosh(x) + 4a b - a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 3 3 2 4 +--R ((- 15b - 20a b )cosh(x) + (3b + 12a b )cosh(x))coth(x) +--R + +--R 3 2 3 3 2 2 +--R ((30b + 40a b )cosh(x) + (- 6b - 24a b )cosh(x))coth(x) +--R + +--R 3 2 3 3 2 2 +--R ((14b - 14a b)cosh(x) + (- 8b + 12a b - 4a b)cosh(x))coth(x) +--R + +--R 3 2 3 3 3 2 2 3 +--R (- 15b - 6a b - 14a )cosh(x) + (3b + 4a b + 12a b - 4a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 2 4 +--R ((- 20b - 15a b )cosh(x) + (12b + 18a b )cosh(x) - 3a b )coth(x) +--R + +--R 3 2 4 3 2 2 2 2 +--R ((40b + 30a b )cosh(x) + (- 24b - 36a b )cosh(x) + 6a b )coth(x) +--R + +--R 3 2 2 2 3 2 2 +--R ((b + 8a b - 9a b)cosh(x) + 3b + 4a b + a b)coth(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R (- 20b - 15a b )cosh(x) + (12b + 19a b + 8a b - 9a )cosh(x) +--R + +--R 2 3 +--R 4a b + a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 15b - 6a b )cosh(x) + (18b + 12a b )cosh(x) +--R + +--R 3 2 +--R (- 3b - 6a b )cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 3 2 5 3 2 3 +--R (30b + 12a b )cosh(x) + (- 36b - 24a b )cosh(x) +--R + +--R 3 2 +--R (6b + 12a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 5 3 2 2 3 +--R (- 14b + 14a b)cosh(x) + (24b - 8a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (10b + 12a b + 2a b)cosh(x) +--R * +--R coth(x) +--R + +--R 3 2 3 5 +--R (- 15b - 20a b + 14a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (18b + 36a b - 8a b - 16a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 3b + 4a b + 12a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b - a b )cosh(x) + (12b + 3a b )cosh(x) +--R + +--R 3 2 2 2 +--R (- 6b - 3a b )cosh(x) + a b +--R * +--R 4 +--R coth(x) +--R + +--R 3 2 6 3 2 4 +--R (12b + 2a b )cosh(x) + (- 24b - 6a b )cosh(x) +--R + +--R 3 2 2 2 +--R (12b + 6a b )cosh(x) - 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- 14b + 14a b)cosh(x) + (31b - 12a b - 19a b)cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (8b + 12a b + 4a b)cosh(x) - b + a b +--R * +--R coth(x) +--R + +--R 3 2 3 6 +--R (- 6b - 15a b + 14a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (12b + 34a b - 12a b - 19a )cosh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 6b + 5a b + 12a b + 4a )cosh(x) + a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 5 3 3 3 4 +--R (- b cosh(x) + 3b cosh(x) - 3b cosh(x) + b cosh(x))coth(x) +--R + +--R 3 7 3 5 3 3 3 2 +--R (2b cosh(x) - 6b cosh(x) + 6b cosh(x) - 2b cosh(x))coth(x) +--R + +--R 3 2 7 3 2 2 5 +--R (- 6b + 6a b)cosh(x) + (16b - 4a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b + 4a b + 6a b)cosh(x) +--R * +--R coth(x) +--R + +--R 3 2 3 7 3 2 2 3 5 +--R (- b - 6a b + 6a )cosh(x) + (3b + 16a b - 4a b - 12a )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R (- 3b - 2a b + 4a b + 6a )cosh(x) + b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 8 3 2 6 3 2 4 +--R (- b + a b)cosh(x) + (3b - 3a b)cosh(x) + (- 3b + 3a b)cosh(x) +--R + +--R 3 2 2 +--R (b - a b)cosh(x) +--R * +--R coth(x) +--R + +--R 2 3 8 2 3 6 2 3 4 +--R (- a b + a )cosh(x) + (3a b - 3a )cosh(x) + (- 3a b + 3a )cosh(x) +--R + +--R 2 3 2 +--R (a b - a )cosh(x) +--R / +--R 3 2 2 8 +--R (a b coth(x) + a b )sinh(x) +--R + +--R 4 3 3 2 2 7 +--R ((b + 6a b )cosh(x)coth(x) + (a b + 6a b )cosh(x))sinh(x) +--R + +--R 4 3 2 3 3 2 2 2 +--R ((6b + 15a b )cosh(x) - 3a b )coth(x) + (6a b + 15a b )cosh(x) +--R + +--R 2 2 +--R - 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 3 4 3 +--R ((15b + 20a b )cosh(x) + (- 3b - 12a b )cosh(x))coth(x) +--R + +--R 3 2 2 3 3 2 2 +--R (15a b + 20a b )cosh(x) + (- 3a b - 12a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 4 3 2 3 +--R ((20b + 15a b )cosh(x) + (- 12b - 18a b )cosh(x) + 3a b )coth(x) +--R + +--R 3 2 2 4 3 2 2 2 2 2 +--R (20a b + 15a b )cosh(x) + (- 12a b - 18a b )cosh(x) + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 4 3 3 +--R (15b + 6a b )cosh(x) + (- 18b - 12a b )cosh(x) +--R + +--R 4 3 +--R (3b + 6a b )cosh(x) +--R * +--R coth(x) +--R + +--R 3 2 2 5 3 2 2 3 +--R (15a b + 6a b )cosh(x) + (- 18a b - 12a b )cosh(x) +--R + +--R 3 2 2 +--R (3a b + 6a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 4 3 4 +--R (6b + a b )cosh(x) + (- 12b - 3a b )cosh(x) +--R + +--R 4 3 2 3 +--R (6b + 3a b )cosh(x) - a b +--R * +--R coth(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (6a b + a b )cosh(x) + (- 12a b - 3a b )cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (6a b + 3a b )cosh(x) - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 4 5 4 3 4 +--R (b cosh(x) - 3b cosh(x) + 3b cosh(x) - b cosh(x))coth(x) +--R + +--R 3 7 3 5 3 3 3 +--R a b cosh(x) - 3a b cosh(x) + 3a b cosh(x) - a b cosh(x) +--R * +--R sinh(x) +--R Type: Expression Integer +--E 139 + +--S 140 of 526 +t0627:= csch(x)^2/(1+coth(x)) +--R +--R +--R 2 +--R csch(x) +--R (140) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 140 + +--S 141 of 526 +r0627:= -log(1+coth(x)) +--R +--R +--R (141) - log(coth(x) + 1) +--R Type: Expression Integer +--E 141 + +--S 142 of 526 +a0627:= integrate(t0627,x) +--R +--R +--R 2sinh(x) +--R (142) log(- -----------------) - 2x +--R sinh(x) - cosh(x) +--R Type: Union(Expression Integer,...) +--E 142 + +--S 143 of 526 +m0627:= a0627-r0627 +--R +--R +--R 2sinh(x) +--R (143) log(coth(x) + 1) + log(- -----------------) - 2x +--R sinh(x) - cosh(x) +--R Type: Expression Integer +--E 143 + +--S 144 of 526 +d0627:= D(m0627,x) +--R +--R +--R - coth(x)sinh(x) + cosh(x) +--R (144) -------------------------- +--R sinh(x) +--R Type: Expression Integer +--E 144 + +--S 145 of 526 +t0628:= csch(x)^3/(1+coth(x)) +--R +--R +--R 3 +--R csch(x) +--R (145) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 145 + +--S 146 of 526 +r0628:= acoth(cosh(x))-csch(x) +--R +--R +--R (146) acoth(cosh(x)) - csch(x) +--R Type: Expression Integer +--E 146 + +--S 147 of 526 +a0628:= integrate(t0628,x) +--R +--R +--R (147) +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(sinh(x) + cosh(x) - 1) +--R + +--R - 2sinh(x) - 2cosh(x) +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Union(Expression Integer,...) +--E 147 + +--S 148 of 526 +m0628:= a0628-r0628 +--R +--R +--R (148) +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)acoth(cosh(x)) +--R + +--R 2 2 +--R csch(x)sinh(x) + (2cosh(x)csch(x) - 2)sinh(x) + (cosh(x) - 1)csch(x) +--R + +--R - 2cosh(x) +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Expression Integer +--E 148 + +--S 149 of 526 +d0628:= D(m0628,x) +--R +--R +--R (149) +--R 5 2 4 +--R sinh(x) + ((- cosh(x) + 1)coth(x)csch(x) + 4cosh(x))sinh(x) +--R + +--R 3 2 3 +--R ((- 4cosh(x) + 4cosh(x))coth(x)csch(x) + 6cosh(x) - 2)sinh(x) +--R + +--R 4 2 3 +--R ((- 6cosh(x) + 8cosh(x) - 2)coth(x)csch(x) + 4cosh(x) - 4cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 4 +--R (- 4cosh(x) + 8cosh(x) - 4cosh(x))coth(x)csch(x) + cosh(x) +--R + +--R 2 +--R 2cosh(x) - 3 +--R * +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- cosh(x) + 3cosh(x) - 3cosh(x) + 1)coth(x)csch(x) + 4cosh(x) +--R + +--R - 4cosh(x) +--R / +--R 2 4 3 3 +--R (cosh(x) - 1)sinh(x) + (4cosh(x) - 4cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (6cosh(x) - 8cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (4cosh(x) - 8cosh(x) + 4cosh(x))sinh(x) + cosh(x) - 3cosh(x) +--R + +--R 2 +--R 3cosh(x) - 1 +--R Type: Expression Integer +--E 149 + +--S 150 of 526 +t0629:= csch(x)^4/(1+coth(x)) +--R +--R +--R 4 +--R csch(x) +--R (150) ----------- +--R coth(x) + 1 +--R Type: Expression Integer +--E 150 + +--S 151 of 526 +r0629:= -1/2*coth(x)*(-2+coth(x)) +--R +--R +--R 2 +--R - coth(x) + 2coth(x) +--R (151) --------------------- +--R 2 +--R Type: Expression Integer +--E 151 + +--S 152 of 526 +a0629:= integrate(t0629,x) +--R +--R +--R (152) +--R - +--R 2 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Union(Expression Integer,...) +--E 152 + +--S 153 of 526 +m0629:= a0629-r0629 +--R +--R +--R (153) +--R 2 4 +--R (coth(x) - 2coth(x))sinh(x) +--R + +--R 2 3 +--R (4cosh(x)coth(x) - 8cosh(x)coth(x))sinh(x) +--R + +--R 2 2 2 2 +--R ((6cosh(x) - 2)coth(x) + (- 12cosh(x) + 4)coth(x))sinh(x) +--R + +--R 3 2 3 +--R ((4cosh(x) - 4cosh(x))coth(x) + (- 8cosh(x) + 8cosh(x))coth(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (cosh(x) - 2cosh(x) + 1)coth(x) + (- 2cosh(x) + 4cosh(x) - 2)coth(x) +--R + +--R - 4 +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Expression Integer +--E 153 + +--S 154 of 526 +d0629:= D(m0629,x) +--R +--R +--R (154) +--R 3 2 6 +--R (- coth(x) + coth(x) + coth(x) - 1)sinh(x) +--R + +--R 3 2 +--R (- 6cosh(x)coth(x) + 6cosh(x)coth(x) + 6cosh(x)coth(x) - 6cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 15cosh(x) + 3)coth(x) + (15cosh(x) - 3)coth(x) +--R + +--R 2 2 +--R (15cosh(x) - 3)coth(x) - 15cosh(x) + 3 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 +--R (- 20cosh(x) + 12cosh(x))coth(x) + (20cosh(x) - 12cosh(x))coth(x) +--R + +--R 3 3 +--R (20cosh(x) - 12cosh(x))coth(x) - 20cosh(x) + 12cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 +--R (- 15cosh(x) + 18cosh(x) - 3)coth(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 18cosh(x) + 3)coth(x) +--R + +--R 4 2 4 2 +--R (15cosh(x) - 18cosh(x) + 3)coth(x) - 15cosh(x) + 18cosh(x) + 5 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 6cosh(x) + 12cosh(x) - 6cosh(x))coth(x) +--R + +--R 5 3 2 +--R (6cosh(x) - 12cosh(x) + 6cosh(x))coth(x) +--R + +--R 5 3 5 3 +--R (6cosh(x) - 12cosh(x) + 6cosh(x))coth(x) - 6cosh(x) + 12cosh(x) +--R + +--R 10cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- cosh(x) + 3cosh(x) - 3cosh(x) + 1)coth(x) +--R + +--R 6 4 2 2 +--R (cosh(x) - 3cosh(x) + 3cosh(x) - 1)coth(x) +--R + +--R 6 4 2 6 4 +--R (cosh(x) - 3cosh(x) + 3cosh(x) - 1)coth(x) - cosh(x) + 3cosh(x) +--R + +--R 2 +--R 5cosh(x) + 1 +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 3)sinh(x) +--R + +--R 3 3 4 2 2 +--R (20cosh(x) - 12cosh(x))sinh(x) + (15cosh(x) - 18cosh(x) + 3)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 12cosh(x) + 6cosh(x))sinh(x) + cosh(x) - 3cosh(x) +--R + +--R 2 +--R 3cosh(x) - 1 +--R Type: Expression Integer +--E 154 + +--S 155 of 526 +t0630:= sinh(x)/(a+b*sech(x)) +--R +--R +--R sinh(x) +--R (155) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 155 + +--S 156 of 526 +r0630:= cosh(x)/a-b*log(b+a*cosh(x))/a^2 +--R +--R +--R - b log(a cosh(x) + b) + a cosh(x) +--R (156) ---------------------------------- +--R 2 +--R a +--R Type: Expression Integer +--E 156 + +--S 157 of 526 +a0630:= integrate(t0630,x) +--R +--R +--R (157) +--R - 2a cosh(x) - 2b 2 +--R (- 2b sinh(x) - 2b cosh(x))log(-----------------) + a sinh(x) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (2a cosh(x) + 2b x)sinh(x) + a cosh(x) + 2b x cosh(x) + a +--R / +--R 2 2 +--R 2a sinh(x) + 2a cosh(x) +--R Type: Union(Expression Integer,...) +--E 157 + +--S 158 of 526 +m0630:= a0630-r0630 +--R +--R +--R (158) +--R (2b sinh(x) + 2b cosh(x))log(a cosh(x) + b) +--R + +--R - 2a cosh(x) - 2b 2 +--R (- 2b sinh(x) - 2b cosh(x))log(-----------------) + a sinh(x) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R 2b x sinh(x) - a cosh(x) + 2b x cosh(x) + a +--R / +--R 2 2 +--R 2a sinh(x) + 2a cosh(x) +--R Type: Expression Integer +--E 158 + +--S 159 of 526 +d0630:= D(m0630,x) +--R +--R +--R 2 2 +--R - sinh(x) + cosh(x) - 1 +--R (159) ------------------------- +--R 2a sinh(x) + 2a cosh(x) +--R Type: Expression Integer +--E 159 + +--S 160 of 526 +t0631:= sinh(x)^2/(a+b*sech(x)) +--R +--R +--R 2 +--R sinh(x) +--R (160) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 160 + +--S 161 of 526 +r0631:= 1/2*(-a^2*x+2*b^2*x+4*b*(a^2-b^2)^(1/2)*_ + atan((a-b)*(cosh(x)-1)/sinh(x)/(a^2-b^2)^(1/2))-_ + 2*a*b*sinh(x)+a^2*cosh(x)*sinh(x))/a^3 +--R +--R +--R (161) +--R +---------+ +--R | 2 2 (b - a)cosh(x) - b + a 2 +--R - 4b\|- b + a atan(----------------------) + (a cosh(x) - 2a b)sinh(x) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R + +--R 2 2 +--R (2b - a )x +--R / +--R 3 +--R 2a +--R Type: Expression Integer +--E 161 + +--S 162 of 526 +a0631:= integrate(t0631,x) +--R +--R +--R (162) +--R [ +--R +-------+ +--R 2 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b +--R + +--R 2 +--R - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b - 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b - 8a )x cosh(x) + 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b - 4a )x cosh(x) + 4a b cosh(x) - a +--R / +--R 3 2 3 3 2 +--R 8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) +--R , +--R +--R +---------+ +--R 2 2 | 2 2 +--R (- 16b sinh(x) - 32b cosh(x)sinh(x) - 16b cosh(x) )\|- b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b - 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b - 8a )x cosh(x) + 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b - 4a )x cosh(x) + 4a b cosh(x) - a +--R / +--R 3 2 3 3 2 +--R 8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) +--R ] +--R Type: Union(List Expression Integer,...) +--E 162 + +--S 163 of 526 +m0631a:= a06311.1-r0631 +--R +--R There are no library operations named a06311 +--R Use HyperDoc Browse or issue +--R )what op a06311 +--R to learn if there is any operation containing " a06311 " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R a06311 with argument type(s) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 163 + +--S 164 of 526 +d0631a:= D(m0631a,x) +--R +--R +--R (163) 0 +--R Type: Polynomial Integer +--E 164 + +--S 165 of 526 +m0631b:= a0631.2-r0631 +--R +--R +--R (164) +--R +---------+ +--R 2 2 | 2 2 +--R (- 16b sinh(x) - 32b cosh(x)sinh(x) - 16b cosh(x) )\|- b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (16b sinh(x) + 32b cosh(x)sinh(x) + 16b cosh(x) )\|- b + a +--R * +--R (b - a)cosh(x) - b + a +--R atan(----------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R + +--R 2 4 3 2 2 2 +--R a sinh(x) + 4a b sinh(x) + (- 2a cosh(x) + 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (- 4a b cosh(x) + 4a b)sinh(x) + a cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) - a +--R / +--R 3 2 3 3 2 +--R 8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) +--R Type: Expression Integer +--E 165 + +--S 166 of 526 +d0631b:= D(m0631b,x) +--R +--R +--R (165) +--R 3 4 8 3 4 2 2 3 7 +--R (- a b - a )sinh(x) + ((- 2a b - 2a )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 3 2 2 2 3 4 3 2 2 3 +--R 2a b cosh(x) + (- 8a b - 10a b + 2a )cosh(x) + 4a b - 4a b - 8a b +--R + +--R 4 +--R - 2a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 4 2 +--R (6a b + 2a )cosh(x) + (4a b - 8a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 +--R (24a b - 16a b - 22a b - 2a )cosh(x) + 8b - 8a b - 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 2 2 3 4 3 +--R 2a cosh(x) + (16a b + 2a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 2 +--R (44a b - 20a b - 22a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R (24b - 24a b - 16a b - 2a b + 2a )cosh(x) + 8a b - 8a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 5 2 2 3 4 4 +--R (- 6a b + 2a )cosh(x) + (4a b + 12a b - 8a )cosh(x) +--R + +--R 3 3 4 3 4 3 3 2 +--R (16a b - 4a b + 4a )cosh(x) + (16b - 16a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 3 +--R (32a b - 24a b - 22a b + 2a )cosh(x) + 8b - 8a b - 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 2 2 3 4 5 +--R - 2a b cosh(x) + (- 8a b + 10a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 36a b + 20a b + 20a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 16b + 16a b + 16a b - 12a b - 4a )cosh(x) +--R + +--R 3 2 2 3 4 2 +--R (48a b - 24a b - 34a b + 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 4 +--R (24b - 24a b - 8a b + 10a b - 2a )cosh(x) + 4a b - 4a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 7 2 2 4 6 +--R (2a b - 2a )cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 40a b + 16a b + 26a b - 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 24b + 24a b + 8a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (32a b - 8a b - 26a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (24b - 24a b - 4a b + 8a b - 4a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (8a b - 8a b - 2a b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 8 3 4 7 +--R (a b - a )cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 6 +--R (- 12a b + 4a b + 10a b - 2a )cosh(x) +--R + +--R 4 3 3 4 5 3 3 4 +--R (- 8b + 8a b - 2a b + 2a )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 4 3 3 4 3 3 2 2 3 4 2 +--R (8b - 8a b + 2a b - 2a )cosh(x) + (4a b - 4a b - 2a b + 2a )cosh(x) +--R + +--R 3 4 3 4 +--R (2a b - 2a )cosh(x) - a b + a +--R / +--R 4 5 6 4 5 3 2 4 5 +--R (4a b + 4a )sinh(x) + ((16a b + 16a )cosh(x) + 8a b + 8a b)sinh(x) +--R + +--R 4 5 2 3 2 4 5 5 4 +--R ((20a b + 28a )cosh(x) + (24a b + 32a b - 8a )cosh(x) + 8a )sinh(x) +--R + +--R 5 3 3 2 4 5 2 +--R 32a cosh(x) + (16a b + 64a b - 32a )cosh(x) +--R + +--R 3 2 4 5 3 2 4 +--R (16a b - 24a b + 24a )cosh(x) - 8a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 4 3 2 4 5 3 +--R (- 20a b + 28a )cosh(x) + (- 16a b + 80a b - 48a )cosh(x) +--R + +--R 3 2 4 5 2 3 2 4 5 +--R (48a b - 72a b + 32a )cosh(x) + (- 24a b + 32a b - 8a )cosh(x) +--R + +--R 4 5 +--R - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 5 3 2 4 5 4 +--R (- 16a b + 16a )cosh(x) + (- 24a b + 56a b - 32a )cosh(x) +--R + +--R 3 2 4 5 3 3 2 4 5 2 +--R (48a b - 72a b + 24a )cosh(x) + (- 24a b + 40a b - 16a )cosh(x) +--R + +--R 4 5 +--R (- 8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 5 6 3 2 4 5 5 +--R (- 4a b + 4a )cosh(x) + (- 8a b + 16a b - 8a )cosh(x) +--R + +--R 3 2 4 5 4 3 2 4 5 3 +--R (16a b - 24a b + 8a )cosh(x) + (- 8a b + 16a b - 8a )cosh(x) +--R + +--R 4 5 2 +--R (- 4a b + 4a )cosh(x) +--R Type: Expression Integer +--E 166 + +--S 167 of 526 +t0632:= sinh(x)^3/(a+b*sech(x)) +--R +--R +--R 3 +--R sinh(x) +--R (166) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 167 + +--S 168 of 526 +r0632:= -(a^2-b^2)*cosh(x)/a^3-1/2*b*cosh(x)^2/a^2+1/3*cosh(x)^3/a+_ + b*(a^2-b^2)*log(b+a*cosh(x))/a^4 +--R +--R +--R (167) +--R 3 2 3 3 2 2 +--R (- 6b + 6a b)log(a cosh(x) + b) + 2a cosh(x) - 3a b cosh(x) +--R + +--R 2 3 +--R (6a b - 6a )cosh(x) +--R / +--R 4 +--R 6a +--R Type: Expression Integer +--E 168 + +--S 169 of 526 +a0632:= integrate(t0632,x) +--R +--R +--R (168) +--R 3 2 3 3 2 2 +--R (- 24b + 24a b)sinh(x) + (- 72b + 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 72b + 72a b)cosh(x) sinh(x) + (- 24b + 24a b)cosh(x) +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b - 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 20a cosh(x) - 30a b cosh(x) + (48a b - 36a )cosh(x) +--R + +--R 3 2 +--R (24b - 24a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 15a cosh(x) - 30a b cosh(x) + (72a b - 54a )cosh(x) +--R + +--R 3 2 2 3 +--R (72b - 72a b)x cosh(x) + 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (48a b - 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (72b - 72a b)x cosh(x) + (24a b - 18a )cosh(x) - 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b - 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R (24b - 24a b)x cosh(x) + (12a b - 9a )cosh(x) - 3a b cosh(x) + a +--R / +--R 4 3 4 2 4 2 4 3 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) +--R Type: Union(Expression Integer,...) +--E 169 + +--S 170 of 526 +m0632:= a0632-r0632 +--R +--R +--R (169) +--R 3 2 3 3 2 2 +--R (24b - 24a b)sinh(x) + (72b - 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (72b - 72a b)cosh(x) sinh(x) + (24b - 24a b)cosh(x) +--R * +--R log(a cosh(x) + b) +--R + +--R 3 2 3 3 2 2 +--R (- 24b + 24a b)sinh(x) + (- 72b + 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 72b + 72a b)cosh(x) sinh(x) + (- 24b + 24a b)cosh(x) +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b - 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 12a cosh(x) - 18a b cosh(x) + (24a b - 12a )cosh(x) +--R + +--R 3 2 +--R (24b - 24a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 +--R - 9a cosh(x) + 6a b cosh(x) + 18a cosh(x) +--R + +--R 3 2 2 3 +--R (72b - 72a b)x cosh(x) + 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R - 18a cosh(x) + 21a b cosh(x) + (- 24a b + 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (72b - 72a b)x cosh(x) + (24a b - 18a )cosh(x) - 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R - 7a cosh(x) + 9a b cosh(x) + (- 12a b + 15a )cosh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R (24b - 24a b)x cosh(x) + (12a b - 9a )cosh(x) - 3a b cosh(x) + a +--R / +--R 4 3 4 2 4 2 4 3 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) +--R Type: Expression Integer +--E 170 + +--S 171 of 526 +d0632:= D(m0632,x) +--R +--R +--R (170) +--R 2 6 2 5 +--R a sinh(x) + (6a cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 4 +--R (7a cosh(x) - 2a b cosh(x) - 4b + 5a )sinh(x) +--R + +--R 2 3 2 2 2 3 +--R (- 4a cosh(x) + 4a b cosh(x) + (- 8b + 12a )cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 2 2 +--R (- 9a cosh(x) + 4a b cosh(x) + 6a cosh(x) - 4b + 3a )sinh(x) +--R + +--R 2 5 4 2 2 3 +--R - 2a cosh(x) - 2a b cosh(x) + (8b - 4a )cosh(x) +--R + +--R 2 2 +--R (- 8b + 6a )cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 6 5 2 2 4 2 2 2 +--R a cosh(x) - 2a b cosh(x) + (4b - 3a )cosh(x) + (- 4b + 3a )cosh(x) +--R + +--R 2 +--R 2a b cosh(x) - a +--R / +--R 3 3 3 2 3 2 3 3 +--R 8a sinh(x) + 24a cosh(x)sinh(x) + 24a cosh(x) sinh(x) + 8a cosh(x) +--R Type: Expression Integer +--E 171 + +--S 172 of 526 +t0633:= sinh(x)^4/(a+b*sech(x)) +--R +--R +--R 4 +--R sinh(x) +--R (171) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 172 + +--S 173 of 526 +r0633:= -5/8*x/a+1/2*b^2*x/a^3+(a^2-b^2)^2*x/a^5-2*b*(a^2-b^2)^(3/2)*_ + atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a^5+b*sinh(x)/a^2-_ + b^3*sinh(x)/a^4-5/8*cosh(x)*sinh(x)/a+1/2*b^2*cosh(x)*sinh(x)/a^3+_ + 1/4*cosh(x)^3*sinh(x)/a-1/3*b*sinh(x)^3/a^2 +--R +--R +--R (172) +--R x +--R +---------+ (b - a)tanh(-) +--R 3 2 | 2 2 2 3 3 +--R (- 48b + 48a b)\|- b + a atan(--------------) - 8a b sinh(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 2 2 4 3 3 +--R (6a cosh(x) + (12a b - 15a )cosh(x) - 24a b + 24a b)sinh(x) +--R + +--R 4 2 2 4 +--R (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R Type: Expression Integer +--E 173 + +--S 174 of 526 +a0633:= integrate(t0633,x) +--R +--R +--R (173) +--R [ +--R 3 2 4 3 2 3 +--R (192b - 192a b)sinh(x) + (768b - 768a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (1152b - 1152a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (768b - 768a b)cosh(x) sinh(x) + (192b - 192a b)cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b +--R + +--R 2 +--R - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 168a cosh(x) - 168a b cosh(x) + (144a b - 144a )cosh(x) - 96a b +--R + +--R 3 +--R 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b + 600a b)cosh(x) + (192b - 288a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b - 480a )cosh(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 960a b + 1200a b)cosh(x) + (768b - 1152a b + 288a )x cosh(x) +--R + +--R 3 3 +--R 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 3 +--R (- 960a b + 1200a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (1152b - 1728a b + 432a )x cosh(x) + (288a b - 360a b)cosh(x) +--R + +--R 2 2 4 +--R - 24a b + 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 3 3 4 4 2 2 4 3 +--R (- 480a b + 600a b)cosh(x) + (768b - 1152a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (288a b - 360a b)cosh(x) + (- 48a b + 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b + 120a b)cosh(x) + (192b - 288a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (96a b - 120a b)cosh(x) + (- 24a b + 24a )cosh(x) + 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R , +--R +--R 3 2 4 3 2 3 +--R (- 384b + 384a b)sinh(x) + (- 1536b + 1536a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (- 2304b + 2304a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (- 1536b + 1536a b)cosh(x) sinh(x) + (- 384b + 384a b)cosh(x) +--R * +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R \|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 168a cosh(x) - 168a b cosh(x) + (144a b - 144a )cosh(x) - 96a b +--R + +--R 3 +--R 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b + 600a b)cosh(x) + (192b - 288a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b - 480a )cosh(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 960a b + 1200a b)cosh(x) + (768b - 1152a b + 288a )x cosh(x) +--R + +--R 3 3 +--R 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 3 +--R (- 960a b + 1200a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (1152b - 1728a b + 432a )x cosh(x) + (288a b - 360a b)cosh(x) +--R + +--R 2 2 4 +--R - 24a b + 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 3 3 4 4 2 2 4 3 +--R (- 480a b + 600a b)cosh(x) + (768b - 1152a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (288a b - 360a b)cosh(x) + (- 48a b + 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b + 120a b)cosh(x) + (192b - 288a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (96a b - 120a b)cosh(x) + (- 24a b + 24a )cosh(x) + 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R ] +--R Type: Union(List Expression Integer,...) +--E 174 + +--S 175 of 526 +m0633:= a0633.1-r0633 +--R +--R +--R (174) +--R 3 2 4 3 2 3 +--R (192b - 192a b)sinh(x) + (768b - 768a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 3 +--R (1152b - 1152a b)cosh(x) sinh(x) + (768b - 768a b)cosh(x) sinh(x) +--R + +--R 3 2 4 +--R (192b - 192a b)cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 3 2 4 3 2 3 +--R (384b - 384a b)sinh(x) + (1536b - 1536a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (2304b - 2304a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (1536b - 1536a b)cosh(x) sinh(x) + (384b - 384a b)cosh(x) +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) + 56a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) + 200a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 120a cosh(x) + 216a b cosh(x) + (48a b - 24a )cosh(x) + 96a b +--R + +--R 3 +--R - 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 24a b cosh(x) + (- 24a b + 120a )cosh(x) +--R + +--R 3 3 +--R (288a b - 168a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R - 120a cosh(x) - 216a b cosh(x) + (- 96a b + 240a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (192a b + 48a b)cosh(x) + 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R - 108a cosh(x) - 168a b cosh(x) + (- 24a b + 120a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 +--R (- 192a b + 432a b)cosh(x) + (288a b - 360a b)cosh(x) - 24a b +--R + +--R 4 +--R 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R - 24a cosh(x) - 56a b cosh(x) + (48a b - 24a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (- 288a b + 408a b)cosh(x) + (288a b - 360a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b + 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (- 96a b + 120a b)cosh(x) + (96a b - 120a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b + 24a )cosh(x) + 8a b cosh(x) - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R Type: Expression Integer +--E 175 + +--S 176 of 526 +d0633:= D(m0633a,x) +--R +--R +--R (175) 0 +--R Type: Polynomial Integer +--E 176 + +--S 177 of 526 +m0633:= a0633.2-r0633 +--R +--R +--R (176) +--R 3 2 4 3 2 3 +--R (- 384b + 384a b)sinh(x) + (- 1536b + 1536a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (- 2304b + 2304a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (- 1536b + 1536a b)cosh(x) sinh(x) + (- 384b + 384a b)cosh(x) +--R * +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R \|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R 3 2 4 3 2 3 +--R (384b - 384a b)sinh(x) + (1536b - 1536a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (2304b - 2304a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (1536b - 1536a b)cosh(x) sinh(x) + (384b - 384a b)cosh(x) +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) + 56a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) + 200a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 120a cosh(x) + 216a b cosh(x) + (48a b - 24a )cosh(x) + 96a b +--R + +--R 3 +--R - 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 24a b cosh(x) + (- 24a b + 120a )cosh(x) +--R + +--R 3 3 +--R (288a b - 168a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R - 120a cosh(x) - 216a b cosh(x) + (- 96a b + 240a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (192a b + 48a b)cosh(x) + 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R - 108a cosh(x) - 168a b cosh(x) + (- 24a b + 120a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 +--R (- 192a b + 432a b)cosh(x) + (288a b - 360a b)cosh(x) - 24a b +--R + +--R 4 +--R 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R - 24a cosh(x) - 56a b cosh(x) + (48a b - 24a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (- 288a b + 408a b)cosh(x) + (288a b - 360a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b + 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (- 96a b + 120a b)cosh(x) + (96a b - 120a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b + 24a )cosh(x) + 8a b cosh(x) - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R Type: Expression Integer +--E 177 + +--S 178 of 526 +d0633:= D(m0633b,x) +--R +--R +--R (177) 0 +--R Type: Polynomial Integer +--E 178 + +--S 179 of 526 +t0634:= sinh(x)/(a+a*sech(x)) +--R +--R +--R sinh(x) +--R (178) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 179 + +--S 180 of 526 +r0634:= -(-cosh(x)+log(1+cosh(x)))/a +--R +--R +--R - log(cosh(x) + 1) + cosh(x) +--R (179) ---------------------------- +--R a +--R Type: Expression Integer +--E 180 + +--S 181 of 526 +a0634:= integrate(t0634,x) +--R +--R +--R (180) +--R 2 +--R (- 4sinh(x) - 4cosh(x))log(sinh(x) + cosh(x) + 1) + sinh(x) +--R + +--R 2 +--R (2cosh(x) + 2x)sinh(x) + cosh(x) + 2x cosh(x) + 1 +--R / +--R 2a sinh(x) + 2a cosh(x) +--R Type: Union(Expression Integer,...) +--E 181 + +--S 182 of 526 +m0634:= a0634-r0634 +--R +--R +--R (181) +--R (- 4sinh(x) - 4cosh(x))log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (2sinh(x) + 2cosh(x))log(cosh(x) + 1) + sinh(x) + 2x sinh(x) - cosh(x) +--R + +--R 2x cosh(x) + 1 +--R / +--R 2a sinh(x) + 2a cosh(x) +--R Type: Expression Integer +--E 182 + +--S 183 of 526 +d0634:= D(m0634,x) +--R +--R +--R (182) +--R 3 2 2 +--R (- cosh(x) + 1)sinh(x) + (- cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 +--R (cosh(x) - cosh(x) - cosh(x) + 1)sinh(x) + cosh(x) - 1 +--R / +--R 2 2 +--R (2a cosh(x) + 2a)sinh(x) + (4a cosh(x) + 6a cosh(x) + 2a)sinh(x) +--R + +--R 3 2 +--R 2a cosh(x) + 4a cosh(x) + 2a cosh(x) +--R Type: Expression Integer +--E 183 + +--S 184 of 526 +t0635:= sinh(x)^2/(a+a*sech(x)) +--R +--R +--R 2 +--R sinh(x) +--R (183) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 184 + +--S 185 of 526 +r0635:= 1/2*(x-2*sinh(x)+cosh(x)*sinh(x))/a +--R +--R +--R (cosh(x) - 2)sinh(x) + x +--R (184) ------------------------ +--R 2a +--R Type: Expression Integer +--E 185 + +--S 186 of 526 +a0635:= integrate(t0635,x) +--R +--R +--R (cosh(x) - 2)sinh(x) + x +--R (185) ------------------------ +--R 2a +--R Type: Union(Expression Integer,...) +--E 186 + +--S 187 of 526 +m0635:= a0635-r0635 +--R +--R +--R (186) 0 +--R Type: Expression Integer +--E 187 + +--S 188 of 526 +d0635:= D(m0635,x) +--R +--R +--R (187) 0 +--R Type: Expression Integer +--E 188 + +--S 189 of 526 +t0636:= sinh(x)^3/(a+a*sech(x)) +--R +--R +--R 3 +--R sinh(x) +--R (188) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 189 + +--S 190 of 526 +r0636:= 1/6*cosh(x)^2*(-3+2*cosh(x))/a +--R +--R +--R 3 2 +--R 2cosh(x) - 3cosh(x) +--R (189) --------------------- +--R 6a +--R Type: Expression Integer +--E 190 + +--S 191 of 526 +a0636:= integrate(t0636,x) +--R +--R +--R 2 3 2 +--R (3cosh(x) - 3)sinh(x) + cosh(x) - 3cosh(x) + 3cosh(x) +--R (190) -------------------------------------------------------- +--R 12a +--R Type: Union(Expression Integer,...) +--E 191 + +--S 192 of 526 +m0636:= a0636-r0636 +--R +--R +--R 2 3 2 +--R (cosh(x) - 1)sinh(x) - cosh(x) + cosh(x) + cosh(x) +--R (191) ----------------------------------------------------- +--R 4a +--R Type: Expression Integer +--E 192 + +--S 193 of 526 +d0636:= D(m0636,x) +--R +--R +--R 3 2 +--R sinh(x) + (- cosh(x) + 1)sinh(x) +--R (192) ---------------------------------- +--R 4a +--R Type: Expression Integer +--E 193 + +--S 194 of 526 +t0637:= sinh(x)^4/(a+a*sech(x)) +--R +--R +--R 4 +--R sinh(x) +--R (193) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 194 + +--S 195 of 526 +r0637:= 1/24/a*(-3*cosh(x)*sinh(x)+6*cosh(x)^3*sinh(x)+8*sinh(x)-_ + 8*sinh(x)*cosh(x)^2-3*x) +--R +--R +--R 3 2 +--R (6cosh(x) - 8cosh(x) - 3cosh(x) + 8)sinh(x) - 3x +--R (194) -------------------------------------------------- +--R 24a +--R Type: Expression Integer +--E 195 + +--S 196 of 526 +a0637:= integrate(t0637,x) +--R +--R +--R 3 3 2 +--R (3cosh(x) - 2)sinh(x) + (3cosh(x) - 6cosh(x) + 6)sinh(x) - 3x +--R (195) ---------------------------------------------------------------- +--R 24a +--R Type: Union(Expression Integer,...) +--E 196 + +--S 197 of 526 +m0637:= a0637-r0637 +--R +--R +--R (196) +--R 3 3 2 +--R (3cosh(x) - 2)sinh(x) + (- 3cosh(x) + 2cosh(x) + 3cosh(x) - 2)sinh(x) +--R ------------------------------------------------------------------------ +--R 24a +--R Type: Expression Integer +--E 197 + +--S 198 of 526 +d0637:= D(m0637,x) +--R +--R +--R (197) +--R 4 2 4 3 2 +--R 3sinh(x) + (- 2cosh(x) + 3)sinh(x) - 3cosh(x) + 2cosh(x) + 3cosh(x) +--R + +--R - 2cosh(x) +--R / +--R 24a +--R Type: Expression Integer +--E 198 + +--S 199 of 526 +t0638:= cosh(x)/(a+b*sech(x)) +--R +--R +--R cosh(x) +--R (198) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 199 + +--S 200 of 526 +r0638:= -b*x/a^2+2*b^2*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/_ + a^2/(a^2-b^2)^(1/2)+sinh(x)/a +--R +--R +--R x +--R (b - a)tanh(-) +---------+ +--R 2 2 | 2 2 +--R - 2b atan(--------------) + (a sinh(x) - b x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (199) --------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression Integer +--E 200 + +--S 201 of 526 +a0638:= integrate(t0638,x) +--R +--R +--R (200) +--R [ +--R 2 2 +--R (2b sinh(x) + 2b cosh(x)) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 2 +--R a sinh(x) + (2a cosh(x) - 2b x)sinh(x) + a cosh(x) - 2b x cosh(x) +--R + +--R - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|b - a +--R , +--R +--R 2 2 +--R (- 4b sinh(x) - 4b cosh(x)) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 +--R a sinh(x) + (2a cosh(x) - 2b x)sinh(x) + a cosh(x) - 2b x cosh(x) +--R + +--R - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 201 + +--S 202 of 526 +m0638a:= a0638.1-r0638 +--R +--R +--R (201) +--R +---------+ +--R 2 2 | 2 2 +--R (2b sinh(x) + 2b cosh(x))\|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R x +--R +-------+ (b - a)tanh(-) +--R 2 2 | 2 2 2 +--R (4b sinh(x) + 4b cosh(x))\|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (- a sinh(x) + a cosh(x) - a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|- b + a \|b - a +--R Type: Expression Integer +--E 202 + +--S 203 of 526 +d0638a:= D(m0638a,x) +--R +--R +--R (202) +--R 2 4 2 3 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((- 4b - 2a b)cosh(x) - 4b + 2a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R (- 2a b + 2a )cosh(x) + (- 8b + 2a b)cosh(x) +--R + +--R 2 2 +--R (- 8b + 2a b - 2a )cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (- a b + a )cosh(x) + (- 4b + 2a b)cosh(x) - 4b cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (- a b - a )sinh(x) + ((- 2a b - 2a )cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((4b - 2a b)cosh(x) - 4b - 2a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R (2a b + 2a )cosh(x) + (8b + 2a b)cosh(x) +--R + +--R 2 2 +--R (- 8b - 2a b - 2a )cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (a b + a )cosh(x) + (4b + 2a b)cosh(x) - 4b cosh(x) - 2a b cosh(x) +--R + +--R 2 +--R - a b - a +--R / +--R 2 3 3 2 3 2 2 2 +--R (2a b - 2a )sinh(x) + ((6a b - 6a )cosh(x) + 4a b - 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R ((6a b - 6a )cosh(x) + (8a b - 8a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 3 3 2 2 2 2 3 +--R (2a b - 2a )cosh(x) + (4a b - 4a b)cosh(x) + (2a b - 2a )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 3 2 2 2 +--R (- 2a b - 2a )sinh(x) + ((- 6a b - 6a )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R ((- 6a b - 6a )cosh(x) + (- 8a b - 8a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 3 3 2 2 2 2 3 +--R (- 2a b - 2a )cosh(x) + (- 4a b - 4a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R Type: Expression Integer +--E 203 + +--S 204 of 526 +m0638b:= a0638.2-r0638 +--R +--R +--R (203) +--R +---------+ +--R | 2 2 +--R 2 2 (a sinh(x) + a cosh(x) + b)\|- b + a +--R (- 4b sinh(x) - 4b cosh(x))atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R x +--R (b - a)tanh(-) +--R 2 2 2 +--R (4b sinh(x) + 4b cosh(x))atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- a sinh(x) + a cosh(x) - a)\|- b + a +--R / +--R +---------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|- b + a +--R Type: Expression Integer +--E 204 + +--S 205 of 526 +d0638b:= D(m0638b,x) +--R +--R +--R (204) +--R 2 4 2 3 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((- 4b - 2a b)cosh(x) - 4b + 2a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R (- 2a b + 2a )cosh(x) + (- 8b + 2a b)cosh(x) +--R + +--R 2 2 +--R (- 8b + 2a b - 2a )cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (- a b + a )cosh(x) + (- 4b + 2a b)cosh(x) - 4b cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (- a b - a )sinh(x) + ((- 2a b - 2a )cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((4b - 2a b)cosh(x) - 4b - 2a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R (2a b + 2a )cosh(x) + (8b + 2a b)cosh(x) +--R + +--R 2 2 +--R (- 8b - 2a b - 2a )cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (a b + a )cosh(x) + (4b + 2a b)cosh(x) - 4b cosh(x) - 2a b cosh(x) +--R + +--R 2 +--R - a b - a +--R / +--R 2 3 3 2 3 2 2 2 +--R (2a b - 2a )sinh(x) + ((6a b - 6a )cosh(x) + 4a b - 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R ((6a b - 6a )cosh(x) + (8a b - 8a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 3 3 2 2 2 2 3 +--R (2a b - 2a )cosh(x) + (4a b - 4a b)cosh(x) + (2a b - 2a )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 3 2 2 2 +--R (- 2a b - 2a )sinh(x) + ((- 6a b - 6a )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R ((- 6a b - 6a )cosh(x) + (- 8a b - 8a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 3 3 2 2 2 2 3 +--R (- 2a b - 2a )cosh(x) + (- 4a b - 4a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R Type: Expression Integer +--E 205 + +--S 206 of 526 +t0639:= cosh(x)^2/(a+b*sech(x)) +--R +--R +--R 2 +--R cosh(x) +--R (205) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 206 + +--S 207 of 526 +r0639:= 1/2*x/a+b^2*x/a^3-2*b^3*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/_ + a^3/(a^2-b^2)^(1/2)-b*sinh(x)/a^2+1/2*cosh(x)*sinh(x)/a +--R +--R +--R (206) +--R x +--R (b - a)tanh(-) +--R 3 2 +--R 4b atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R ((a cosh(x) - 2a b)sinh(x) + (2b + a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R Type: Expression Integer +--E 207 + +--S 208 of 526 +a0639:= integrate(t0639,x) +--R +--R +--R (207) +--R [ +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b + 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b + 8a )x cosh(x) + 4a b) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b + 4a )x cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|b - a +--R , +--R +--R 3 2 3 3 2 +--R (16b sinh(x) + 32b cosh(x)sinh(x) + 16b cosh(x) ) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b + 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b + 8a )x cosh(x) + 4a b) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b + 4a )x cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 3 3 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 208 + +--S 209 of 526 +m0639a:= a0639.1-r0639 +--R +--R +--R (208) +--R +---------+ +--R 3 2 3 3 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (- 16b sinh(x) - 32b cosh(x)sinh(x) - 16b cosh(x) )\|b - a +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 3 2 2 2 +--R a sinh(x) + 4a b sinh(x) + (- 2a cosh(x) + 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (- 4a b cosh(x) + 4a b)sinh(x) + a cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) - a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 3 2 3 3 2 | 2 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|- b + a \|b - a +--R Type: Expression Integer +--E 209 + +--S 210 of 526 +d0639a:= D(m0639a,x) +--R +--R +--R (209) +--R 2 3 6 2 3 2 2 5 +--R (- a b + a )sinh(x) + ((- 2a b + 2a )cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 2 3 +--R ((a b - a )cosh(x) + (- 8a b + 8a b)cosh(x) + 4a b - a b + a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 3 2 3 2 2 +--R ((4a b - 4a )cosh(x) + (8b + 8a b )cosh(x) + 8b - 4a b + 4a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 2 2 3 +--R (a b - a )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 3 2 3 2 3 2 2 +--R (24b + 2a b - 2a )cosh(x) + (24b - 8a b + 8a b)cosh(x) +--R + +--R 2 2 3 +--R 4a b + a b - a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 2 4 +--R (- 2a b + 2a )cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 3 2 3 3 2 2 2 +--R (24b - 8a b )cosh(x) + (24b - 4a b + 4a b)cosh(x) +--R + +--R 2 2 3 +--R (8a b + 2a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 3 2 2 3 4 3 3 +--R (- a b + a )cosh(x) + (8b - 4a b - a b + a )cosh(x) + 8b cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4a b + a b - a )cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 6 2 3 2 2 5 +--R (a b + a )sinh(x) + ((2a b + 2a )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 2 3 4 +--R ((- a b - a )cosh(x) + (8a b + 8a b)cosh(x) + 4a b + a b + a )sinh(x) +--R + +--R 2 3 3 3 2 3 2 2 +--R ((- 4a b - 4a )cosh(x) + (- 8b + 8a b )cosh(x) + 8b + 4a b + 4a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 2 2 3 +--R (- a b - a )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 3 2 3 2 3 2 2 2 +--R (- 24b - 2a b - 2a )cosh(x) + (24b + 8a b + 8a b)cosh(x) + 4a b +--R + +--R 2 3 +--R - a b - a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 2 4 +--R (2a b + 2a )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 3 2 3 3 2 2 2 +--R (- 24b - 8a b )cosh(x) + (24b + 4a b + 4a b)cosh(x) +--R + +--R 2 2 3 +--R (8a b - 2a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 3 2 2 3 4 3 3 +--R (a b + a )cosh(x) + (- 8b - 4a b + a b + a )cosh(x) + 8b cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4a b - a b - a )cosh(x) - a b - a +--R / +--R 3 4 4 3 4 2 2 3 3 +--R (4a b - 4a )sinh(x) + ((16a b - 16a )cosh(x) + 8a b - 8a b)sinh(x) +--R + +--R 3 4 2 2 2 3 3 4 +--R ((24a b - 24a )cosh(x) + (24a b - 24a b)cosh(x) + 4a b - 4a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R (16a b - 16a )cosh(x) + (24a b - 24a b)cosh(x) +--R + +--R 3 4 +--R (8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 2 2 3 3 3 4 2 +--R (4a b - 4a )cosh(x) + (8a b - 8a b)cosh(x) + (4a b - 4a )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 4 4 3 4 2 2 3 3 +--R (- 4a b - 4a )sinh(x) + ((- 16a b - 16a )cosh(x) - 8a b - 8a b)sinh(x) +--R + +--R 3 4 2 2 2 3 3 4 +--R ((- 24a b - 24a )cosh(x) + (- 24a b - 24a b)cosh(x) - 4a b - 4a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R (- 16a b - 16a )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 3 4 +--R (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 2 2 3 3 3 4 2 +--R (- 4a b - 4a )cosh(x) + (- 8a b - 8a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R Type: Expression Integer +--E 210 + +--S 211 of 526 +m0639b:= a0639.2-r0639 +--R +--R +--R (210) +--R 3 2 3 3 2 +--R (16b sinh(x) + 32b cosh(x)sinh(x) + 16b cosh(x) ) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R x +--R (b - a)tanh(-) +--R 3 2 3 3 2 2 +--R (- 16b sinh(x) - 32b cosh(x)sinh(x) - 16b cosh(x) )atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 3 2 2 2 +--R a sinh(x) + 4a b sinh(x) + (- 2a cosh(x) + 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (- 4a b cosh(x) + 4a b)sinh(x) + a cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 3 3 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|- b + a +--R Type: Expression Integer +--E 211 + +--S 212 of 526 +d0639b:= D(m0639b,x) +--R +--R +--R (211) +--R 2 3 6 2 3 2 2 5 +--R (- a b + a )sinh(x) + ((- 2a b + 2a )cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 2 3 +--R ((a b - a )cosh(x) + (- 8a b + 8a b)cosh(x) + 4a b - a b + a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 3 2 3 2 2 +--R ((4a b - 4a )cosh(x) + (8b + 8a b )cosh(x) + 8b - 4a b + 4a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 2 2 3 +--R (a b - a )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 3 2 3 2 3 2 2 +--R (24b + 2a b - 2a )cosh(x) + (24b - 8a b + 8a b)cosh(x) +--R + +--R 2 2 3 +--R 4a b + a b - a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 2 4 +--R (- 2a b + 2a )cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 3 2 3 3 2 2 2 +--R (24b - 8a b )cosh(x) + (24b - 4a b + 4a b)cosh(x) +--R + +--R 2 2 3 +--R (8a b + 2a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 3 2 2 3 4 3 3 +--R (- a b + a )cosh(x) + (8b - 4a b - a b + a )cosh(x) + 8b cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4a b + a b - a )cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 6 2 3 2 2 5 +--R (a b + a )sinh(x) + ((2a b + 2a )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 2 3 4 +--R ((- a b - a )cosh(x) + (8a b + 8a b)cosh(x) + 4a b + a b + a )sinh(x) +--R + +--R 2 3 3 3 2 3 2 2 +--R ((- 4a b - 4a )cosh(x) + (- 8b + 8a b )cosh(x) + 8b + 4a b + 4a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 2 2 3 +--R (- a b - a )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 3 2 3 2 3 2 2 2 +--R (- 24b - 2a b - 2a )cosh(x) + (24b + 8a b + 8a b)cosh(x) + 4a b +--R + +--R 2 3 +--R - a b - a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 2 4 +--R (2a b + 2a )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 3 2 3 3 2 2 2 +--R (- 24b - 8a b )cosh(x) + (24b + 4a b + 4a b)cosh(x) +--R + +--R 2 2 3 +--R (8a b - 2a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 3 2 2 3 4 3 3 +--R (a b + a )cosh(x) + (- 8b - 4a b + a b + a )cosh(x) + 8b cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4a b - a b - a )cosh(x) - a b - a +--R / +--R 3 4 4 3 4 2 2 3 3 +--R (4a b - 4a )sinh(x) + ((16a b - 16a )cosh(x) + 8a b - 8a b)sinh(x) +--R + +--R 3 4 2 2 2 3 3 4 +--R ((24a b - 24a )cosh(x) + (24a b - 24a b)cosh(x) + 4a b - 4a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R (16a b - 16a )cosh(x) + (24a b - 24a b)cosh(x) +--R + +--R 3 4 +--R (8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 2 2 3 3 3 4 2 +--R (4a b - 4a )cosh(x) + (8a b - 8a b)cosh(x) + (4a b - 4a )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 4 4 3 4 2 2 3 3 +--R (- 4a b - 4a )sinh(x) + ((- 16a b - 16a )cosh(x) - 8a b - 8a b)sinh(x) +--R + +--R 3 4 2 2 2 3 3 4 +--R ((- 24a b - 24a )cosh(x) + (- 24a b - 24a b)cosh(x) - 4a b - 4a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R (- 16a b - 16a )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 3 4 +--R (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 2 2 3 3 3 4 2 +--R (- 4a b - 4a )cosh(x) + (- 8a b - 8a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R Type: Expression Integer +--E 212 + +--S 213 of 526 +t0640:= cosh(x)^3/(a+b*sech(x)) +--R +--R +--R 3 +--R cosh(x) +--R (212) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 213 + +--S 214 of 526 +r0640:= -1/2*b*x/a^2-b^3*x/a^4+2*b^4*atan((a-b)*tanh(1/2*x)/_ + (a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)+sinh(x)/a+_ + b^2*sinh(x)/a^3-1/2*b*cosh(x)*sinh(x)/a^2+1/3*sinh(x)^3/a +--R +--R +--R (213) +--R x +--R (b - a)tanh(-) +--R 4 2 +--R - 12b atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 2 2 3 3 2 +--R (2a sinh(x) + (- 3a b cosh(x) + 6a b + 6a )sinh(x) + (- 6b - 3a b)x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R Type: Expression Integer +--E 214 + +--S 215 of 526 +a0640:= integrate(t0640,x) +--R +--R +--R (214) +--R [ +--R 4 3 4 2 4 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 4 3 +--R 24b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b + 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 20a cosh(x) - 30a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 +--R (- 24b - 12a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 15a cosh(x) - 30a b cosh(x) + (72a b + 54a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 72b - 36a b)x cosh(x) - 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 72b - 36a b)x cosh(x) + (- 24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 24b - 12a b)x cosh(x) + (- 12a b - 9a )cosh(x) +--R + +--R 2 3 +--R 3a b cosh(x) - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 3 4 2 4 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 4 3 +--R 24a cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 4 3 4 2 4 2 +--R - 48b sinh(x) - 144b cosh(x)sinh(x) - 144b cosh(x) sinh(x) +--R + +--R 4 3 +--R - 48b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b + 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 20a cosh(x) - 30a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 +--R (- 24b - 12a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 15a cosh(x) - 30a b cosh(x) + (72a b + 54a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 72b - 36a b)x cosh(x) - 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 72b - 36a b)x cosh(x) + (- 24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 24b - 12a b)x cosh(x) + (- 12a b - 9a )cosh(x) +--R + +--R 2 3 +--R 3a b cosh(x) - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 4 2 4 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 4 3 +--R 24a cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 215 + +--S 216 of 526 +m0640:= a0640.1-r0640 +--R +--R +--R (215) +--R 4 3 4 2 4 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 4 3 +--R 24b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 4 3 4 2 4 2 +--R 48b sinh(x) + 144b cosh(x)sinh(x) + 144b cosh(x) sinh(x) +--R + +--R 4 3 +--R 48b cosh(x) +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 6 3 2 5 +--R - 7a sinh(x) + (- 18a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (- 9a cosh(x) - 3a b cosh(x) - 12a b - 15a )sinh(x) +--R + +--R 3 3 2 2 2 3 3 +--R (12a cosh(x) + 6a b cosh(x) + (- 24a b - 36a )cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 2 3 2 +--R (15a cosh(x) + 6a b cosh(x) - 18a cosh(x) - 12a b - 9a )sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 3a b cosh(x) + (24a b + 12a )cosh(x) +--R + +--R 2 3 2 +--R (- 24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (- 12a b - 9a )cosh(x) + 3a b cosh(x) - a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) ) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 216 + +--S 217 of 526 +d0640:= D(m0640a,x) +--R +--R +--R (216) 0 +--R Type: Polynomial Integer +--E 217 + +--S 218 of 526 +m0640:= a0640.2-r0640 +--R +--R +--R (217) +--R 4 3 4 2 4 2 +--R - 48b sinh(x) - 144b cosh(x)sinh(x) - 144b cosh(x) sinh(x) +--R + +--R 4 3 +--R - 48b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 4 3 4 2 4 2 +--R 48b sinh(x) + 144b cosh(x)sinh(x) + 144b cosh(x) sinh(x) +--R + +--R 4 3 +--R 48b cosh(x) +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 6 3 2 5 +--R - 7a sinh(x) + (- 18a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (- 9a cosh(x) - 3a b cosh(x) - 12a b - 15a )sinh(x) +--R + +--R 3 3 2 2 2 3 3 +--R (12a cosh(x) + 6a b cosh(x) + (- 24a b - 36a )cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 2 3 2 +--R (15a cosh(x) + 6a b cosh(x) - 18a cosh(x) - 12a b - 9a )sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 3a b cosh(x) + (24a b + 12a )cosh(x) +--R + +--R 2 3 2 +--R (- 24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (- 12a b - 9a )cosh(x) + 3a b cosh(x) - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) ) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 218 + +--S 219 of 526 +d0640:= D(m0640b,x) +--R +--R +--R (218) 0 +--R Type: Polynomial Integer +--E 219 + +--S 220 of 526 +t0641:= cosh(x)^4/(a+b*sech(x)) +--R +--R +--R 4 +--R cosh(x) +--R (219) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 220 + +--S 221 of 526 +r0641:= 3/8*x/a+1/2*b^2*x/a^3+b^4*x/a^5-2*b^5*atan((a-b)*tanh(1/2*x)/_ + (a^2-b^2)^(1/2))/a^5/(a^2-b^2)^(1/2)-b*sinh(x)/a^2-_ + b^3*sinh(x)/a^4+3/8*cosh(x)*sinh(x)/a+1/2*b^2*cosh(x)*sinh(x)/a^3+_ + 1/4*cosh(x)^3*sinh(x)/a-1/3*b*sinh(x)^3/a^2 +--R +--R +--R (220) +--R x +--R (b - a)tanh(-) +--R 5 2 +--R 48b atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 +--R - 8a b sinh(x) +--R + +--R 4 3 2 2 4 3 3 +--R (6a cosh(x) + (12a b + 9a )cosh(x) - 24a b - 24a b)sinh(x) +--R + +--R 4 2 2 4 +--R (24b + 12a b + 9a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 24a \|- b + a +--R Type: Expression Integer +--E 221 + +--S 222 of 526 +a0641:= integrate(t0641,x) +--R +--R +--R (221) +--R [ +--R 5 4 5 3 5 2 2 +--R 192b sinh(x) + 768b cosh(x)sinh(x) + 1152b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768b cosh(x) sinh(x) + 192b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 +--R 168a cosh(x) - 168a b cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 3 3 +--R - 96a b - 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b - 360a b)cosh(x) + (192b + 96a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b + 480a )cosh(x) +--R + +--R 3 3 2 +--R (- 960a b - 720a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (768b + 384a b + 288a )x cosh(x) + 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 3 +--R (- 960a b - 720a b)cosh(x) +--R + +--R 4 2 2 4 2 +--R (1152b + 576a b + 432a )x cosh(x) +--R + +--R 3 3 2 2 4 +--R (288a b + 216a b)cosh(x) - 24a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 3 3 4 +--R (- 480a b - 360a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (768b + 384a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (288a b + 216a b)cosh(x) + (- 48a b - 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b - 72a b)cosh(x) + (192b + 96a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (96a b + 72a b)cosh(x) + (- 24a b - 24a )cosh(x) + 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 5 4 5 3 5 2 2 +--R 384b sinh(x) + 1536b cosh(x)sinh(x) + 2304b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 1536b cosh(x) sinh(x) + 384b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 +--R 168a cosh(x) - 168a b cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 3 3 +--R - 96a b - 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b - 360a b)cosh(x) + (192b + 96a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b + 480a )cosh(x) +--R + +--R 3 3 2 +--R (- 960a b - 720a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (768b + 384a b + 288a )x cosh(x) + 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 3 +--R (- 960a b - 720a b)cosh(x) +--R + +--R 4 2 2 4 2 +--R (1152b + 576a b + 432a )x cosh(x) +--R + +--R 3 3 2 2 4 +--R (288a b + 216a b)cosh(x) - 24a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 3 3 4 +--R (- 480a b - 360a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (768b + 384a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (288a b + 216a b)cosh(x) + (- 48a b - 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b - 72a b)cosh(x) + (192b + 96a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (96a b + 72a b)cosh(x) + (- 24a b - 24a )cosh(x) + 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 222 + +--S 223 of 526 +m0641:= a0641.1-r0641 +--R +--R +--R (222) +--R 5 4 5 3 5 2 2 +--R 192b sinh(x) + 768b cosh(x)sinh(x) + 1152b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768b cosh(x) sinh(x) + 192b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 5 4 5 3 5 2 2 +--R - 384b sinh(x) - 1536b cosh(x)sinh(x) - 2304b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R - 1536b cosh(x) sinh(x) - 384b cosh(x) +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) + 56a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) + 200a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 120a cosh(x) + 216a b cosh(x) + (48a b + 72a )cosh(x) + 96a b +--R + +--R 3 +--R 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 24a b cosh(x) + (- 24a b + 72a )cosh(x) +--R + +--R 3 3 +--R (288a b + 408a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R - 120a cosh(x) - 216a b cosh(x) + (- 96a b + 48a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (192a b + 432a b)cosh(x) + 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R - 108a cosh(x) - 168a b cosh(x) + (- 24a b + 72a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 +--R (- 192a b + 48a b)cosh(x) + (288a b + 216a b)cosh(x) - 24a b +--R + +--R 4 +--R - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R - 24a cosh(x) - 56a b cosh(x) + (48a b + 72a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (- 288a b - 168a b)cosh(x) + (288a b + 216a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b - 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (- 96a b - 72a b)cosh(x) + (96a b + 72a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b - 24a )cosh(x) + 8a b cosh(x) - 3a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 223 + +--S 224 of 526 +d0641:= D(m0641a,x) +--R +--R +--R (223) 0 +--R Type: Polynomial Integer +--E 224 + +--S 225 of 526 +m0641:= a0641.2-r0641 +--R +--R +--R (224) +--R 5 4 5 3 5 2 2 +--R 384b sinh(x) + 1536b cosh(x)sinh(x) + 2304b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 1536b cosh(x) sinh(x) + 384b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 5 4 5 3 5 2 2 +--R - 384b sinh(x) - 1536b cosh(x)sinh(x) - 2304b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R - 1536b cosh(x) sinh(x) - 384b cosh(x) +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) + 56a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) + 200a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 120a cosh(x) + 216a b cosh(x) + (48a b + 72a )cosh(x) + 96a b +--R + +--R 3 +--R 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 24a b cosh(x) + (- 24a b + 72a )cosh(x) +--R + +--R 3 3 +--R (288a b + 408a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R - 120a cosh(x) - 216a b cosh(x) + (- 96a b + 48a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (192a b + 432a b)cosh(x) + 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R - 108a cosh(x) - 168a b cosh(x) + (- 24a b + 72a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 +--R (- 192a b + 48a b)cosh(x) + (288a b + 216a b)cosh(x) - 24a b +--R + +--R 4 +--R - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R - 24a cosh(x) - 56a b cosh(x) + (48a b + 72a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (- 288a b - 168a b)cosh(x) + (288a b + 216a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b - 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (- 96a b - 72a b)cosh(x) + (96a b + 72a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b - 24a )cosh(x) + 8a b cosh(x) - 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 225 + +--S 226 of 526 +d0641:= D(m0641b,x) +--R +--R +--R (225) 0 +--R Type: Polynomial Integer +--E 226 + +--S 227 of 526 +t0642:= cosh(x)/(a+a*sech(x)) +--R +--R +--R cosh(x) +--R (226) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 227 + +--S 228 of 526 +r0642:= -x/a+sinh(x)/a+sinh(x)/a/(1+cosh(x)) +--R +--R +--R (cosh(x) + 2)sinh(x) - x cosh(x) - x +--R (227) ------------------------------------ +--R a cosh(x) + a +--R Type: Expression Integer +--E 228 + +--S 229 of 526 +a0642:= integrate(t0642,x) +--R +--R +--R (228) +--R 2 2 +--R sinh(x) + (2cosh(x) - 2x + 2)sinh(x) + cosh(x) - 2x cosh(x) - 2x - 5 +--R ---------------------------------------------------------------------- +--R 2a sinh(x) + 2a cosh(x) + 2a +--R Type: Union(Expression Integer,...) +--E 229 + +--S 230 of 526 +m0642:= a0642-r0642 +--R +--R +--R (229) +--R 2 3 2 +--R (- cosh(x) - 3)sinh(x) + (- 2cosh(x) - 2)sinh(x) + cosh(x) + cosh(x) +--R + +--R - 5cosh(x) - 5 +--R / +--R 2 +--R (2a cosh(x) + 2a)sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R Type: Expression Integer +--E 230 + +--S 231 of 526 +d0642:= D(m0642,x) +--R +--R +--R (230) +--R 4 2 3 +--R 2sinh(x) + (cosh(x) + 6cosh(x) + 5)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) + 2cosh(x) + 3cosh(x) + 2)sinh(x) +--R + +--R 4 3 2 5 +--R (- cosh(x) - 6cosh(x) - 4cosh(x) + 6cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 4 3 2 +--R - 4cosh(x) - 2cosh(x) + 4cosh(x) + 3cosh(x) +--R / +--R 2 2 +--R (2a cosh(x) + 4a cosh(x) + 2a)sinh(x) +--R + +--R 3 2 4 +--R (4a cosh(x) + 12a cosh(x) + 12a cosh(x) + 4a)sinh(x) + 2a cosh(x) +--R + +--R 3 2 +--R 8a cosh(x) + 12a cosh(x) + 8a cosh(x) + 2a +--R Type: Expression Integer +--E 231 + +--S 232 of 526 +t0643:= cosh(x)^2/(a+a*sech(x)) +--R +--R +--R 2 +--R cosh(x) +--R (231) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 232 + +--S 233 of 526 +r0643:= 1/2*(3*x+3*x*cosh(x)-4*sinh(x)-cosh(x)*sinh(x)+_ + sinh(x)*cosh(x)^2)/a/(1+cosh(x)) +--R +--R +--R 2 +--R (cosh(x) - cosh(x) - 4)sinh(x) + 3x cosh(x) + 3x +--R (232) ------------------------------------------------- +--R 2a cosh(x) + 2a +--R Type: Expression Integer +--E 233 + +--S 234 of 526 +a0643:= integrate(t0643,x) +--R +--R +--R (233) +--R 3 2 +--R sinh(x) + (3cosh(x) - 4)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4cosh(x) + 12x - 7)sinh(x) + cosh(x) - 4cosh(x) +--R + +--R (12x - 1)cosh(x) + 12x + 20 +--R / +--R 8a sinh(x) + 8a cosh(x) + 8a +--R Type: Union(Expression Integer,...) +--E 234 + +--S 235 of 526 +m0643:= a0643-r0643 +--R +--R +--R (234) +--R 3 2 2 +--R (cosh(x) + 1)sinh(x) + (- cosh(x) + 3cosh(x) + 12)sinh(x) +--R + +--R 3 2 4 3 +--R (- cosh(x) - cosh(x) + 9cosh(x) + 9)sinh(x) + cosh(x) - 3cosh(x) +--R + +--R 2 +--R - 5cosh(x) + 19cosh(x) + 20 +--R / +--R 2 +--R (8a cosh(x) + 8a)sinh(x) + 8a cosh(x) + 16a cosh(x) + 8a +--R Type: Expression Integer +--E 235 + +--S 236 of 526 +d0643:= D(m0643,x) +--R +--R +--R (235) +--R 2 4 +--R (- 2cosh(x) - 4cosh(x) - 10)sinh(x) +--R + +--R 2 3 +--R (- 5cosh(x) - 26cosh(x) - 21)sinh(x) +--R + +--R 4 3 2 2 +--R (4cosh(x) + 5cosh(x) - 4cosh(x) - 15cosh(x) - 10)sinh(x) +--R + +--R 4 3 2 6 +--R (5cosh(x) + 26cosh(x) + 16cosh(x) - 26cosh(x) - 21)sinh(x) - 2cosh(x) +--R + +--R 5 4 3 2 +--R - cosh(x) + 14cosh(x) + 12cosh(x) - 12cosh(x) - 11cosh(x) +--R / +--R 2 2 +--R (8a cosh(x) + 16a cosh(x) + 8a)sinh(x) +--R + +--R 3 2 4 +--R (16a cosh(x) + 48a cosh(x) + 48a cosh(x) + 16a)sinh(x) + 8a cosh(x) +--R + +--R 3 2 +--R 32a cosh(x) + 48a cosh(x) + 32a cosh(x) + 8a +--R Type: Expression Integer +--E 236 + +--S 237 of 526 +t0644:= cosh(x)^3/(a+a*sech(x)) +--R +--R +--R 3 +--R cosh(x) +--R (236) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 237 + +--S 238 of 526 +r0644:= 1/6*(7*cosh(x)*sinh(x)-sinh(x)*cosh(x)^2+_ + 16*sinh(x)+2*cosh(x)^3*sinh(x)-9*x*cosh(x)-9*x)/a/(1+cosh(x)) +--R +--R +--R 3 2 +--R (2cosh(x) - cosh(x) + 7cosh(x) + 16)sinh(x) - 9x cosh(x) - 9x +--R (237) --------------------------------------------------------------- +--R 6a cosh(x) + 6a +--R Type: Expression Integer +--E 238 + +--S 239 of 526 +a0644:= integrate(t0644,x) +--R +--R +--R (238) +--R 4 3 2 2 +--R sinh(x) + (4cosh(x) - 1)sinh(x) + (6cosh(x) - 9cosh(x) + 20)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 3cosh(x) + 32cosh(x) - 36x + 39)sinh(x) + cosh(x) +--R + +--R 3 2 +--R - 3cosh(x) + 20cosh(x) + (- 36x + 3)cosh(x) - 36x - 69 +--R / +--R 24a sinh(x) + 24a cosh(x) + 24a +--R Type: Union(Expression Integer,...) +--E 239 + +--S 240 of 526 +m0644:= a0644-r0644 +--R +--R +--R (239) +--R 4 2 3 +--R (cosh(x) + 1)sinh(x) + (4cosh(x) + 3cosh(x) - 1)sinh(x) +--R + +--R 3 2 2 +--R (- 2cosh(x) + cosh(x) - 17cosh(x) - 44)sinh(x) +--R + +--R 4 3 2 5 +--R (- 4cosh(x) - 3cosh(x) + 5cosh(x) - 21cosh(x) - 25)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R - 2cosh(x) + 17cosh(x) + 23cosh(x) - 66cosh(x) - 69 +--R / +--R 2 +--R (24a cosh(x) + 24a)sinh(x) + 24a cosh(x) + 48a cosh(x) + 24a +--R Type: Expression Integer +--E 240 + +--S 241 of 526 +d0644:= D(m0644,x) +--R +--R +--R (240) +--R 2 5 +--R (3cosh(x) + 6cosh(x) + 3)sinh(x) +--R + +--R 3 2 4 +--R (- cosh(x) + 6cosh(x) + 15cosh(x) + 32)sinh(x) +--R + +--R 4 3 2 3 +--R (- 2cosh(x) - 4cosh(x) + 25cosh(x) + 102cosh(x) + 75)sinh(x) +--R + +--R 5 4 3 2 2 +--R (6cosh(x) + 4cosh(x) + 9cosh(x) + 38cosh(x) + 59cosh(x) + 32)sinh(x) +--R + +--R 6 5 4 3 2 +--R - cosh(x) - 2cosh(x) - 24cosh(x) - 94cosh(x) - 47cosh(x) +--R + +--R 96cosh(x) + 72 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 5cosh(x) - 10cosh(x) - 20cosh(x) - 54cosh(x) - 19cosh(x) +--R + +--R 2 +--R 64cosh(x) + 44cosh(x) +--R / +--R 2 2 +--R (24a cosh(x) + 48a cosh(x) + 24a)sinh(x) +--R + +--R 3 2 4 +--R (48a cosh(x) + 144a cosh(x) + 144a cosh(x) + 48a)sinh(x) + 24a cosh(x) +--R + +--R 3 2 +--R 96a cosh(x) + 144a cosh(x) + 96a cosh(x) + 24a +--R Type: Expression Integer +--E 241 + +--S 242 of 526 +t0645:= cosh(x)^4/(a+a*sech(x)) +--R +--R +--R 4 +--R cosh(x) +--R (241) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 242 + +--S 243 of 526 +r0645:= 1/24*(-64*sinh(x)-2*cosh(x)^3*sinh(x)+6*cosh(x)^4*sinh(x)-_ + 19*cosh(x)*sinh(x)+13*sinh(x)*cosh(x)^2+45*x+_ + 45*x*cosh(x))/a/(1+cosh(x)) +--R +--R +--R (242) +--R 4 3 2 +--R (6cosh(x) - 2cosh(x) + 13cosh(x) - 19cosh(x) - 64)sinh(x) +--R + +--R 45x cosh(x) + 45x +--R / +--R 24a cosh(x) + 24a +--R Type: Expression Integer +--E 243 + +--S 244 of 526 +a0645:= integrate(t0645,x) +--R +--R +--R (243) +--R 5 4 +--R 3sinh(x) + (15cosh(x) - 8)sinh(x) +--R + +--R 2 3 +--R (30cosh(x) - 8cosh(x) + 35)sinh(x) +--R + +--R 3 2 2 +--R (30cosh(x) - 48cosh(x) + 135cosh(x) - 160)sinh(x) +--R + +--R 4 3 2 +--R (15cosh(x) - 8cosh(x) + 105cosh(x) - 160cosh(x) + 360x - 288)sinh(x) +--R + +--R 5 4 3 2 +--R 3cosh(x) - 8cosh(x) + 45cosh(x) - 160cosh(x) + (360x - 48)cosh(x) +--R + +--R 360x + 552 +--R / +--R 192a sinh(x) + 192a cosh(x) + 192a +--R Type: Union(Expression Integer,...) +--E 244 + +--S 245 of 526 +m0645:= a0645-r0645 +--R +--R +--R (244) +--R 5 2 4 +--R (3cosh(x) + 3)sinh(x) + (15cosh(x) + 7cosh(x) - 8)sinh(x) +--R + +--R 3 2 3 +--R (30cosh(x) + 22cosh(x) + 27cosh(x) + 35)sinh(x) +--R + +--R 4 3 2 2 +--R (- 18cosh(x) - 2cosh(x) - 17cosh(x) + 127cosh(x) + 352)sinh(x) +--R + +--R 5 4 3 2 +--R (- 33cosh(x) - 25cosh(x) + 9cosh(x) - 7cosh(x) + 216cosh(x) + 224) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 3cosh(x) - 5cosh(x) + 37cosh(x) - 115cosh(x) - 208cosh(x) +--R + +--R 504cosh(x) + 552 +--R / +--R 2 +--R (192a cosh(x) + 192a)sinh(x) + 192a cosh(x) + 384a cosh(x) + 192a +--R Type: Expression Integer +--E 245 + +--S 246 of 526 +d0645:= D(m0645,x) +--R +--R +--R (245) +--R 2 6 +--R (12cosh(x) + 24cosh(x) + 12)sinh(x) +--R + +--R 3 2 5 +--R (72cosh(x) + 159cosh(x) + 102cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 4 +--R (36cosh(x) + 155cosh(x) + 126cosh(x) - 69cosh(x) - 268)sinh(x) +--R + +--R 5 4 3 2 +--R - 48cosh(x) - 98cosh(x) + 20cosh(x) - 59cosh(x) - 714cosh(x) +--R + +--R - 585 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 12cosh(x) - 90cosh(x) + 64cosh(x) + 297cosh(x) + 14cosh(x) +--R + +--R - 421cosh(x) - 280 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 24cosh(x) - 61cosh(x) - 26cosh(x) + 264cosh(x) + 866cosh(x) +--R + +--R 2 +--R 397cosh(x) - 816cosh(x) - 600 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 36cosh(x) - 89cosh(x) - 106cosh(x) + 64cosh(x) + 534cosh(x) +--R + +--R 3 2 +--R 353cosh(x) - 392cosh(x) - 328cosh(x) +--R / +--R 2 2 +--R (192a cosh(x) + 384a cosh(x) + 192a)sinh(x) +--R + +--R 3 2 +--R (384a cosh(x) + 1152a cosh(x) + 1152a cosh(x) + 384a)sinh(x) +--R + +--R 4 3 2 +--R 192a cosh(x) + 768a cosh(x) + 1152a cosh(x) + 768a cosh(x) + 192a +--R Type: Expression Integer +--E 246 + +--S 247 of 526 +t0646:= tanh(x)/(a+b*sech(x)) +--R +--R +--R tanh(x) +--R (246) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 247 + +--S 248 of 526 +r0646:= log(b+a*cosh(x))/a +--R +--R +--R log(a cosh(x) + b) +--R (247) ------------------ +--R a +--R Type: Expression Integer +--E 248 + +--S 249 of 526 +a0646:= integrate(t0646,x) +--R +--R +--R - 2a cosh(x) - 2b +--R log(-----------------) - x +--R sinh(x) - cosh(x) +--R (248) -------------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 249 + +--S 250 of 526 +m0646:= a0646-r0646 +--R +--R +--R - 2a cosh(x) - 2b +--R - log(a cosh(x) + b) + log(-----------------) - x +--R sinh(x) - cosh(x) +--R (249) ------------------------------------------------- +--R a +--R Type: Expression Integer +--E 250 + +--S 251 of 526 +d0646:= D(m0646,x) +--R +--R +--R (250) 0 +--R Type: Expression Integer +--E 251 + +--S 252 of 526 +t0647:= tanh(x)^2/(a+b*sech(x)) +--R +--R +--R 2 +--R tanh(x) +--R (251) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 252 + +--S 253 of 526 +r0647:= (b*x-atan(sinh(x))*a+2*(a^2-b^2)^(1/2)*_ + atan((a-b)*(cosh(x)-1)/sinh(x)/(a^2-b^2)^(1/2)))/a/b +--R +--R +--R +---------+ +--R | 2 2 (b - a)cosh(x) - b + a +--R - a atan(sinh(x)) - 2\|- b + a atan(----------------------) + b x +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R (252) ------------------------------------------------------------------- +--R a b +--R Type: Expression Integer +--E 253 + +--S 254 of 526 +a0647:= integrate(t0647,x) +--R +--R +--R (253) +--R [ +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b +--R + +--R 2 +--R - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R - 2a atan(sinh(x) + cosh(x)) + b x +--R / +--R a b +--R , +--R +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R - 2\|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R - 2a atan(sinh(x) + cosh(x)) + b x +--R / +--R a b +--R ] +--R Type: Union(List Expression Integer,...) +--E 254 + +--S 255 of 526 +m0647:= a0647.1-r0647 +--R +--R +--R (254) +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R - 2a atan(sinh(x) + cosh(x)) + a atan(sinh(x)) +--R + +--R +---------+ +--R | 2 2 (b - a)cosh(x) - b + a +--R 2\|- b + a atan(----------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R / +--R a b +--R Type: Expression Integer +--E 255 + +--S 256 of 526 +d0647:= D(m0647a,x) +--R +--R +--R (255) 0 +--R Type: Polynomial Integer +--E 256 + +--S 257 of 526 +m0647:= a0647.2-r0647 +--R +--R +--R (256) +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R - 2\|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R - 2a atan(sinh(x) + cosh(x)) + a atan(sinh(x)) +--R + +--R +---------+ +--R | 2 2 (b - a)cosh(x) - b + a +--R 2\|- b + a atan(----------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R / +--R a b +--R Type: Expression Integer +--E 257 + +--S 258 of 526 +d0647:= D(m0647b,x) +--R +--R +--R (257) 0 +--R Type: Polynomial Integer +--E 258 + +--S 259 of 526 +t0648:= tanh(x)^3/(a+b*sech(x)) +--R +--R +--R 3 +--R tanh(x) +--R (258) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 259 + +--S 260 of 526 +r0648:= a*log(cosh(x))/b^2-(a^2-b^2)*log(b+a*cosh(x))/b^2/a+sech(x)/b +--R +--R +--R 2 2 2 +--R (b - a )log(a cosh(x) + b) + a log(cosh(x)) + a b sech(x) +--R (259) ---------------------------------------------------------- +--R 2 +--R a b +--R Type: Expression Integer +--E 260 + +--S 261 of 526 +a0648:= integrate(t0648,x) +--R +--R +--R (260) +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a ) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (b - a )sinh(x) + (2b - 2a )cosh(x)sinh(x) + (b - a )cosh(x) +--R + +--R 2 2 +--R b - a +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 +--R - b x sinh(x) + (- 2b x cosh(x) + 2a b)sinh(x) - b x cosh(x) +--R + +--R 2 +--R 2a b cosh(x) - b x +--R / +--R 2 2 2 2 2 2 +--R a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) + a b +--R Type: Union(Expression Integer,...) +--E 261 + +--S 262 of 526 +m0648:= a0648-r0648 +--R +--R +--R (261) +--R 2 2 2 2 2 +--R (- b + a )sinh(x) + (- 2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- b + a )cosh(x) - b + a +--R * +--R log(a cosh(x) + b) +--R + +--R 2 2 2 2 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a )log(cosh(x)) +--R + +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a ) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (b - a )sinh(x) + (2b - 2a )cosh(x)sinh(x) + (b - a )cosh(x) +--R + +--R 2 2 +--R b - a +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- a b sech(x) - b x)sinh(x) +--R + +--R 2 +--R (- 2a b cosh(x)sech(x) - 2b x cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (- a b cosh(x) - a b)sech(x) - b x cosh(x) + 2a b cosh(x) - b x +--R / +--R 2 2 2 2 2 2 +--R a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) + a b +--R Type: Expression Integer +--E 262 + +--S 263 of 526 +d0648:= D(m0648,x) +--R +--R +--R (262) +--R 4 3 +--R sech(x)sinh(x) + 4cosh(x)sech(x)sinh(x) +--R + +--R 2 2 3 +--R (6cosh(x) + 2)sech(x)sinh(x) + (4cosh(x) + 4cosh(x))sech(x)sinh(x) +--R + +--R 4 2 +--R (cosh(x) + 2cosh(x) + 1)sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 2 3 +--R - 2sinh(x) - 6cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) - 2cosh(x) +--R + +--R 2cosh(x) +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R Type: Expression Integer +--E 263 + +--S 264 of 526 +t0649:= tanh(x)^4/(a+b*sech(x)) +--R +--R +--R 4 +--R tanh(x) +--R (263) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 264 + +--S 265 of 526 +r0649:= x/a+a^2*atan(sinh(x))/b^3-3/2*atan(sinh(x))/b-_ + 2*(a^2-b^2)^(3/2)*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a/b^3-_ + a*tanh(x)/b^2+1/2*sech(x)*tanh(x)/b +--R +--R +--R (264) +--R 2 3 +--R (- 3a b + 2a )atan(sinh(x)) +--R + +--R x +--R +---------+ (b - a)tanh(-) +--R 2 2 | 2 2 2 +--R (- 4b + 4a )\|- b + a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 +--R (a b sech(x) - 2a b)tanh(x) + 2b x +--R / +--R 3 +--R 2a b +--R Type: Expression Integer +--E 265 + +--S 266 of 526 +a0649:= integrate(t0649,x) +--R +--R +--R (265) +--R [ +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b - 6a )cosh(x) + 2b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b - 4a )cosh(x) + (4b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b - a )cosh(x) + (2b - 2a )cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b +--R + +--R 2 +--R - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 3 4 2 3 3 +--R (- 3a b + 2a )sinh(x) + (- 12a b + 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 18a b + 12a )cosh(x) - 6a b + 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 12a b + 8a )cosh(x) + (- 12a b + 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 3a b + 2a )cosh(x) + (- 6a b + 4a )cosh(x) - 3a b + 2a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 4 3 2 3 +--R b x sinh(x) + (4b x cosh(x) + a b )sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (6b x cosh(x) + 3a b cosh(x) + 2b x + 2a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (4b x cosh(x) + 3a b cosh(x) + (4b x + 4a b)cosh(x) - a b )sinh(x) +--R + +--R 3 4 2 3 3 2 2 2 3 +--R b x cosh(x) + a b cosh(x) + (2b x + 2a b)cosh(x) - a b cosh(x) + b x +--R + +--R 2 +--R 2a b +--R / +--R 3 4 3 3 3 2 3 2 +--R a b sinh(x) + 4a b cosh(x)sinh(x) + (6a b cosh(x) + 2a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (4a b cosh(x) + 4a b cosh(x))sinh(x) + a b cosh(x) + 2a b cosh(x) +--R + +--R 3 +--R a b +--R , +--R +--R 2 2 4 2 2 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 12a )cosh(x) - 4b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 8a )cosh(x) + (- 8b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + (- 4b + 4a )cosh(x) - 2b + 2a +--R * +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R \|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R 2 3 4 2 3 3 +--R (- 3a b + 2a )sinh(x) + (- 12a b + 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 18a b + 12a )cosh(x) - 6a b + 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 12a b + 8a )cosh(x) + (- 12a b + 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 3a b + 2a )cosh(x) + (- 6a b + 4a )cosh(x) - 3a b + 2a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 4 3 2 3 +--R b x sinh(x) + (4b x cosh(x) + a b )sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (6b x cosh(x) + 3a b cosh(x) + 2b x + 2a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (4b x cosh(x) + 3a b cosh(x) + (4b x + 4a b)cosh(x) - a b )sinh(x) +--R + +--R 3 4 2 3 3 2 2 2 3 +--R b x cosh(x) + a b cosh(x) + (2b x + 2a b)cosh(x) - a b cosh(x) + b x +--R + +--R 2 +--R 2a b +--R / +--R 3 4 3 3 3 2 3 2 +--R a b sinh(x) + 4a b cosh(x)sinh(x) + (6a b cosh(x) + 2a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (4a b cosh(x) + 4a b cosh(x))sinh(x) + a b cosh(x) + 2a b cosh(x) +--R + +--R 3 +--R a b +--R ] +--R Type: Union(List Expression Integer,...) +--E 266 + +--S 267 of 526 +m0649:= a0649.1-r0649 +--R +--R +--R (266) +--R 2 2 4 2 2 3 +--R (2b - 2a )sinh(x) + (8b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - 2a )cosh(x) + (4b - 4a )cosh(x) + 2b - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 2 3 4 2 3 3 +--R (- 6a b + 4a )sinh(x) + (- 24a b + 16a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 36a b + 24a )cosh(x) - 12a b + 8a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 24a b + 16a )cosh(x) + (- 24a b + 16a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 6a b + 4a )cosh(x) + (- 12a b + 8a )cosh(x) - 6a b + 4a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 4 2 3 3 +--R (3a b - 2a )sinh(x) + (12a b - 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((18a b - 12a )cosh(x) + 6a b - 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((12a b - 8a )cosh(x) + (12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (3a b - 2a )cosh(x) + (6a b - 4a )cosh(x) + 3a b - 2a +--R * +--R atan(sinh(x)) +--R + +--R 2 2 4 2 2 3 +--R (4b - 4a )sinh(x) + (16b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b - 24a )cosh(x) + 8b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b - 16a )cosh(x) + (16b - 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b - 4a )cosh(x) + (8b - 8a )cosh(x) + 4b - 4a +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 +--R (- a b sech(x) + 2a b)sinh(x) +--R + +--R 2 2 3 +--R (- 4a b cosh(x)sech(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 2 +--R ((- 6a b cosh(x) - 2a b )sech(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (- 4a b cosh(x) - 4a b cosh(x))sech(x) + 8a b cosh(x) +--R + +--R 2 +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 4 +--R (- a b cosh(x) - 2a b cosh(x) - a b )sech(x) + 2a b cosh(x) +--R + +--R 2 2 2 +--R 4a b cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 2 3 2 2 2 +--R 2a b sinh(x) + (6a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (6a b cosh(x) + 8a b cosh(x) - 2a b )sinh(x) + 2a b cosh(x) +--R + +--R 2 2 2 2 +--R 4a b cosh(x) - 2a b cosh(x) + 4a b +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a b sinh(x) + 8a b cosh(x)sinh(x) + (12a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (8a b cosh(x) + 8a b cosh(x))sinh(x) + 2a b cosh(x) + 4a b cosh(x) +--R + +--R 3 +--R 2a b +--R Type: Expression Integer +--E 267 + +--S 268 of 526 +d0649:= D(m0649a,x) +--R +--R +--R (267) 0 +--R Type: Polynomial Integer +--E 268 + +--S 269 of 526 +m0649:= a0649.2-r0649 +--R +--R +--R (268) +--R 2 2 4 2 2 3 +--R (- 4b + 4a )sinh(x) + (- 16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 24b + 24a )cosh(x) - 8b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 16b + 16a )cosh(x) + (- 16b + 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 4b + 4a )cosh(x) + (- 8b + 8a )cosh(x) - 4b + 4a +--R * +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R \|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R 2 3 4 2 3 3 +--R (- 6a b + 4a )sinh(x) + (- 24a b + 16a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 36a b + 24a )cosh(x) - 12a b + 8a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 24a b + 16a )cosh(x) + (- 24a b + 16a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 6a b + 4a )cosh(x) + (- 12a b + 8a )cosh(x) - 6a b + 4a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 4 2 3 3 +--R (3a b - 2a )sinh(x) + (12a b - 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((18a b - 12a )cosh(x) + 6a b - 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((12a b - 8a )cosh(x) + (12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (3a b - 2a )cosh(x) + (6a b - 4a )cosh(x) + 3a b - 2a +--R * +--R atan(sinh(x)) +--R + +--R 2 2 4 2 2 3 +--R (4b - 4a )sinh(x) + (16b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b - 24a )cosh(x) + 8b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b - 16a )cosh(x) + (16b - 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b - 4a )cosh(x) + (8b - 8a )cosh(x) + 4b - 4a +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 +--R (- a b sech(x) + 2a b)sinh(x) +--R + +--R 2 2 3 +--R (- 4a b cosh(x)sech(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 2 +--R ((- 6a b cosh(x) - 2a b )sech(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (- 4a b cosh(x) - 4a b cosh(x))sech(x) + 8a b cosh(x) +--R + +--R 2 +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 4 +--R (- a b cosh(x) - 2a b cosh(x) - a b )sech(x) + 2a b cosh(x) +--R + +--R 2 2 2 +--R 4a b cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 2 3 2 2 2 +--R 2a b sinh(x) + (6a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (6a b cosh(x) + 8a b cosh(x) - 2a b )sinh(x) + 2a b cosh(x) +--R + +--R 2 2 2 2 +--R 4a b cosh(x) - 2a b cosh(x) + 4a b +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a b sinh(x) + 8a b cosh(x)sinh(x) + (12a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (8a b cosh(x) + 8a b cosh(x))sinh(x) + 2a b cosh(x) + 4a b cosh(x) +--R + +--R 3 +--R 2a b +--R Type: Expression Integer +--E 269 + +--S 270 of 526 +d0649:= D(m0649b,x) +--R +--R +--R (269) 0 +--R Type: Polynomial Integer +--E 270 + +--S 271 of 526 +t0650:= tanh(x)/(a+a*sech(x)) +--R +--R +--R tanh(x) +--R (270) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 271 + +--S 272 of 526 +r0650:= log(1+cosh(x))/a +--R +--R +--R log(cosh(x) + 1) +--R (271) ---------------- +--R a +--R Type: Expression Integer +--E 272 + +--S 273 of 526 +a0650:= integrate(t0650,x) +--R +--R +--R 2log(sinh(x) + cosh(x) + 1) - x +--R (272) ------------------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 273 + +--S 274 of 526 +m0650:= a0650-r0650 +--R +--R +--R 2log(sinh(x) + cosh(x) + 1) - log(cosh(x) + 1) - x +--R (273) -------------------------------------------------- +--R a +--R Type: Expression Integer +--E 274 + +--S 275 of 526 +d0650:= D(m0650,x) +--R +--R +--R 2 2 +--R - sinh(x) + cosh(x) - 1 +--R (274) ---------------------------------------------------- +--R 2 +--R (a cosh(x) + a)sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression Integer +--E 275 + +--S 276 of 526 +t0651:= tanh(x)^2/(a+a*sech(x)) +--R +--R +--R 2 +--R tanh(x) +--R (275) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 276 + +--S 277 of 526 +r0651:= -(-x+atan(sinh(x)))/a +--R +--R +--R - atan(sinh(x)) + x +--R (276) ------------------- +--R a +--R Type: Expression Integer +--E 277 + +--S 278 of 526 +a0651:= integrate(t0651,x) +--R +--R +--R - 2atan(sinh(x) + cosh(x)) + x +--R (277) ------------------------------ +--R a +--R Type: Union(Expression Integer,...) +--E 278 + +--S 279 of 526 +m0651:= a0651-r0651 +--R +--R +--R - 2atan(sinh(x) + cosh(x)) + atan(sinh(x)) +--R (278) ------------------------------------------ +--R a +--R Type: Expression Integer +--E 279 + +--S 280 of 526 +d0651:= D(m0651,x) +--R +--R +--R (279) +--R 3 2 2 3 +--R - 2sinh(x) - cosh(x)sinh(x) + (2cosh(x) - 2)sinh(x) + cosh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + (a cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Expression Integer +--E 280 + +--S 281 of 526 +t0652:= tanh(x)^3/(a+a*sech(x)) +--R +--R +--R 3 +--R tanh(x) +--R (280) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 281 + +--S 282 of 526 +r0652:= log(cosh(x))/a+sech(x)/a +--R +--R +--R log(cosh(x)) + sech(x) +--R (281) ---------------------- +--R a +--R Type: Expression Integer +--E 282 + +--S 283 of 526 +a0652:= integrate(t0652,x) +--R +--R +--R (282) +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - x sinh(x) + (- 2x cosh(x) + 2)sinh(x) - x cosh(x) + 2cosh(x) - x +--R / +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Union(Expression Integer,...) +--E 283 + +--S 284 of 526 +m0652:= a0652-r0652 +--R +--R +--R (283) +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)log(cosh(x)) +--R + +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (- sech(x) - x)sinh(x) + (- 2cosh(x)sech(x) - 2x cosh(x) + 2)sinh(x) +--R + +--R 2 2 +--R (- cosh(x) - 1)sech(x) - x cosh(x) + 2cosh(x) - x +--R / +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Expression Integer +--E 284 + +--S 285 of 526 +d0652:= D(m0652,x) +--R +--R +--R (284) +--R 4 3 +--R sech(x)sinh(x) + 4cosh(x)sech(x)sinh(x) +--R + +--R 2 2 3 +--R (6cosh(x) + 2)sech(x)sinh(x) + (4cosh(x) + 4cosh(x))sech(x)sinh(x) +--R + +--R 4 2 +--R (cosh(x) + 2cosh(x) + 1)sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 2 3 +--R - 2sinh(x) - 6cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) - 2cosh(x) +--R + +--R 2cosh(x) +--R / +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression Integer +--E 285 + +--S 286 of 526 +t0653:= tanh(x)^4/(a+a*sech(x)) +--R +--R +--R 4 +--R tanh(x) +--R (285) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 286 + +--S 287 of 526 +r0653:= x/a-1/2*atan(sinh(x))/a-tanh(x)/a+1/2*sech(x)*tanh(x)/a +--R +--R +--R - atan(sinh(x)) + (sech(x) - 2)tanh(x) + 2x +--R (286) ------------------------------------------- +--R 2a +--R Type: Expression Integer +--E 287 + +--S 288 of 526 +a0653:= integrate(t0653,x) +--R +--R +--R (287) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) - 4cosh(x))sinh(x) - cosh(x) - 2cosh(x) - 1 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 4 3 +--R x sinh(x) + (4x cosh(x) + 1)sinh(x) +--R + +--R 2 2 +--R (6x cosh(x) + 3cosh(x) + 2x + 2)sinh(x) +--R + +--R 3 2 4 +--R (4x cosh(x) + 3cosh(x) + (4x + 4)cosh(x) - 1)sinh(x) + x cosh(x) +--R + +--R 3 2 +--R cosh(x) + (2x + 2)cosh(x) - cosh(x) + x + 2 +--R / +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Union(Expression Integer,...) +--E 288 + +--S 289 of 526 +m0653:= a0653-r0653 +--R +--R +--R (288) +--R 4 3 2 2 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 8cosh(x) - 8cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) - 2 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R * +--R atan(sinh(x)) +--R + +--R 4 3 +--R (- sech(x) + 2)sinh(x) + (- 4cosh(x)sech(x) + 8cosh(x))sinh(x) +--R + +--R 2 2 2 +--R ((- 6cosh(x) - 2)sech(x) + 12cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R ((- 4cosh(x) - 4cosh(x))sech(x) + 8cosh(x) + 8cosh(x))sinh(x) +--R + +--R 4 2 4 2 +--R (- cosh(x) - 2cosh(x) - 1)sech(x) + 2cosh(x) + 4cosh(x) + 2 +--R * +--R tanh(x) +--R + +--R 3 2 2 +--R 2sinh(x) + (6cosh(x) + 4)sinh(x) + (6cosh(x) + 8cosh(x) - 2)sinh(x) +--R + +--R 3 2 +--R 2cosh(x) + 4cosh(x) - 2cosh(x) + 4 +--R / +--R 4 3 2 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a)sinh(x) +--R + +--R 3 4 2 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R Type: Expression Integer +--E 289 + +--S 290 of 526 +d0653:= D(m0653,x) +--R +--R +--R (289) +--R 8 7 +--R (2sech(x) - 2)sinh(x) + (12cosh(x)sech(x) - 12cosh(x))sinh(x) +--R + +--R 2 2 6 +--R ((30cosh(x) + 8)sech(x) - 30cosh(x) - 8)sinh(x) +--R + +--R 3 3 5 +--R ((40cosh(x) + 36cosh(x))sech(x) - 40cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 2 +--R (30cosh(x) + 66cosh(x) + 12)sech(x) - 30cosh(x) - 66cosh(x) +--R + +--R - 12 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 5 +--R (12cosh(x) + 64cosh(x) + 36cosh(x))sech(x) - 12cosh(x) +--R + +--R 3 +--R - 64cosh(x) - 36cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 6 +--R (2cosh(x) + 36cosh(x) + 42cosh(x) + 8)sech(x) - 2cosh(x) +--R + +--R 4 2 +--R - 36cosh(x) - 42cosh(x) - 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 5 +--R (12cosh(x) + 24cosh(x) + 12cosh(x))sech(x) - 12cosh(x) +--R + +--R 3 +--R - 24cosh(x) - 12cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 6 +--R (2cosh(x) + 6cosh(x) + 6cosh(x) + 2)sech(x) - 2cosh(x) +--R + +--R 4 2 +--R - 6cosh(x) - 6cosh(x) - 2 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R (- sech(x) + 2)sinh(x) + (- 6cosh(x)sech(x) + 12cosh(x) - 4)sinh(x) +--R + +--R 2 2 6 +--R ((- 15cosh(x) - 4)sech(x) + 30cosh(x) - 19cosh(x))sinh(x) +--R + +--R 3 3 2 +--R (- 20cosh(x) - 18cosh(x))sech(x) + 40cosh(x) - 34cosh(x) +--R + +--R 4cosh(x) + 4 +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 4 3 +--R (- 15cosh(x) - 33cosh(x) - 6)sech(x) + 30cosh(x) - 25cosh(x) +--R + +--R 2 +--R 18cosh(x) + 7cosh(x) - 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 5 +--R (- 6cosh(x) - 32cosh(x) - 18cosh(x))sech(x) + 12cosh(x) +--R + +--R 3 2 +--R 32cosh(x) - 4cosh(x) - 12cosh(x) + 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 6 +--R (- cosh(x) - 18cosh(x) - 21cosh(x) - 4)sech(x) + 2cosh(x) +--R + +--R 5 4 3 2 +--R 11cosh(x) + 28cosh(x) - 14cosh(x) - 14cosh(x) + 23cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 5 +--R (- 6cosh(x) - 12cosh(x) - 6cosh(x))sech(x) + 6cosh(x) + 12cosh(x) +--R + +--R 4 3 2 +--R - 8cosh(x) - 8cosh(x) + 30cosh(x) - 4cosh(x) - 4 +--R * +--R sinh(x) +--R + +--R 6 4 2 7 6 +--R (- cosh(x) - 3cosh(x) - 3cosh(x) - 1)sech(x) + cosh(x) + 2cosh(x) +--R + +--R 5 4 3 2 +--R - cosh(x) - 2cosh(x) + 11cosh(x) - 2cosh(x) - 3cosh(x) + 2 +--R / +--R 8 7 2 6 +--R 2a sinh(x) + 12a cosh(x)sinh(x) + (30a cosh(x) + 8a)sinh(x) +--R + +--R 3 5 +--R (40a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (30a cosh(x) + 66a cosh(x) + 12a)sinh(x) +--R + +--R 5 3 3 +--R (12a cosh(x) + 64a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (2a cosh(x) + 36a cosh(x) + 42a cosh(x) + 8a)sinh(x) +--R + +--R 5 3 6 +--R (12a cosh(x) + 24a cosh(x) + 12a cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 4 2 +--R 6a cosh(x) + 6a cosh(x) + 2a +--R Type: Expression Integer +--E 290 + +--S 291 of 526 +t0654:= coth(x)/(a+b*sech(x)) +--R +--R +--R coth(x) +--R (290) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 291 + +--S 292 of 526 +r0654:= log(1-cosh(x))/(2*a+2*b)+log(1+cosh(x))/(2*a-2*b)-_ + b^2*log(b+a*cosh(x))/a/(a^2-b^2) +--R +--R +--R (291) +--R 2 2 +--R 2b log(a cosh(x) + b) + (- a b - a )log(cosh(x) + 1) +--R + +--R 2 +--R (a b - a )log(- cosh(x) + 1) +--R / +--R 2 3 +--R 2a b - 2a +--R Type: Expression Integer +--E 292 + +--S 293 of 526 +a0654:= integrate(t0654,x) +--R +--R +--R (292) +--R 2 +--R (- a b - a )log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 - 2a cosh(x) - 2b +--R (a b - a )log(sinh(x) + cosh(x) - 1) + b log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- b + a )x +--R / +--R 2 3 +--R a b - a +--R Type: Union(Expression Integer,...) +--E 293 + +--S 294 of 526 +m0654:= a0654-r0654 +--R +--R +--R (293) +--R 2 +--R (- 2a b - 2a )log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (2a b - 2a )log(sinh(x) + cosh(x) - 1) - 2b log(a cosh(x) + b) +--R + +--R 2 2 - 2a cosh(x) - 2b +--R (a b + a )log(cosh(x) + 1) + 2b log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 +--R (- a b + a )log(- cosh(x) + 1) + (- 2b + 2a )x +--R / +--R 2 3 +--R 2a b - 2a +--R Type: Expression Integer +--E 294 + +--S 295 of 526 +d0654:= D(m0654,x) +--R +--R +--R (294) +--R 3 2 2 +--R (a cosh(x) - b)sinh(x) + (a cosh(x) - 2b cosh(x) + a)sinh(x) +--R + +--R 3 2 4 +--R (- a cosh(x) + b cosh(x) + a cosh(x) - b)sinh(x) - a cosh(x) +--R + +--R 3 +--R 2b cosh(x) - 2b cosh(x) + a +--R / +--R 2 2 2 2 2 2 +--R ((b - a )cosh(x) - b + a )sinh(x) +--R + +--R 2 2 3 2 2 2 2 4 +--R ((2b - 2a )cosh(x) + (- 2b + 2a )cosh(x))sinh(x) + (b - a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + b - a +--R Type: Expression Integer +--E 295 + +--S 296 of 526 +t0655:= coth(x)^2/(a+b*sech(x)) +--R +--R +--R 2 +--R coth(x) +--R (295) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 296 + +--S 297 of 526 +r0655:= x/a+2*b^3*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(3/2)+_ + 1/2*sinh(x)/(a+b)/(1-cosh(x))-1/2*sinh(x)/(a-b)/(1+cosh(x)) +--R +--R +--R (296) +--R x +--R (b - a)tanh(-) +--R 3 2 3 2 +--R (2b cosh(x) - 2b )atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R ((a cosh(x) - a b)sinh(x) + (b - a )x cosh(x) + (- b + a )x)\|- b + a +--R / +--R +---------+ +--R 2 3 2 2 3 | 2 2 +--R ((a b - a )cosh(x) - a b + a )\|- b + a +--R Type: Expression Integer +--E 297 + +--S 298 of 526 +a0655:= integrate(t0655,x) +--R +--R +--R (297) +--R [ +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 2 2 2 2 +--R (b - a )x sinh(x) + ((2b - 2a )x cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (b - a )x cosh(x) - 2a b cosh(x) + (- b + a )x + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 2 3 2 2 3 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )cosh(x) - a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 2 3 3 2 3 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) - 2b ) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 2 2 2 +--R (b - a )x sinh(x) + ((2b - 2a )x cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (b - a )x cosh(x) - 2a b cosh(x) + (- b + a )x + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 3 2 2 3 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )cosh(x) - a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 298 + +--S 299 of 526 +m0655:= a0655.1-r0655 +--R +--R +--R (298) +--R 3 2 3 2 3 3 3 +--R (b cosh(x) - b )sinh(x) + (2b cosh(x) - 2b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 +--R b cosh(x) - 2b cosh(x) + b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 3 2 3 2 3 3 3 +--R (- 2b cosh(x) + 2b )sinh(x) + (- 4b cosh(x) + 4b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 +--R - 2b cosh(x) + 4b cosh(x) - 2b +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 2 +--R (- a cosh(x) + a b)sinh(x) + (- 2a cosh(x) + 2a b cosh(x))sinh(x) +--R + +--R 2 3 2 2 +--R (- a cosh(x) - a b cosh(x) + a cosh(x) + a b)sinh(x) +--R + +--R 3 2 2 2 +--R - 2a b cosh(x) + 2a cosh(x) + 2a b cosh(x) - 2a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 2 3 2 2 3 2 +--R ((a b - a )cosh(x) - a b + a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((2a b - 2a )cosh(x) + (- 2a b + 2a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (a b - a )cosh(x) + (- 2a b + 2a )cosh(x) + a b - a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 299 + +--S 300 of 526 +d0655:= D(m0655a,x) +--R +--R +--R (299) 0 +--R Type: Polynomial Integer +--E 300 + +--S 301 of 526 +m0655:= a0655.2-r0655 +--R +--R +--R (300) +--R 3 2 3 2 3 3 3 +--R (2b cosh(x) - 2b )sinh(x) + (4b cosh(x) - 4b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 +--R 2b cosh(x) - 4b cosh(x) + 2b +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 3 2 3 2 3 3 3 +--R (- 2b cosh(x) + 2b )sinh(x) + (- 4b cosh(x) + 4b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 +--R - 2b cosh(x) + 4b cosh(x) - 2b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 2 +--R (- a cosh(x) + a b)sinh(x) + (- 2a cosh(x) + 2a b cosh(x))sinh(x) +--R + +--R 2 3 2 2 +--R (- a cosh(x) - a b cosh(x) + a cosh(x) + a b)sinh(x) +--R + +--R 3 2 2 2 +--R - 2a b cosh(x) + 2a cosh(x) + 2a b cosh(x) - 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 3 2 2 3 2 +--R ((a b - a )cosh(x) - a b + a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((2a b - 2a )cosh(x) + (- 2a b + 2a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (a b - a )cosh(x) + (- 2a b + 2a )cosh(x) + a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 301 + +--S 302 of 526 +d0655:= D(m0655b,x) +--R +--R +--R (301) 0 +--R Type: Polynomial Integer +--E 302 + +--S 303 of 526 +t0656:= coth(x)^3/(a+b*sech(x)) +--R +--R +--R 3 +--R coth(x) +--R (302) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 303 + +--S 304 of 526 +r0656:= 1/4/(a+b)/(1-cosh(x))+1/4/(a-b)/(1+cosh(x))+_ + 1/4*(2*a+3*b)*log(1-cosh(x))/(a+b)^2+_ + 1/4*(2*a-3*b)*log(1+cosh(x))/(a-b)^2+_ + b^4*log(b+a*cosh(x))/a/(a^2-b^2)^2 +--R +--R +--R (303) +--R 4 2 4 +--R (4b cosh(x) - 4b )log(a cosh(x) + b) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R ((- 3a b - 4a b + a b + 2a )cosh(x) + 3a b + 4a b - a b - 2a ) +--R * +--R log(cosh(x) + 1) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R ((3a b - 4a b - a b + 2a )cosh(x) - 3a b + 4a b + a b - 2a ) +--R * +--R log(- cosh(x) + 1) +--R + +--R 3 3 2 2 4 +--R (- 2a b + 2a b)cosh(x) + 2a b - 2a +--R / +--R 4 3 2 5 2 4 3 2 5 +--R (4a b - 8a b + 4a )cosh(x) - 4a b + 8a b - 4a +--R Type: Expression Integer +--E 304 + +--S 305 of 526 +a0656:= integrate(t0656,x) +--R +--R +--R (304) +--R 3 2 2 3 4 4 +--R (- 3a b - 4a b + a b + 2a )sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 12a b - 16a b + 4a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (- 18a b - 24a b + 6a b + 12a )cosh(x) + 6a b + 8a b - 2a b +--R + +--R 4 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 12a b - 16a b + 4a b + 8a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (12a b + 16a b - 4a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 3a b - 4a b + a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (6a b + 8a b - 2a b - 4a )cosh(x) - 3a b - 4a b + a b + 2a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 2 3 4 4 +--R (3a b - 4a b - a b + 2a )sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (12a b - 16a b - 4a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (18a b - 24a b - 6a b + 12a )cosh(x) - 6a b + 8a b + 2a b +--R + +--R 4 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (12a b - 16a b - 4a b + 8a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12a b + 16a b + 4a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (3a b - 4a b - a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 6a b + 8a b + 2a b - 4a )cosh(x) + 3a b - 4a b - a b + 2a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 4 4 3 4 2 4 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) - 4b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (8b cosh(x) - 8b cosh(x))sinh(x) + 2b cosh(x) - 4b cosh(x) + 2b +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 2 2 4 4 +--R (- 2b + 4a b - 2a )x sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R ((- 8b + 16a b - 8a )x cosh(x) - 2a b + 2a b)sinh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (- 12b + 24a b - 12a )x cosh(x) + (- 6a b + 6a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 +--R (4b - 8a b + 4a )x + 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 8b + 16a b - 8a )x cosh(x) + (- 6a b + 6a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((8b - 16a b + 8a )x + 8a b - 8a )cosh(x) - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 2b + 4a b - 2a )x cosh(x) + (- 2a b + 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 3 3 +--R ((4b - 8a b + 4a )x + 4a b - 4a )cosh(x) + (- 2a b + 2a b)cosh(x) +--R + +--R 4 2 2 4 +--R (- 2b + 4a b - 2a )x +--R / +--R 4 3 2 5 4 4 3 2 5 3 +--R (2a b - 4a b + 2a )sinh(x) + (8a b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 2 +--R ((12a b - 24a b + 12a )cosh(x) - 4a b + 8a b - 4a )sinh(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((8a b - 16a b + 8a )cosh(x) + (- 8a b + 16a b - 8a )cosh(x))sinh(x) +--R + +--R 4 3 2 5 4 4 3 2 5 2 4 +--R (2a b - 4a b + 2a )cosh(x) + (- 4a b + 8a b - 4a )cosh(x) + 2a b +--R + +--R 3 2 5 +--R - 4a b + 2a +--R Type: Union(Expression Integer,...) +--E 305 + +--S 306 of 526 +m0656:= a0656-r0656 +--R +--R +--R (305) +--R 3 2 2 3 4 2 3 2 2 3 +--R (- 6a b - 8a b + 2a b + 4a )cosh(x) + 6a b + 8a b - 2a b +--R + +--R 4 +--R - 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 24a b - 32a b + 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (24a b + 32a b - 8a b - 16a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 36a b - 48a b + 12a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (48a b + 64a b - 16a b - 32a )cosh(x) - 12a b - 16a b + 4a b +--R + +--R 4 +--R 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 24a b - 32a b + 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (48a b + 64a b - 16a b - 32a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 24a b - 32a b + 8a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 6 +--R (- 6a b - 8a b + 2a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (18a b + 24a b - 6a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 18a b - 24a b + 6a b + 12a )cosh(x) + 6a b + 8a b - 2a b - 4a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R ((6a b - 8a b - 2a b + 4a )cosh(x) - 6a b + 8a b + 2a b - 4a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (24a b - 32a b - 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 24a b + 32a b + 8a b - 16a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (36a b - 48a b - 12a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 +--R (- 48a b + 64a b + 16a b - 32a )cosh(x) + 12a b - 16a b +--R + +--R 3 4 +--R - 4a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (24a b - 32a b - 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 48a b + 64a b + 16a b - 32a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (24a b - 32a b - 8a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 6 +--R (6a b - 8a b - 2a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 18a b + 24a b + 6a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (18a b - 24a b - 6a b + 12a )cosh(x) - 6a b + 8a b + 2a b - 4a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 2 4 4 +--R (- 4b cosh(x) + 4b )sinh(x) +--R + +--R 4 3 4 3 +--R (- 16b cosh(x) + 16b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (- 24b cosh(x) + 32b cosh(x) - 8b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (- 16b cosh(x) + 32b cosh(x) - 16b cosh(x))sinh(x) - 4b cosh(x) +--R + +--R 4 4 4 2 4 +--R 12b cosh(x) - 12b cosh(x) + 4b +--R * +--R log(a cosh(x) + b) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R ((3a b + 4a b - a b - 2a )cosh(x) - 3a b - 4a b + a b + 2a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (12a b + 16a b - 4a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12a b - 16a b + 4a b + 8a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (18a b + 24a b - 6a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (- 24a b - 32a b + 8a b + 16a )cosh(x) + 6a b + 8a b - 2a b +--R + +--R 4 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (12a b + 16a b - 4a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 24a b - 32a b + 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (12a b + 16a b - 4a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 6 +--R (3a b + 4a b - a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 9a b - 12a b + 3a b + 6a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (9a b + 12a b - 3a b - 6a )cosh(x) - 3a b - 4a b + a b + 2a +--R * +--R log(cosh(x) + 1) +--R + +--R 4 2 4 4 4 3 4 3 +--R (4b cosh(x) - 4b )sinh(x) + (16b cosh(x) - 16b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (24b cosh(x) - 32b cosh(x) + 8b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (16b cosh(x) - 32b cosh(x) + 16b cosh(x))sinh(x) + 4b cosh(x) +--R + +--R 4 4 4 2 4 +--R - 12b cosh(x) + 12b cosh(x) - 4b +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R ((- 3a b + 4a b + a b - 2a )cosh(x) + 3a b - 4a b - a b + 2a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 12a b + 16a b + 4a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (12a b - 16a b - 4a b + 8a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 18a b + 24a b + 6a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (24a b - 32a b - 8a b + 16a )cosh(x) - 6a b + 8a b + 2a b +--R + +--R 4 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 12a b + 16a b + 4a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (24a b - 32a b - 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12a b + 16a b + 4a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 6 +--R (- 3a b + 4a b + a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (9a b - 12a b - 3a b + 6a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 9a b + 12a b + 3a b - 6a )cosh(x) + 3a b - 4a b - a b + 2a +--R * +--R log(- cosh(x) + 1) +--R + +--R 4 2 2 4 2 3 3 +--R (- 4b + 8a b - 4a )x cosh(x) + (2a b - 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 +--R (4b - 8a b + 4a )x - 2a b + 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 16b + 32a b - 16a )x cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((16b - 32a b + 16a )x - 8a b + 8a )cosh(x) + 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 +--R (- 24b + 48a b - 24a )x cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 +--R ((32b - 64a b + 32a )x - 4a b + 4a )cosh(x) +--R + +--R 3 3 4 2 2 4 2 2 4 +--R (8a b - 8a b)cosh(x) + (- 8b + 16a b - 8a )x - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (- 16b + 32a b - 16a )x cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 +--R ((32b - 64a b + 32a )x + 8a b - 8a )cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((- 16b + 32a b - 16a )x - 8a b + 8a )cosh(x) + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (- 4b + 8a b - 4a )x cosh(x) + (- 2a b + 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 4 +--R ((12b - 24a b + 12a )x + 6a b - 6a )cosh(x) +--R + +--R 3 3 3 +--R (- 4a b + 4a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 3 3 +--R ((- 12b + 24a b - 12a )x - 4a b + 4a )cosh(x) + (6a b - 6a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 +--R (4b - 8a b + 4a )x - 2a b + 2a +--R / +--R 4 3 2 5 2 4 3 2 5 4 +--R ((4a b - 8a b + 4a )cosh(x) - 4a b + 8a b - 4a )sinh(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((16a b - 32a b + 16a )cosh(x) + (- 16a b + 32a b - 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 5 4 4 3 2 5 2 +--R (24a b - 48a b + 24a )cosh(x) + (- 32a b + 64a b - 32a )cosh(x) +--R + +--R 4 3 2 5 +--R 8a b - 16a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 5 5 4 3 2 5 3 +--R (16a b - 32a b + 16a )cosh(x) + (- 32a b + 64a b - 32a )cosh(x) +--R + +--R 4 3 2 5 +--R (16a b - 32a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 5 6 4 3 2 5 4 +--R (4a b - 8a b + 4a )cosh(x) + (- 12a b + 24a b - 12a )cosh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (12a b - 24a b + 12a )cosh(x) - 4a b + 8a b - 4a +--R Type: Expression Integer +--E 306 + +--S 307 of 526 +d0656:= D(m0656,x) +--R +--R +--R (306) +--R 2 3 3 3 2 2 2 3 7 +--R ((2a b - a )cosh(x) + (- 2b + a b)cosh(x) - a b cosh(x) + b )sinh(x) +--R + +--R 2 3 4 3 2 3 +--R (10a b - 5a )cosh(x) + (- 12b + 6a b)cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 2a b - 2a )cosh(x) + 6b cosh(x) - 2a b + a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 5 3 2 4 +--R (18a b - 9a )cosh(x) + (- 26b + 13a b)cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (3a b - 9a )cosh(x) + (13b + a b)cosh(x) + (- 9a b + 6a )cosh(x) +--R + +--R 3 2 +--R b - 2a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 6 3 2 5 +--R (10a b - 5a )cosh(x) + (- 20b + 10a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (14a b - 15a )cosh(x) + (4b + 8a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 14a b + 9a )cosh(x) + (8b - 10a b)cosh(x) - 2a b + 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 7 3 2 6 +--R (- 10a b + 5a )cosh(x) + (10b - 5a b)cosh(x) +--R + +--R 2 3 5 3 2 4 3 3 +--R (21a b - 10a )cosh(x) + (- 29b + 18a b)cosh(x) - 7a cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (16b - 9a b)cosh(x) + (- 11a b + 12a )cosh(x) + 3b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 8 3 2 7 2 6 +--R (- 18a b + 9a )cosh(x) + (28b - 14a b)cosh(x) + 18a b cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 50b + 16a b)cosh(x) + (16a b - 24a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (16b + 10a b)cosh(x) + (- 14a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 12a b)cosh(x) - 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 9 3 2 8 +--R (- 10a b + 5a )cosh(x) + (18b - 9a b)cosh(x) +--R + +--R 2 3 7 3 2 6 +--R (9a b + 3a )cosh(x) + (- 33b + 5a b)cosh(x) +--R + +--R 2 3 5 3 2 4 +--R (9a b - 15a )cosh(x) + (15b + 15a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (- 5a b + a )cosh(x) + (- 3b - 9a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 3a b + 6a )cosh(x) + 3b - 2a b +--R * +--R sinh(x) +--R + +--R 2 3 10 3 2 9 2 3 8 +--R (- 2a b + a )cosh(x) + (4b - 2a b)cosh(x) + (2a b + a )cosh(x) +--R + +--R 3 7 3 6 3 2 5 3 4 +--R - 8b cosh(x) - 2a cosh(x) + (8b + 4a b)cosh(x) - 2a cosh(x) +--R + +--R 3 3 2 3 2 3 2 2 3 +--R - 8b cosh(x) + (2a b + a )cosh(x) + (4b - 2a b)cosh(x) - 2a b + a +--R / +--R 4 2 2 4 4 4 2 2 4 2 4 +--R (b - 2a b + a )cosh(x) + (- 2b + 4a b - 2a )cosh(x) + b +--R + +--R 2 2 4 +--R - 2a b + a +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (6b - 12a b + 6a )cosh(x) + (- 12b + 24a b - 12a )cosh(x) +--R + +--R 4 2 2 4 +--R (6b - 12a b + 6a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (15b - 30a b + 15a )cosh(x) + (- 33b + 66a b - 33a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (21b - 42a b + 21a )cosh(x) - 3b + 6a b - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 7 4 2 2 4 5 +--R (20b - 40a b + 20a )cosh(x) + (- 52b + 104a b - 52a )cosh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R (44b - 88a b + 44a )cosh(x) + (- 12b + 24a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (15b - 30a b + 15a )cosh(x) + (- 48b + 96a b - 48a )cosh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (54b - 108a b + 54a )cosh(x) + (- 24b + 48a b - 24a )cosh(x) +--R + +--R 4 2 2 4 +--R 3b - 6a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (6b - 12a b + 6a )cosh(x) + (- 24b + 48a b - 24a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (36b - 72a b + 36a )cosh(x) + (- 24b + 48a b - 24a )cosh(x) +--R + +--R 4 2 2 4 +--R (6b - 12a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 10 4 2 2 4 8 +--R (b - 2a b + a )cosh(x) + (- 5b + 10a b - 5a )cosh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (10b - 20a b + 10a )cosh(x) + (- 10b + 20a b - 10a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (5b - 10a b + 5a )cosh(x) - b + 2a b - a +--R Type: Expression Integer +--E 307 + +--S 308 of 526 +t0657:= coth(x)^2/(a+a*sech(x)) +--R +--R +--R 2 +--R coth(x) +--R (307) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 308 + +--S 309 of 526 +r0657:= 1/3*(2-cosh(x)-4*cosh(x)^2+3*x*cosh(x)*sinh(x)+_ + 3*x*sinh(x))/sinh(x)/a/(1+cosh(x)) +--R +--R +--R 2 +--R (3x cosh(x) + 3x)sinh(x) - 4cosh(x) - cosh(x) + 2 +--R (308) -------------------------------------------------- +--R (3a cosh(x) + 3a)sinh(x) +--R Type: Expression Integer +--E 309 + +--S 310 of 526 +a0657:= integrate(t0657,x) +--R +--R +--R (309) +--R 2 2 +--R - 2sinh(x) + ((3x + 4)cosh(x) + 3x + 4)sinh(x) - 2cosh(x) - cosh(x) +--R --------------------------------------------------------------------- +--R (3a cosh(x) + 3a)sinh(x) +--R Type: Union(Expression Integer,...) +--E 310 + +--S 311 of 526 +m0657:= a0657-r0657 +--R +--R +--R 2 2 +--R - 2sinh(x) + (4cosh(x) + 4)sinh(x) + 2cosh(x) - 2 +--R (310) --------------------------------------------------- +--R (3a cosh(x) + 3a)sinh(x) +--R Type: Expression Integer +--E 311 + +--S 312 of 526 +d0657:= D(m0657,x) +--R +--R +--R (311) +--R 4 2 4 3 2 +--R 2sinh(x) + (2cosh(x) + 2)sinh(x) - 2cosh(x) - 2cosh(x) + 2cosh(x) +--R + +--R 2cosh(x) +--R / +--R 2 2 +--R (3a cosh(x) + 6a cosh(x) + 3a)sinh(x) +--R Type: Expression Integer +--E 312 + +--S 313 of 526 +t0658:= coth(x)^4/(a+a*sech(x)) +--R +--R +--R 4 +--R coth(x) +--R (312) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 313 + +--S 314 of 526 +r0658:= 1/15*(-8+7*cosh(x)+27*cosh(x)^2-8*cosh(x)^3-_ + 23*cosh(x)^4+15*sinh(x)*x*cosh(x)^3+_ + 15*sinh(x)*cosh(x)^2*x-15*x*cosh(x)*sinh(x)-_ + 15*x*sinh(x))/sinh(x)^3/a/(1+cosh(x)) +--R +--R +--R (313) +--R 3 2 4 +--R (15x cosh(x) + 15x cosh(x) - 15x cosh(x) - 15x)sinh(x) - 23cosh(x) +--R + +--R 3 2 +--R - 8cosh(x) + 27cosh(x) + 7cosh(x) - 8 +--R / +--R 3 +--R (15a cosh(x) + 15a)sinh(x) +--R Type: Expression Integer +--E 314 + +--S 315 of 526 +a0658:= integrate(t0658,x) +--R +--R +--R (314) +--R 4 3 +--R - 23sinh(x) + ((60x + 92)cosh(x) + 30x + 46)sinh(x) +--R + +--R 2 2 +--R (- 138cosh(x) - 48cosh(x) + 16)sinh(x) +--R + +--R 3 2 +--R (60x + 92)cosh(x) + (90x + 138)cosh(x) + (- 60x - 92)cosh(x) - 90x +--R + +--R - 138 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R - 23cosh(x) - 16cosh(x) + 16cosh(x) + 8cosh(x) - 25 +--R / +--R 3 +--R (60a cosh(x) + 30a)sinh(x) +--R + +--R 3 2 +--R (60a cosh(x) + 90a cosh(x) - 60a cosh(x) - 90a)sinh(x) +--R Type: Union(Expression Integer,...) +--E 315 + +--S 316 of 526 +m0658:= a0658-r0658 +--R +--R +--R (315) +--R 6 +--R (- 23cosh(x) - 23)sinh(x) +--R + +--R 2 5 +--R ((60x + 92)cosh(x) + (90x + 138)cosh(x) + 30x + 46)sinh(x) +--R + +--R 3 2 4 +--R (- 138cosh(x) - 186cosh(x) - 32cosh(x) + 16)sinh(x) +--R + +--R 4 3 2 +--R 92cosh(x) + (60x + 230)cosh(x) + (60x + 46)cosh(x) +--R + +--R (- 60x - 230)cosh(x) - 60x - 138 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 2 +--R (69cosh(x) + 39cosh(x) - 92cosh(x) - 58cosh(x) + cosh(x) - 9)sinh(x) +--R + +--R 6 5 4 3 +--R - 60x cosh(x) - 150x cosh(x) + 30x cosh(x) + 300x cosh(x) +--R + +--R 2 +--R 120x cosh(x) - 150x cosh(x) - 90x +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 92cosh(x) + 170cosh(x) - 152cosh(x) - 360cosh(x) + 50cosh(x) +--R + +--R 2 +--R 238cosh(x) + 10cosh(x) - 48 +--R / +--R 2 5 +--R (60a cosh(x) + 90a cosh(x) + 30a)sinh(x) +--R + +--R 4 3 2 3 +--R (60a cosh(x) + 150a cosh(x) + 30a cosh(x) - 150a cosh(x) - 90a)sinh(x) +--R Type: Expression Integer +--E 316 + +--S 317 of 526 +d0658:= D(m0658,x) +--R +--R +--R (316) +--R 2 10 +--R (46cosh(x) + 92cosh(x) + 46)sinh(x) +--R + +--R 4 3 2 8 +--R (- 64cosh(x) - 169cosh(x) - 242cosh(x) - 233cosh(x) - 96)sinh(x) +--R + +--R 5 4 3 2 +--R - 240x cosh(x) - 720x cosh(x) - 780x cosh(x) - 360x cosh(x) +--R + +--R - 60x cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 948cosh(x) + 2631cosh(x) + 2712cosh(x) + 1762cosh(x) +--R + +--R 2 +--R 1208cosh(x) + 535cosh(x) + 54 +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 240x cosh(x) - 1200x cosh(x) - 1740x cosh(x) - 120x cosh(x) +--R + +--R 3 2 +--R 1680x cosh(x) + 1320x cosh(x) + 300x cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 248cosh(x) + 1429cosh(x) + 1700cosh(x) - 1099cosh(x) +--R + +--R 4 3 2 +--R - 2634cosh(x) - 153cosh(x) + 1740cosh(x) + 1073cosh(x) + 196 +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 240x cosh(x) + 720x cosh(x) + 60x cosh(x) - 1560x cosh(x) +--R + +--R 5 4 3 2 +--R - 1020x cosh(x) + 960x cosh(x) + 900x cosh(x) - 120x cosh(x) +--R + +--R - 180x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 626cosh(x) - 1583cosh(x) + 386cosh(x) + 3212cosh(x) +--R + +--R 6 5 4 3 2 +--R 604cosh(x) - 2394cosh(x) - 362cosh(x) + 984cosh(x) - 2cosh(x) +--R + +--R - 219cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 240x cosh(x) + 1200x cosh(x) + 1500x cosh(x) - 1800x cosh(x) +--R + +--R 7 6 5 4 +--R - 5400x cosh(x) - 1800x cosh(x) + 4800x cosh(x) + 4200x cosh(x) +--R + +--R 3 2 +--R - 600x cosh(x) - 1800x cosh(x) - 540x cosh(x) +--R * +--R sinh(x) +--R + +--R 12 11 10 9 +--R - 552cosh(x) - 2400cosh(x) - 1914cosh(x) + 5310cosh(x) +--R + +--R 8 7 6 5 4 +--R 8934cosh(x) - 1848cosh(x) - 10548cosh(x) - 3066cosh(x) + 4710cosh(x) +--R + +--R 3 2 +--R 2436cosh(x) - 630cosh(x) - 432cosh(x) +--R / +--R 4 3 2 +--R (120a cosh(x) + 360a cosh(x) + 390a cosh(x) + 180a cosh(x) + 30a) +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 240a cosh(x) + 960a cosh(x) + 1140a cosh(x) - 120a cosh(x) +--R + +--R 2 +--R - 1200a cosh(x) - 840a cosh(x) - 180a +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 120a cosh(x) + 600a cosh(x) + 870a cosh(x) - 300a cosh(x) +--R + +--R 4 3 2 +--R - 1830a cosh(x) - 1200a cosh(x) + 570a cosh(x) + 900a cosh(x) + 270a +--R * +--R 4 +--R sinh(x) +--R Type: Expression Integer +--E 317 + +--S 318 of 526 +t0659:= sech(x)^3/(a+b*sech(x)) +--R +--R +--R 3 +--R sech(x) +--R (317) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 318 + +--S 319 of 526 +r0659:= -a*atan(sinh(x))/b^2+2*a^2*atan((a-b)*tanh(1/2*x)/_ + (a^2-b^2)^(1/2))/b^2/(a^2-b^2)^(1/2)+tanh(x)/b +--R +--R +--R (318) +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 2 +--R - a\|- b + a atan(sinh(x)) - 2a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R b tanh(x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression Integer +--E 319 + +--S 320 of 526 +a0659:= integrate(t0659,x) +--R +--R +--R (319) +--R [ +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)\|b - a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R +-------+ +--R | 2 2 +--R - 2b\|b - a +--R / +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b )\|b - a +--R , +--R +--R 2 2 2 2 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)\|- b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +--R | 2 2 +--R - 2b\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b )\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 320 + +--S 321 of 526 +m0659:= a0659.1-r0659 +--R +--R +--R (320) +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a )\|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a)\|- b + a \|b - a +--R * +--R atan(sinh(x)) +--R + +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) + 2a )\|b - a +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 +--R ((- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b)tanh(x) - 2b) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 2 2 | 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b )\|- b + a \|b - a +--R Type: Expression Integer +--E 321 + +--S 322 of 526 +d0659:= D(m0659a,x) +--R +--R +--R (321) 0 +--R Type: Polynomial Integer +--E 322 + +--S 323 of 526 +m0659:= a0659.2-r0659 +--R +--R +--R (322) +--R 2 2 2 2 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)\|- b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a)\|- b + a +--R * +--R atan(sinh(x)) +--R + +--R x +--R (b - a)tanh(-) +--R 2 2 2 2 2 2 2 +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) + 2a )atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 +--R ((- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b)tanh(x) - 2b) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b )\|- b + a +--R Type: Expression Integer +--E 323 + +--S 324 of 526 +d0659:= D(m0659b,x) +--R +--R +--R (323) 0 +--R Type: Polynomial Integer +--E 324 + +--S 325 of 526 +t0660:= sech(x)^4/(a+b*sech(x)) +--R +--R +--R 4 +--R sech(x) +--R (324) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 325 + +--S 326 of 526 +r0660:= a^2*atan(sinh(x))/b^3+1/2*atan(sinh(x))/b-_ + 2*a^3*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/b^3/(a^2-b^2)^(1/2)-_ + a*tanh(x)/b^2+1/2*sech(x)*tanh(x)/b +--R +--R +--R (325) +--R x +--R +---------+ (b - a)tanh(-) +--R 2 2 | 2 2 3 2 +--R (b + 2a )\|- b + a atan(sinh(x)) + 4a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (b sech(x) - 2a b)tanh(x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R Type: Expression Integer +--E 326 + +--S 327 of 526 +a0660:= integrate(t0660,x) +--R +--R +--R (326) +--R [ +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 2 4 2 2 3 +--R (b + 2a )sinh(x) + (4b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a )cosh(x) + 2b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a )cosh(x) + (4b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b + 2a )cosh(x) + (2b + 4a )cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R b sinh(x) + (3b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (3b cosh(x) + 4a b cosh(x) - b )sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b cosh(x) + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 3 4 3 3 3 2 3 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 4 2 2 3 +--R (b + 2a )sinh(x) + (4b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a )cosh(x) + 2b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a )cosh(x) + (4b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b + 2a )cosh(x) + (2b + 4a )cosh(x) + b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R b sinh(x) + (3b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (3b cosh(x) + 4a b cosh(x) - b )sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b cosh(x) + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 4 3 3 3 2 3 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 327 + +--S 328 of 526 +m0660:= a0660.1-r0660 +--R +--R +--R (327) +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 2 2 4 2 2 3 +--R (2b + 4a )sinh(x) + (8b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 24a )cosh(x) + 4b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 16a )cosh(x) + (8b + 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + 4a )cosh(x) + (4b + 8a )cosh(x) + 2b + 4a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a atan(sinh(x) + cosh(x)) +--R + +--R 2 2 4 2 2 3 +--R (- b - 2a )sinh(x) + (- 4b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b - 12a )cosh(x) - 2b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b - 8a )cosh(x) + (- 4b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b - 2a )cosh(x) + (- 2b - 4a )cosh(x) - b - 2a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a atan(sinh(x)) +--R + +--R 3 4 3 3 3 2 3 2 +--R - 4a sinh(x) - 16a cosh(x)sinh(x) + (- 24a cosh(x) - 8a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (- 16a cosh(x) - 16a cosh(x))sinh(x) - 4a cosh(x) - 8a cosh(x) - 4a +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 +--R (- b sech(x) + 2a b)sinh(x) +--R + +--R 2 3 +--R (- 4b cosh(x)sech(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b cosh(x) - 2b )sech(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 3 +--R (- 4b cosh(x) - 4b cosh(x))sech(x) + 8a b cosh(x) +--R + +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- b cosh(x) - 2b cosh(x) - b )sech(x) + 2a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 2 3 2 2 +--R 2b sinh(x) + (6b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (6b cosh(x) + 8a b cosh(x) - 2b )sinh(x) + 2b cosh(x) +--R + +--R 2 2 +--R 4a b cosh(x) - 2b cosh(x) + 4a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) + 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) + 8b cosh(x))sinh(x) + 2b cosh(x) + 4b cosh(x) + 2b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 328 + +--S 329 of 526 +d0660:= D(m0660a,x) +--R +--R +--R (328) 0 +--R Type: Polynomial Integer +--E 329 + +--S 330 of 526 +m0660:= a0660.2-r0660 +--R +--R +--R (329) +--R 3 4 3 3 3 2 3 2 +--R 4a sinh(x) + 16a cosh(x)sinh(x) + (24a cosh(x) + 8a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (16a cosh(x) + 16a cosh(x))sinh(x) + 4a cosh(x) + 8a cosh(x) + 4a +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 4 2 2 3 +--R (2b + 4a )sinh(x) + (8b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 24a )cosh(x) + 4b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 16a )cosh(x) + (8b + 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + 4a )cosh(x) + (4b + 8a )cosh(x) + 2b + 4a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x) + cosh(x)) +--R + +--R 2 2 4 2 2 3 +--R (- b - 2a )sinh(x) + (- 4b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b - 12a )cosh(x) - 2b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b - 8a )cosh(x) + (- 4b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b - 2a )cosh(x) + (- 2b - 4a )cosh(x) - b - 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x)) +--R + +--R 3 4 3 3 3 2 3 2 +--R - 4a sinh(x) - 16a cosh(x)sinh(x) + (- 24a cosh(x) - 8a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (- 16a cosh(x) - 16a cosh(x))sinh(x) - 4a cosh(x) - 8a cosh(x) - 4a +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 +--R (- b sech(x) + 2a b)sinh(x) +--R + +--R 2 3 +--R (- 4b cosh(x)sech(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b cosh(x) - 2b )sech(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 3 +--R (- 4b cosh(x) - 4b cosh(x))sech(x) + 8a b cosh(x) +--R + +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- b cosh(x) - 2b cosh(x) - b )sech(x) + 2a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 2 3 2 2 +--R 2b sinh(x) + (6b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (6b cosh(x) + 8a b cosh(x) - 2b )sinh(x) + 2b cosh(x) +--R + +--R 2 2 +--R 4a b cosh(x) - 2b cosh(x) + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) + 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) + 8b cosh(x))sinh(x) + 2b cosh(x) + 4b cosh(x) + 2b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 330 + +--S 331 of 526 +d0660:= D(m0660b,x) +--R +--R +--R (330) 0 +--R Type: Polynomial Integer +--E 331 + +--S 332 of 526 +t0661:= sech(x)^3/(a+a*sech(x)) +--R +--R +--R 3 +--R sech(x) +--R (331) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 332 + +--S 333 of 526 +r0661:= -atan(sinh(x))/a+sinh(x)/a/(1+cosh(x))+tanh(x)/a +--R +--R +--R (- cosh(x) - 1)atan(sinh(x)) + (cosh(x) + 1)tanh(x) + sinh(x) +--R (332) ------------------------------------------------------------- +--R a cosh(x) + a +--R Type: Expression Integer +--E 333 + +--S 334 of 526 +a0661:= integrate(t0661,x) +--R +--R +--R (333) +--R 3 2 +--R - 2sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (- 6cosh(x) - 4cosh(x) - 2)sinh(x) - 2cosh(x) - 2cosh(x) +--R + +--R - 2cosh(x) - 2 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R - 2sinh(x) + (- 4cosh(x) - 2)sinh(x) - 2cosh(x) - 2cosh(x) - 4 +--R / +--R 3 2 +--R a sinh(x) + (3a cosh(x) + a)sinh(x) +--R + +--R 2 3 2 +--R (3a cosh(x) + 2a cosh(x) + a)sinh(x) + a cosh(x) + a cosh(x) +--R + +--R a cosh(x) + a +--R Type: Union(Expression Integer,...) +--E 334 + +--S 335 of 526 +m0661:= a0661-r0661 +--R +--R +--R (334) +--R 3 2 2 +--R (- 2cosh(x) - 2)sinh(x) + (- 6cosh(x) - 8cosh(x) - 2)sinh(x) +--R + +--R 3 2 4 +--R (- 6cosh(x) - 10cosh(x) - 6cosh(x) - 2)sinh(x) - 2cosh(x) +--R + +--R 3 2 +--R - 4cosh(x) - 4cosh(x) - 4cosh(x) - 2 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 2 2 +--R (cosh(x) + 1)sinh(x) + (3cosh(x) + 4cosh(x) + 1)sinh(x) +--R + +--R 3 2 4 3 +--R (3cosh(x) + 5cosh(x) + 3cosh(x) + 1)sinh(x) + cosh(x) + 2cosh(x) +--R + +--R 2 +--R 2cosh(x) + 2cosh(x) + 1 +--R * +--R atan(sinh(x)) +--R + +--R 3 2 2 +--R (- cosh(x) - 1)sinh(x) + (- 3cosh(x) - 4cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 +--R (- 3cosh(x) - 5cosh(x) - 3cosh(x) - 1)sinh(x) - cosh(x) +--R + +--R 3 2 +--R - 2cosh(x) - 2cosh(x) - 2cosh(x) - 1 +--R * +--R tanh(x) +--R + +--R 4 3 +--R - sinh(x) + (- 3cosh(x) - 1)sinh(x) +--R + +--R 2 2 +--R (- 3cosh(x) - 4cosh(x) - 3)sinh(x) +--R + +--R 3 2 3 2 +--R (- cosh(x) - 5cosh(x) - 7cosh(x) - 3)sinh(x) - 2cosh(x) - 4cosh(x) +--R + +--R - 6cosh(x) - 4 +--R / +--R 3 2 2 +--R (a cosh(x) + a)sinh(x) + (3a cosh(x) + 4a cosh(x) + a)sinh(x) +--R + +--R 3 2 4 +--R (3a cosh(x) + 5a cosh(x) + 3a cosh(x) + a)sinh(x) + a cosh(x) +--R + +--R 3 2 +--R 2a cosh(x) + 2a cosh(x) + 2a cosh(x) + a +--R Type: Expression Integer +--E 335 + +--S 336 of 526 +d0661:= D(m0661,x) +--R +--R +--R (335) +--R 2 8 +--R (cosh(x) + 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 7 +--R (6cosh(x) + 14cosh(x) + 10cosh(x) + 2)sinh(x) +--R + +--R 4 3 2 6 +--R (15cosh(x) + 40cosh(x) + 39cosh(x) + 18cosh(x) + 4)sinh(x) +--R + +--R 5 4 3 2 +--R (20cosh(x) + 60cosh(x) + 78cosh(x) + 62cosh(x) + 30cosh(x) + 6) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 15cosh(x) + 50cosh(x) + 88cosh(x) + 108cosh(x) + 83cosh(x) +--R + +--R 34cosh(x) + 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 6cosh(x) + 22cosh(x) + 58cosh(x) + 106cosh(x) + 114cosh(x) +--R + +--R 2 +--R 74cosh(x) + 30cosh(x) + 6 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 4cosh(x) + 23cosh(x) + 62cosh(x) + 87cosh(x) +--R + +--R 3 2 +--R 80cosh(x) + 53cosh(x) + 22cosh(x) + 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 6cosh(x) + 22cosh(x) + 38cosh(x) + 46cosh(x) + 42cosh(x) +--R + +--R 2 +--R 26cosh(x) + 10cosh(x) + 2 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 4cosh(x) + 8cosh(x) + 12cosh(x) + 14cosh(x) +--R + +--R 3 2 +--R 12cosh(x) + 8cosh(x) + 4cosh(x) + 1 +--R * +--R 2 +--R tanh(x) +--R + +--R 10 9 2 8 +--R sinh(x) + (6cosh(x) + 2)sinh(x) + (13cosh(x) + 7cosh(x) + 3)sinh(x) +--R + +--R 3 2 7 +--R (8cosh(x) - 2cosh(x) + 6cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 6 +--R (- 15cosh(x) - 44cosh(x) - 18cosh(x) + cosh(x) + 2)sinh(x) +--R + +--R 5 4 3 2 5 +--R (- 34cosh(x) - 84cosh(x) - 70cosh(x) - 36cosh(x) + 8)sinh(x) +--R + +--R 6 5 4 3 2 +--R - 29cosh(x) - 68cosh(x) - 83cosh(x) - 77cosh(x) - 26cosh(x) +--R + +--R cosh(x) - 2 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 12cosh(x) - 18cosh(x) - 34cosh(x) - 64cosh(x) - 56cosh(x) +--R + +--R 2 +--R - 34cosh(x) - 10cosh(x) + 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 2cosh(x) + 8cosh(x) + 8cosh(x) - 21cosh(x) - 45cosh(x) +--R + +--R 3 2 +--R - 34cosh(x) - 2cosh(x) + 3cosh(x) - 3 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 5 4 3 +--R 6cosh(x) + 10cosh(x) - 14cosh(x) - 4cosh(x) + 14cosh(x) +--R + +--R - 10cosh(x) - 2 +--R * +--R sinh(x) +--R + +--R 9 8 7 6 5 4 +--R cosh(x) + 2cosh(x) + cosh(x) - cosh(x) + 3cosh(x) + 7cosh(x) +--R + +--R 3 2 +--R - cosh(x) - 7cosh(x) - 4cosh(x) - 1 +--R / +--R 2 8 +--R (a cosh(x) + 2a cosh(x) + a)sinh(x) +--R + +--R 3 2 7 +--R (6a cosh(x) + 14a cosh(x) + 10a cosh(x) + 2a)sinh(x) +--R + +--R 4 3 2 6 +--R (15a cosh(x) + 40a cosh(x) + 39a cosh(x) + 18a cosh(x) + 4a)sinh(x) +--R + +--R 5 4 3 2 +--R 20a cosh(x) + 60a cosh(x) + 78a cosh(x) + 62a cosh(x) +--R + +--R 30a cosh(x) + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 15a cosh(x) + 50a cosh(x) + 88a cosh(x) + 108a cosh(x) +--R + +--R 2 +--R 83a cosh(x) + 34a cosh(x) + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 6a cosh(x) + 22a cosh(x) + 58a cosh(x) + 106a cosh(x) +--R + +--R 3 2 +--R 114a cosh(x) + 74a cosh(x) + 30a cosh(x) + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R a cosh(x) + 4a cosh(x) + 23a cosh(x) + 62a cosh(x) + 87a cosh(x) +--R + +--R 3 2 +--R 80a cosh(x) + 53a cosh(x) + 22a cosh(x) + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 6a cosh(x) + 22a cosh(x) + 38a cosh(x) + 46a cosh(x) +--R + +--R 3 2 +--R 42a cosh(x) + 26a cosh(x) + 10a cosh(x) + 2a +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R a cosh(x) + 4a cosh(x) + 8a cosh(x) + 12a cosh(x) + 14a cosh(x) +--R + +--R 3 2 +--R 12a cosh(x) + 8a cosh(x) + 4a cosh(x) + a +--R Type: Expression Integer +--E 336 + +--S 337 of 526 +t0662:= csch(x)^3/(a+a*sech(x)) +--R +--R +--R 3 +--R csch(x) +--R (336) ------------- +--R a sech(x) + a +--R Type: Expression Integer +--E 337 + +--S 338 of 526 +r0662:= 1/8*atanh(cosh(x))/a+1/8/a/(1-cosh(x))+1/8/a/(1+cosh(x))^2 +--R +--R +--R (337) +--R 3 2 2 +--R (cosh(x) + cosh(x) - cosh(x) - 1)atanh(cosh(x)) - cosh(x) - cosh(x) - 2 +--R -------------------------------------------------------------------------- +--R 3 2 +--R 8a cosh(x) + 8a cosh(x) - 8a cosh(x) - 8a +--R Type: Expression Integer +--E 338 + +--S 339 of 526 +a0662:= integrate(t0662,x) +--R +--R +--R (338) +--R 6 5 +--R sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 2 4 +--R (15cosh(x) + 10cosh(x) - 1)sinh(x) +--R + +--R 3 2 3 +--R (20cosh(x) + 20cosh(x) - 4cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 2 +--R (15cosh(x) + 20cosh(x) - 6cosh(x) - 12cosh(x) - 1)sinh(x) +--R + +--R 5 4 3 2 +--R (6cosh(x) + 10cosh(x) - 4cosh(x) - 12cosh(x) - 2cosh(x) + 2) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) + 2cosh(x) - cosh(x) - 4cosh(x) - cosh(x) + 2cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 6 5 +--R - sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 2 4 +--R (- 15cosh(x) - 10cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 +--R (- 20cosh(x) - 20cosh(x) + 4cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 2 +--R (- 15cosh(x) - 20cosh(x) + 6cosh(x) + 12cosh(x) + 1)sinh(x) +--R + +--R 5 4 3 2 +--R (- 6cosh(x) - 10cosh(x) + 4cosh(x) + 12cosh(x) + 2cosh(x) - 2) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - cosh(x) - 2cosh(x) + cosh(x) + 4cosh(x) + cosh(x) - 2cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 5 4 +--R - 2sinh(x) + (- 10cosh(x) - 4)sinh(x) +--R + +--R 2 3 +--R (- 20cosh(x) - 16cosh(x) - 20)sinh(x) +--R + +--R 3 2 2 +--R (- 20cosh(x) - 24cosh(x) - 60cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 +--R (- 10cosh(x) - 16cosh(x) - 60cosh(x) - 8cosh(x) - 2)sinh(x) +--R + +--R 5 4 3 2 +--R - 2cosh(x) - 4cosh(x) - 20cosh(x) - 4cosh(x) - 2cosh(x) +--R / +--R 6 5 +--R 8a sinh(x) + (48a cosh(x) + 16a)sinh(x) +--R + +--R 2 4 +--R (120a cosh(x) + 80a cosh(x) - 8a)sinh(x) +--R + +--R 3 2 3 +--R (160a cosh(x) + 160a cosh(x) - 32a cosh(x) - 32a)sinh(x) +--R + +--R 4 3 2 2 +--R (120a cosh(x) + 160a cosh(x) - 48a cosh(x) - 96a cosh(x) - 8a)sinh(x) +--R + +--R 5 4 3 2 +--R 48a cosh(x) + 80a cosh(x) - 32a cosh(x) - 96a cosh(x) +--R + +--R - 16a cosh(x) + 16a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 8a cosh(x) + 16a cosh(x) - 8a cosh(x) - 32a cosh(x) - 8a cosh(x) +--R + +--R 16a cosh(x) + 8a +--R Type: Union(Expression Integer,...) +--E 339 + +--S 340 of 526 +m0662:= a0662-r0662 +--R +--R +--R (339) +--R 3 2 6 +--R (cosh(x) + cosh(x) - cosh(x) - 1)sinh(x) +--R + +--R 4 3 2 5 +--R (6cosh(x) + 8cosh(x) - 4cosh(x) - 8cosh(x) - 2)sinh(x) +--R + +--R 5 4 3 2 +--R (15cosh(x) + 25cosh(x) - 6cosh(x) - 26cosh(x) - 9cosh(x) + 1) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 20cosh(x) + 40cosh(x) - 4cosh(x) - 48cosh(x) - 20cosh(x) +--R + +--R 8cosh(x) + 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 15cosh(x) + 35cosh(x) - cosh(x) - 53cosh(x) - 27cosh(x) +--R + +--R 2 +--R 17cosh(x) + 13cosh(x) + 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 5 4 3 +--R 6cosh(x) + 16cosh(x) - 32cosh(x) - 20cosh(x) + 16cosh(x) +--R + +--R 2 +--R 16cosh(x) - 2 +--R * +--R sinh(x) +--R + +--R 9 8 6 5 4 3 +--R cosh(x) + 3cosh(x) - 8cosh(x) - 6cosh(x) + 6cosh(x) + 8cosh(x) +--R + +--R - 3cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 6 +--R (- cosh(x) - cosh(x) + cosh(x) + 1)sinh(x) +--R + +--R 4 3 2 5 +--R (- 6cosh(x) - 8cosh(x) + 4cosh(x) + 8cosh(x) + 2)sinh(x) +--R + +--R 5 4 3 2 +--R (- 15cosh(x) - 25cosh(x) + 6cosh(x) + 26cosh(x) + 9cosh(x) - 1) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 20cosh(x) - 40cosh(x) + 4cosh(x) + 48cosh(x) + 20cosh(x) +--R + +--R - 8cosh(x) - 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 15cosh(x) - 35cosh(x) + cosh(x) + 53cosh(x) + 27cosh(x) +--R + +--R 2 +--R - 17cosh(x) - 13cosh(x) - 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 5 4 3 +--R - 6cosh(x) - 16cosh(x) + 32cosh(x) + 20cosh(x) - 16cosh(x) +--R + +--R 2 +--R - 16cosh(x) + 2 +--R * +--R sinh(x) +--R + +--R 9 8 6 5 4 +--R - cosh(x) - 3cosh(x) + 8cosh(x) + 6cosh(x) - 6cosh(x) +--R + +--R 3 +--R - 8cosh(x) + 3cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 2 6 +--R (- cosh(x) - cosh(x) + cosh(x) + 1)sinh(x) +--R + +--R 4 3 2 5 +--R (- 6cosh(x) - 8cosh(x) + 4cosh(x) + 8cosh(x) + 2)sinh(x) +--R + +--R 5 4 3 2 +--R (- 15cosh(x) - 25cosh(x) + 6cosh(x) + 26cosh(x) + 9cosh(x) - 1) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 20cosh(x) - 40cosh(x) + 4cosh(x) + 48cosh(x) + 20cosh(x) +--R + +--R - 8cosh(x) - 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 15cosh(x) - 35cosh(x) + cosh(x) + 53cosh(x) + 27cosh(x) +--R + +--R 2 +--R - 17cosh(x) - 13cosh(x) - 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 5 4 3 +--R - 6cosh(x) - 16cosh(x) + 32cosh(x) + 20cosh(x) - 16cosh(x) +--R + +--R 2 +--R - 16cosh(x) + 2 +--R * +--R sinh(x) +--R + +--R 9 8 6 5 4 +--R - cosh(x) - 3cosh(x) + 8cosh(x) + 6cosh(x) - 6cosh(x) +--R + +--R 3 +--R - 8cosh(x) + 3cosh(x) + 1 +--R * +--R atanh(cosh(x)) +--R + +--R 2 6 +--R (cosh(x) + cosh(x) + 2)sinh(x) +--R + +--R 3 2 5 +--R (4cosh(x) + 6cosh(x) + 16cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) + 11cosh(x) + 45cosh(x) + 33cosh(x) + 2)sinh(x) +--R + +--R 4 3 2 3 +--R (4cosh(x) + 40cosh(x) + 48cosh(x) + 24cosh(x) + 12)sinh(x) +--R + +--R 6 5 4 3 2 +--R - 5cosh(x) - 9cosh(x) - 20cosh(x) + 2cosh(x) + 55cosh(x) +--R + +--R 39cosh(x) + 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 4cosh(x) - 10cosh(x) - 48cosh(x) - 38cosh(x) + 44cosh(x) +--R + +--R 2 +--R 42cosh(x) + 8cosh(x) + 6 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - cosh(x) - 3cosh(x) - 19cosh(x) - 19cosh(x) + 11cosh(x) +--R + +--R 3 2 +--R 15cosh(x) + 7cosh(x) + 7cosh(x) + 2 +--R / +--R 3 2 6 +--R (8a cosh(x) + 8a cosh(x) - 8a cosh(x) - 8a)sinh(x) +--R + +--R 4 3 2 5 +--R (48a cosh(x) + 64a cosh(x) - 32a cosh(x) - 64a cosh(x) - 16a)sinh(x) +--R + +--R 5 4 3 2 +--R 120a cosh(x) + 200a cosh(x) - 48a cosh(x) - 208a cosh(x) +--R + +--R - 72a cosh(x) + 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 160a cosh(x) + 320a cosh(x) - 32a cosh(x) - 384a cosh(x) +--R + +--R 2 +--R - 160a cosh(x) + 64a cosh(x) + 32a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 120a cosh(x) + 280a cosh(x) - 8a cosh(x) - 424a cosh(x) +--R + +--R 3 2 +--R - 216a cosh(x) + 136a cosh(x) + 104a cosh(x) + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 5 4 +--R 48a cosh(x) + 128a cosh(x) - 256a cosh(x) - 160a cosh(x) +--R + +--R 3 2 +--R 128a cosh(x) + 128a cosh(x) - 16a +--R * +--R sinh(x) +--R + +--R 9 8 6 5 4 +--R 8a cosh(x) + 24a cosh(x) - 64a cosh(x) - 48a cosh(x) + 48a cosh(x) +--R + +--R 3 +--R 64a cosh(x) - 24a cosh(x) - 8a +--R Type: Expression Integer +--E 340 + +--S 341 of 526 +d0662:= D(m0662,x) +--R +--R +--R (340) +--R 9 2 8 +--R - cosh(x)sinh(x) + (- 8cosh(x) - 2cosh(x))sinh(x) +--R + +--R 3 2 7 +--R (- 28cosh(x) - 14cosh(x) + 2cosh(x))sinh(x) +--R + +--R 4 3 2 6 +--R (- 56cosh(x) - 42cosh(x) + 12cosh(x) + 6cosh(x))sinh(x) +--R + +--R 5 4 3 2 +--R (- 62cosh(x) - 62cosh(x) + 14cosh(x) + 14cosh(x) + 8cosh(x) + 8) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 16cosh(x) - 30cosh(x) - 40cosh(x) - 20cosh(x) + 40cosh(x) +--R + +--R 34cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 52cosh(x) + 38cosh(x) - 122cosh(x) - 92cosh(x) + 64cosh(x) +--R + +--R 2 +--R 46cosh(x) + 6cosh(x) + 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 72cosh(x) + 66cosh(x) - 124cosh(x) - 106cosh(x) + 32cosh(x) +--R + +--R 3 2 +--R 14cosh(x) + 20cosh(x) + 26cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R 39cosh(x) + 38cosh(x) - 54cosh(x) - 50cosh(x) - 8cosh(x) +--R + +--R 4 3 2 +--R - 14cosh(x) + 22cosh(x) + 26cosh(x) + cosh(x) +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 5 +--R 8cosh(x) + 8cosh(x) - 8cosh(x) - 8cosh(x) - 8cosh(x) - 8cosh(x) +--R + +--R 4 3 +--R 8cosh(x) + 8cosh(x) +--R / +--R 5 4 3 2 +--R (a cosh(x) + a cosh(x) - 2a cosh(x) - 2a cosh(x) + a cosh(x) + a) +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 8a cosh(x) + 10a cosh(x) - 14a cosh(x) - 20a cosh(x) +--R + +--R 2 +--R 4a cosh(x) + 10a cosh(x) + 2a +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 28a cosh(x) + 42a cosh(x) - 44a cosh(x) - 86a cosh(x) +--R + +--R 3 2 +--R 4a cosh(x) + 46a cosh(x) + 12a cosh(x) - 2a +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 56a cosh(x) + 98a cosh(x) - 82a cosh(x) - 214a cosh(x) +--R + +--R 4 3 2 +--R - 10a cosh(x) + 134a cosh(x) + 42a cosh(x) - 18a cosh(x) - 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 70a cosh(x) + 140a cosh(x) - 100a cosh(x) - 340a cosh(x) +--R + +--R 5 4 3 2 +--R - 40a cosh(x) + 260a cosh(x) + 100a cosh(x) - 60a cosh(x) +--R + +--R - 30a cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 56a cosh(x) + 126a cosh(x) - 82a cosh(x) - 352a cosh(x) +--R + +--R 6 5 4 3 +--R - 64a cosh(x) + 332a cosh(x) + 156a cosh(x) - 112a cosh(x) +--R + +--R 2 +--R - 72a cosh(x) + 6a cosh(x) + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 28a cosh(x) + 70a cosh(x) - 44a cosh(x) - 230a cosh(x) +--R + +--R 7 6 5 4 +--R - 56a cosh(x) + 268a cosh(x) + 152a cosh(x) - 124a cosh(x) +--R + +--R 3 2 +--R - 100a cosh(x) + 14a cosh(x) + 20a cosh(x) + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 12 11 10 9 +--R 8a cosh(x) + 22a cosh(x) - 14a cosh(x) - 86a cosh(x) +--R + +--R 8 7 6 5 +--R - 26a cosh(x) + 124a cosh(x) + 84a cosh(x) - 76a cosh(x) +--R + +--R 4 3 2 +--R - 76a cosh(x) + 14a cosh(x) + 26a cosh(x) + 2a cosh(x) - 2a +--R * +--R sinh(x) +--R + +--R 13 12 11 10 9 +--R a cosh(x) + 3a cosh(x) - 2a cosh(x) - 14a cosh(x) - 5a cosh(x) +--R + +--R 8 7 6 5 4 +--R 25a cosh(x) + 20a cosh(x) - 20a cosh(x) - 25a cosh(x) + 5a cosh(x) +--R + +--R 3 2 +--R 14a cosh(x) + 2a cosh(x) - 3a cosh(x) - a +--R Type: Expression Integer +--E 341 + +--S 342 of 526 +t0663:= sinh(x)/(a+b*csch(x)) +--R +--R +--R sinh(x) +--R (341) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 342 + +--S 343 of 526 +r0663:= -b*x/a^2-2*b^2*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/_ + a^2/(a^2+b^2)^(1/2)+cosh(x)/a +--R +--R +--R x +--R b tanh(-) - a +-------+ +--R 2 2 | 2 2 +--R 2b atanh(-------------) + (a cosh(x) - b x)\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (342) ----------------------------------------------------- +--R +-------+ +--R 2 | 2 2 +--R a \|b + a +--R Type: Expression Integer +--E 343 + +--S 344 of 526 +a0663:= integrate(t0663,x) +--R +--R +--R (343) +--R 2 2 +--R (2b sinh(x) + 2b cosh(x)) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b - 2a )sinh(x) + (- 2a b - 2a )cosh(x) - 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 2 +--R a sinh(x) + (2a cosh(x) - 2b x)sinh(x) + a cosh(x) - 2b x cosh(x) +--R + +--R a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|b + a +--R Type: Union(Expression Integer,...) +--E 344 + +--S 345 of 526 +m0663:= a0663-r0663 +--R +--R +--R (344) +--R 2 2 +--R (2b sinh(x) + 2b cosh(x)) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b - 2a )sinh(x) + (- 2a b - 2a )cosh(x) - 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R x +--R b tanh(-) - a +--R 2 2 2 +--R (- 4b sinh(x) - 4b cosh(x))atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (a sinh(x) - a cosh(x) + a)\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|b + a +--R Type: Expression Integer +--E 345 + +--S 346 of 526 +d0663:= D(m0663,x) +--R +--R +--R (345) +--R 4 2 3 2 2 +--R - a b sinh(x) + (- 2a b cosh(x) - 4b )sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 3 2 2 4 +--R (2a b cosh(x) - 4b cosh(x) - 2a b cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R 2a sinh(x) + (4a cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 +--R (4a b cosh(x) - 8b )sinh(x) +--R + +--R 2 3 2 2 2 +--R (- 4a cosh(x) - 4a b cosh(x) + (- 16b + 4a )cosh(x) + 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 +--R - 2a cosh(x) - 4a b cosh(x) + (- 8b + 4a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 3 2 2 +--R a b sinh(x) + (2a b cosh(x) + 4b )sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 3 2 2 4 +--R (- 2a b cosh(x) + 4b cosh(x) + 2a b cosh(x))sinh(x) - a b cosh(x) +--R + +--R 2 +--R 2a b cosh(x) - a b +--R / +--R 2 3 2 2 2 +--R 2a b sinh(x) + (6a b cosh(x) + 4a b )sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (6a b cosh(x) + 8a b cosh(x) - 2a b)sinh(x) + 2a b cosh(x) +--R + +--R 2 2 2 +--R 4a b cosh(x) - 2a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 3 3 2 2 +--R - 4a sinh(x) + (- 12a cosh(x) - 8a b)sinh(x) +--R + +--R 3 2 2 3 3 3 +--R (- 12a cosh(x) - 16a b cosh(x) + 4a )sinh(x) - 4a cosh(x) +--R + +--R 2 2 3 +--R - 8a b cosh(x) + 4a cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 3 2 2 2 +--R - 2a b sinh(x) + (- 6a b cosh(x) - 4a b )sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 6a b cosh(x) - 8a b cosh(x) + 2a b)sinh(x) - 2a b cosh(x) +--R + +--R 2 2 2 +--R - 4a b cosh(x) + 2a b cosh(x) +--R Type: Expression Integer +--E 346 + +--S 347 of 526 +t0664:= sinh(x)^2/(a+b*csch(x)) +--R +--R +--R 2 +--R sinh(x) +--R (346) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 347 + +--S 348 of 526 +r0664:= -1/2*x/a+b^2*x/a^3+2*b^3*atanh((a-b*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/a^3/(a^2+b^2)^(1/2)-b*cosh(x)/a^2+_ + 1/2*cosh(x)*sinh(x)/a +--R +--R +--R (347) +--R x +--R b tanh(-) - a +--R 3 2 +--R - 4b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (a cosh(x)sinh(x) - 2a b cosh(x) + (2b - a )x)\|b + a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2a \|b + a +--R Type: Expression Integer +--E 348 + +--S 349 of 526 +a0664:= integrate(t0664,x) +--R +--R +--R (348) +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b - 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b - 8a )x cosh(x) - 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b - 4a )x cosh(x) - 4a b cosh(x) - a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|b + a +--R Type: Union(Expression Integer,...) +--E 349 + +--S 350 of 526 +m0664:= a0664-r0664 +--R +--R +--R (349) +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R x +--R b tanh(-) - a +--R 3 2 3 3 2 2 +--R (16b sinh(x) + 32b cosh(x)sinh(x) + 16b cosh(x) )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 4 3 2 2 2 +--R a sinh(x) - 4a b sinh(x) + (- 2a cosh(x) - 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (4a b cosh(x) - 4a b)sinh(x) + a cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - 4a b cosh(x) - a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|b + a +--R Type: Expression Integer +--E 350 + +--S 351 of 526 +d0664:= D(m0664,x) +--R +--R +--R (350) +--R 2 6 2 5 +--R - a b sinh(x) - 2a b cosh(x)sinh(x) +--R + +--R 2 2 2 3 2 4 +--R (a b cosh(x) + 4a b cosh(x) + 8b + a b)sinh(x) +--R + +--R 2 3 2 2 3 3 +--R (4a b cosh(x) + 8a b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 2 2 +--R (a b cosh(x) + (24b - 2a b)cosh(x) + 4a b cosh(x) + a b)sinh(x) +--R + +--R 2 5 2 4 3 3 2 2 +--R - 2a b cosh(x) - 8a b cosh(x) + 8b cosh(x) + 8a b cosh(x) +--R + +--R 2 +--R 2a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - a b cosh(x) - 4a b cosh(x) + a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 +--R a b cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 5 +--R 2a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (- 2a cosh(x) - 8a b cosh(x) - 8a b - 2a )sinh(x) +--R + +--R 3 3 2 2 2 3 3 +--R (- 8a cosh(x) - 16a b cosh(x) - 16a b cosh(x) + 16b )sinh(x) +--R + +--R 3 4 3 2 3 2 2 3 +--R (- 2a cosh(x) + 4a cosh(x) + (48b - 8a b)cosh(x) - 8a b - 2a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 +--R 4a cosh(x) + 16a b cosh(x) + 16a b cosh(x) +--R + +--R 3 2 2 2 3 +--R (48b - 16a b)cosh(x) + (- 16a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R 2a cosh(x) + 8a b cosh(x) + (8a b - 2a )cosh(x) +--R + +--R 3 2 3 2 3 2 3 +--R (16b - 8a b)cosh(x) + (- 8a b - 2a )cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 5 +--R a b sinh(x) + 2a b cosh(x)sinh(x) +--R + +--R 2 2 2 3 2 4 +--R (- a b cosh(x) - 4a b cosh(x) - 8b - a b)sinh(x) +--R + +--R 2 3 2 2 3 3 +--R (- 4a b cosh(x) - 8a b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 2 2 +--R (- a b cosh(x) + (- 24b + 2a b)cosh(x) - 4a b cosh(x) - a b)sinh(x) +--R + +--R 2 5 2 4 3 3 2 2 +--R 2a b cosh(x) + 8a b cosh(x) - 8b cosh(x) - 8a b cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R a b cosh(x) + 4a b cosh(x) - a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 +--R - a b cosh(x) + a b +--R / +--R 3 4 3 2 2 3 +--R 4a b sinh(x) + (16a b cosh(x) + 8a b )sinh(x) +--R + +--R 3 2 2 2 3 2 +--R (24a b cosh(x) + 24a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 3 2 2 2 3 +--R (16a b cosh(x) + 24a b cosh(x) - 8a b cosh(x))sinh(x) +--R + +--R 3 4 2 2 3 3 2 +--R 4a b cosh(x) + 8a b cosh(x) - 4a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 4 4 3 3 +--R - 8a sinh(x) + (- 32a cosh(x) - 16a b)sinh(x) +--R + +--R 4 2 3 4 2 +--R (- 48a cosh(x) - 48a b cosh(x) + 8a )sinh(x) +--R + +--R 4 3 3 2 4 4 4 +--R (- 32a cosh(x) - 48a b cosh(x) + 16a cosh(x))sinh(x) - 8a cosh(x) +--R + +--R 3 3 4 2 +--R - 16a b cosh(x) + 8a cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 4 3 2 2 3 +--R - 4a b sinh(x) + (- 16a b cosh(x) - 8a b )sinh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 24a b cosh(x) - 24a b cosh(x) + 4a b)sinh(x) +--R + +--R 3 3 2 2 2 3 3 4 +--R (- 16a b cosh(x) - 24a b cosh(x) + 8a b cosh(x))sinh(x) - 4a b cosh(x) +--R + +--R 2 2 3 3 2 +--R - 8a b cosh(x) + 4a b cosh(x) +--R Type: Expression Integer +--E 351 + +--S 352 of 526 +t0665:= sinh(x)^3/(a+b*csch(x)) +--R +--R +--R 3 +--R sinh(x) +--R (351) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 352 + +--S 353 of 526 +r0665:= 1/2*b*x/a^2-b^3*x/a^4-2*b^4*atanh((a-b*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/a^4/(a^2+b^2)^(1/2)-cosh(x)/a+_ + b^2*cosh(x)/a^3+1/3*cosh(x)^3/a-1/2*b*cosh(x)*sinh(x)/a^2 +--R +--R +--R (352) +--R x +--R b tanh(-) - a +--R 4 2 +--R 12b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 3 2 3 +--R - 3a b cosh(x)sinh(x) + 2a cosh(x) + (6a b - 6a )cosh(x) +--R + +--R 3 2 +--R (- 6b + 3a b)x +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6a \|b + a +--R Type: Expression Integer +--E 353 + +--S 354 of 526 +a0665:= integrate(t0665,x) +--R +--R +--R (353) +--R 4 3 4 2 4 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 4 3 +--R 24b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b - 2a )sinh(x) + (- 2a b - 2a )cosh(x) - 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b - 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 20a cosh(x) - 30a b cosh(x) + (48a b - 36a )cosh(x) +--R + +--R 3 2 +--R (- 24b + 12a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 15a cosh(x) - 30a b cosh(x) + (72a b - 54a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 72b + 36a b)x cosh(x) + 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (48a b - 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 72b + 36a b)x cosh(x) + (24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b - 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R (- 24b + 12a b)x cosh(x) + (12a b - 9a )cosh(x) + 3a b cosh(x) + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) ) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression Integer,...) +--E 354 + +--S 355 of 526 +m0665:= a0665-r0665 +--R +--R +--R (354) +--R 4 3 4 2 4 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 4 3 +--R 24b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b - 2a )sinh(x) + (- 2a b - 2a )cosh(x) - 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 4 3 4 2 4 2 +--R - 48b sinh(x) - 144b cosh(x)sinh(x) - 144b cosh(x) sinh(x) +--R + +--R 4 3 +--R - 48b cosh(x) +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 3a b cosh(x) + 12a b - 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 3 +--R (12a cosh(x) + 6a b cosh(x) + (24a b - 12a )cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 2 3 2 +--R (- 9a cosh(x) + 6a b cosh(x) + 18a cosh(x) + 12a b - 9a )sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R - 18a cosh(x) - 3a b cosh(x) + (- 24a b + 36a )cosh(x) +--R + +--R 2 3 2 +--R (24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R - 7a cosh(x) - 3a b cosh(x) + (- 12a b + 15a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (12a b - 9a )cosh(x) + 3a b cosh(x) + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) ) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression Integer +--E 355 + +--S 356 of 526 +d0665:= D(m0665,x) +--R +--R +--R (355) +--R 3 8 3 2 2 7 +--R a b sinh(x) + (8a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 2 2 2 3 6 +--R (20a b cosh(x) + 20a b cosh(x) + 4a b)sinh(x) +--R + +--R 3 3 2 2 2 3 3 4 +--R 16a b cosh(x) + 28a b cosh(x) + (- 8a b + 16a b)cosh(x) - 16b +--R + +--R 2 2 +--R 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R - 10a b cosh(x) - 4a b cosh(x) + (- 24a b + 28a b)cosh(x) +--R + +--R 4 2 2 3 +--R (- 64b + 32a b )cosh(x) - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 2 2 4 3 3 3 +--R - 24a b cosh(x) - 36a b cosh(x) + (- 16a b + 24a b)cosh(x) +--R + +--R 4 2 2 2 3 2 2 +--R (- 96b + 40a b )cosh(x) - 8a b cosh(x) + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 2 2 5 3 3 4 +--R - 12a b cosh(x) - 20a b cosh(x) + (16a b + 4a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 64b + 8a b )cosh(x) + (- 24a b + 12a b)cosh(x) +--R + +--R 2 2 3 +--R 12a b cosh(x) - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 6 3 3 5 +--R 4a b cosh(x) + (24a b - 8a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- 16b - 16a b )cosh(x) + (- 24a b + 16a b)cosh(x) +--R + +--R 2 2 2 3 +--R 12a b cosh(x) - 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 2 2 7 3 3 6 2 2 5 +--R a b cosh(x) + 4a b cosh(x) + (8a b - 4a b)cosh(x) - 8a b cosh(x) +--R + +--R 3 3 4 2 2 3 3 2 3 +--R (- 8a b + 6a b)cosh(x) + 4a b cosh(x) - 4a b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 8 4 3 7 +--R - 2a sinh(x) + (- 16a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 4 6 +--R (- 40a cosh(x) - 40a b cosh(x) - 8a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R - 32a cosh(x) - 56a b cosh(x) + (16a b - 32a )cosh(x) + 16a b +--R + +--R 3 +--R - 16a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 20a cosh(x) + 8a b cosh(x) + (48a b - 56a )cosh(x) +--R + +--R 3 3 4 4 +--R (48a b - 64a b)cosh(x) - 32b + 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 48a cosh(x) + 72a b cosh(x) + (32a b - 48a )cosh(x) +--R + +--R 3 3 2 4 2 2 3 +--R (32a b - 80a b)cosh(x) + (- 128b + 16a b )cosh(x) + 16a b +--R + +--R 3 +--R - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 24a cosh(x) + 40a b cosh(x) + (- 32a b - 8a )cosh(x) +--R + +--R 3 3 3 4 2 2 4 2 +--R (- 32a b - 16a b)cosh(x) + (- 192b + 48a b - 24a )cosh(x) +--R + +--R 3 3 4 +--R (48a b - 24a b)cosh(x) + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 2 2 4 5 +--R - 8a b cosh(x) + (- 48a b + 16a )cosh(x) +--R + +--R 3 3 4 4 2 2 4 3 +--R (- 48a b + 32a b)cosh(x) + (- 128b + 48a b - 32a )cosh(x) +--R + +--R 3 3 2 4 +--R (48a b - 24a b)cosh(x) + 16a cosh(x) +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R - 2a cosh(x) - 8a b cosh(x) + (- 16a b + 8a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 16a b + 16a b)cosh(x) + (- 32b + 16a b - 12a )cosh(x) +--R + +--R 3 3 3 4 2 4 +--R (16a b - 8a b)cosh(x) + 8a cosh(x) - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 8 3 2 2 7 +--R - a b sinh(x) + (- 8a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 2 2 2 3 6 +--R (- 20a b cosh(x) - 20a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 3 2 2 2 3 3 4 +--R - 16a b cosh(x) - 28a b cosh(x) + (8a b - 16a b)cosh(x) + 16b +--R + +--R 2 2 +--R - 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R 10a b cosh(x) + 4a b cosh(x) + (24a b - 28a b)cosh(x) +--R + +--R 4 2 2 3 +--R (64b - 32a b )cosh(x) + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 2 2 4 3 3 3 +--R 24a b cosh(x) + 36a b cosh(x) + (16a b - 24a b)cosh(x) +--R + +--R 4 2 2 2 3 2 2 +--R (96b - 40a b )cosh(x) + 8a b cosh(x) - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 2 2 5 3 3 4 +--R 12a b cosh(x) + 20a b cosh(x) + (- 16a b - 4a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 2 2 +--R (64b - 8a b )cosh(x) + (24a b - 12a b)cosh(x) - 12a b cosh(x) +--R + +--R 3 +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 6 3 3 5 4 2 2 4 +--R - 4a b cosh(x) + (- 24a b + 8a b)cosh(x) + (16b + 16a b )cosh(x) +--R + +--R 3 3 3 2 2 2 3 +--R (24a b - 16a b)cosh(x) - 12a b cosh(x) + 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 2 2 7 3 3 6 2 2 5 +--R - a b cosh(x) - 4a b cosh(x) + (- 8a b + 4a b)cosh(x) + 8a b cosh(x) +--R + +--R 3 3 4 2 2 3 3 2 3 +--R (8a b - 6a b)cosh(x) - 4a b cosh(x) + 4a b cosh(x) - a b +--R / +--R 4 5 4 3 2 4 +--R 8a b sinh(x) + (40a b cosh(x) + 16a b )sinh(x) +--R + +--R 4 2 3 2 4 3 +--R (80a b cosh(x) + 64a b cosh(x) - 8a b)sinh(x) +--R + +--R 4 3 3 2 2 4 2 +--R (80a b cosh(x) + 96a b cosh(x) - 24a b cosh(x))sinh(x) +--R + +--R 4 4 3 2 3 4 2 +--R (40a b cosh(x) + 64a b cosh(x) - 24a b cosh(x) )sinh(x) +--R + +--R 4 5 3 2 4 4 3 +--R 8a b cosh(x) + 16a b cosh(x) - 8a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 5 5 4 4 +--R - 16a sinh(x) + (- 80a cosh(x) - 32a b)sinh(x) +--R + +--R 5 2 4 5 3 +--R (- 160a cosh(x) - 128a b cosh(x) + 16a )sinh(x) +--R + +--R 5 3 4 2 5 2 +--R (- 160a cosh(x) - 192a b cosh(x) + 48a cosh(x))sinh(x) +--R + +--R 5 4 4 3 5 2 +--R (- 80a cosh(x) - 128a b cosh(x) + 48a cosh(x) )sinh(x) +--R + +--R 5 5 4 4 5 3 +--R - 16a cosh(x) - 32a b cosh(x) + 16a cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 5 4 3 2 4 +--R - 8a b sinh(x) + (- 40a b cosh(x) - 16a b )sinh(x) +--R + +--R 4 2 3 2 4 3 +--R (- 80a b cosh(x) - 64a b cosh(x) + 8a b)sinh(x) +--R + +--R 4 3 3 2 2 4 2 +--R (- 80a b cosh(x) - 96a b cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 4 4 3 2 3 4 2 +--R (- 40a b cosh(x) - 64a b cosh(x) + 24a b cosh(x) )sinh(x) +--R + +--R 4 5 3 2 4 4 3 +--R - 8a b cosh(x) - 16a b cosh(x) + 8a b cosh(x) +--R Type: Expression Integer +--E 356 + +--S 357 of 526 +t0666:= sinh(x)^4/(a+b*csch(x)) +--R +--R +--R 4 +--R sinh(x) +--R (356) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 357 + +--S 358 of 526 +r0666:= 3/8*x/a-1/2*b^2*x/a^3+b^4*x/a^5+_ + 2*b^5*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^5/(a^2+b^2)^(1/2)+_ + b*cosh(x)/a^2-b^3*cosh(x)/a^4-1/3*b*cosh(x)^3/a^2-_ + 3/8*cosh(x)*sinh(x)/a+1/2*b^2*cosh(x)*sinh(x)/a^3+_ + 1/4*cosh(x)*sinh(x)^3/a +--R +--R +--R (357) +--R x +--R b tanh(-) - a +--R 5 2 +--R - 48b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 3 2 2 4 3 3 +--R 6a cosh(x)sinh(x) + (12a b - 9a )cosh(x)sinh(x) - 8a b cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 24a b + 24a b)cosh(x) + (24b - 12a b + 9a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 5 | 2 2 +--R 24a \|b + a +--R Type: Expression Integer +--E 358 + +--S 359 of 526 +a0666:= integrate(t0666,x) +--R +--R +--R (358) +--R 5 4 5 3 5 2 2 +--R 192b sinh(x) + 768b cosh(x)sinh(x) + 1152b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768b cosh(x) sinh(x) + 192b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 +--R 168a cosh(x) - 168a b cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 3 3 +--R - 96a b + 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b + 360a b)cosh(x) + (192b - 96a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b - 480a )cosh(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 960a b + 720a b)cosh(x) + (768b - 384a b + 288a )x cosh(x) +--R + +--R 3 3 +--R - 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 3 +--R (- 960a b + 720a b)cosh(x) +--R + +--R 4 2 2 4 2 +--R (1152b - 576a b + 432a )x cosh(x) +--R + +--R 3 3 2 2 4 +--R (- 288a b + 216a b)cosh(x) - 24a b + 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 3 3 4 +--R (- 480a b + 360a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (768b - 384a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (- 288a b + 216a b)cosh(x) + (- 48a b + 48a )cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b + 72a b)cosh(x) + (192b - 96a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (- 96a b + 72a b)cosh(x) + (- 24a b + 24a )cosh(x) - 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression Integer,...) +--E 359 + +--S 360 of 526 +m0666:= a0666-r0666 +--R +--R +--R (359) +--R 5 4 5 3 5 2 2 +--R 192b sinh(x) + 768b cosh(x)sinh(x) + 1152b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768b cosh(x) sinh(x) + 192b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 5 4 5 3 5 2 2 +--R 384b sinh(x) + 1536b cosh(x)sinh(x) + 2304b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 1536b cosh(x) sinh(x) + 384b cosh(x) +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (- 24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (- 108a cosh(x) - 56a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 +--R - 120a cosh(x) - 168a b cosh(x) + (48a b - 72a )cosh(x) +--R + +--R 3 3 +--R - 96a b + 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 216a b cosh(x) + (- 24a b - 72a )cosh(x) +--R + +--R 3 3 +--R (- 288a b + 168a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 120a cosh(x) - 24a b cosh(x) + (- 96a b - 48a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (- 192a b - 48a b)cosh(x) - 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) + 216a b cosh(x) + (- 24a b - 72a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 +--R (192a b - 432a b)cosh(x) + (- 288a b + 216a b)cosh(x) - 24a b +--R + +--R 4 +--R 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) + 200a b cosh(x) + (48a b - 72a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (288a b - 408a b)cosh(x) + (- 288a b + 216a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b + 48a )cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) + 56a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (96a b - 120a b)cosh(x) + (- 96a b + 72a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b + 24a )cosh(x) - 8a b cosh(x) - 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression Integer +--E 360 + +--S 361 of 526 +d0666:= D(m0666,x) +--R +--R +--R (360) +--R 4 10 4 3 2 9 +--R - 3a b sinh(x) + (- 14a b cosh(x) - 8a b )sinh(x) +--R + +--R 4 2 3 2 2 3 4 8 +--R (- 27a b cosh(x) - 40a b cosh(x) - 8a b + 5a b)sinh(x) +--R + +--R 4 3 3 2 2 2 3 4 +--R - 32a b cosh(x) - 88a b cosh(x) + (- 48a b + 12a b)cosh(x) +--R + +--R 3 2 +--R - 4a b +--R * +--R 7 +--R sinh(x) +--R + +--R 4 4 3 2 3 2 3 4 2 +--R - 30a b cosh(x) - 104a b cosh(x) + (- 96a b - 8a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (16a b - 36a b )cosh(x) + 32b - 16a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 3 2 4 2 3 4 3 +--R - 12a b cosh(x) - 40a b cosh(x) + (- 48a b - 60a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 3 2 +--R (64a b - 124a b )cosh(x) + (160b - 80a b )cosh(x) + 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 3 2 5 2 3 4 4 +--R 26a b cosh(x) + 72a b cosh(x) + (80a b - 94a b)cosh(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (80a b - 204a b )cosh(x) + (320b - 144a b + 18a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (16a b + 4a b )cosh(x) - 8a b - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 3 2 6 2 3 4 5 +--R 48a b cosh(x) + 120a b cosh(x) + (112a b - 76a b)cosh(x) +--R + +--R 3 2 4 5 2 3 4 3 +--R - 156a b cosh(x) + (320b - 96a b + 32a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (64a b - 24a b )cosh(x) + (- 32a b - 16a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 3 2 7 2 3 4 6 +--R 33a b cosh(x) + 72a b cosh(x) + (32a b - 32a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 4 +--R (- 80a b - 28a b )cosh(x) + (160b + 16a b + 18a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 4 +--R (96a b - 56a b )cosh(x) + (- 48a b - 24a b)cosh(x) + 5a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 3 2 8 2 3 4 7 +--R 10a b cosh(x) + 16a b cosh(x) + (- 16a b - 4a b)cosh(x) +--R + +--R 4 3 2 6 5 2 3 5 +--R (- 64a b + 28a b )cosh(x) + (32b + 48a b )cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (64a b - 44a b )cosh(x) + (- 32a b - 16a b)cosh(x) +--R + +--R 4 +--R 10a b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 10 2 3 4 8 4 3 2 7 +--R a b cosh(x) + (- 8a b + a b)cosh(x) + (- 16a b + 12a b )cosh(x) +--R + +--R 2 3 4 6 4 3 2 5 +--R (16a b - 2a b)cosh(x) + (16a b - 12a b )cosh(x) +--R + +--R 2 3 4 4 4 2 4 +--R (- 8a b - 4a b)cosh(x) + 5a b cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 10 5 4 9 +--R 6a sinh(x) + (28a cosh(x) + 16a b)sinh(x) +--R + +--R 5 2 4 3 2 5 8 +--R (54a cosh(x) + 80a b cosh(x) + 16a b - 10a )sinh(x) +--R + +--R 5 3 4 2 3 2 5 4 +--R (64a cosh(x) + 176a b cosh(x) + (96a b - 24a )cosh(x) + 8a b) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 4 3 3 2 5 2 +--R 60a cosh(x) + 208a b cosh(x) + (192a b + 16a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (- 32a b + 72a b)cosh(x) - 32a b + 32a b + 4a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 4 4 3 2 5 3 +--R 24a cosh(x) + 80a b cosh(x) + (96a b + 120a )cosh(x) +--R + +--R 2 3 4 2 4 3 2 +--R (- 128a b + 248a b)cosh(x) + (- 128a b + 160a b )cosh(x) +--R + +--R 5 4 +--R 64b - 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 6 4 5 3 2 5 4 +--R - 52a cosh(x) - 144a b cosh(x) + (- 160a b + 188a )cosh(x) +--R + +--R 2 3 4 3 +--R (- 160a b + 408a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 160a b + 288a b - 36a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (320b - 32a b - 8a b)cosh(x) - 32a b + 16a b + 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 7 4 6 3 2 5 5 +--R - 96a cosh(x) - 240a b cosh(x) + (- 224a b + 152a )cosh(x) +--R + +--R 4 4 3 2 5 3 +--R 312a b cosh(x) + (192a b - 64a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (640b - 128a b + 48a b)cosh(x) +--R + +--R 4 3 2 5 +--R (- 128a b + 64a b + 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 8 4 7 3 2 5 6 +--R - 66a cosh(x) - 144a b cosh(x) + (- 64a b + 64a )cosh(x) +--R + +--R 2 3 4 5 4 3 2 5 4 +--R (160a b + 56a b)cosh(x) + (160a b - 32a b - 36a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (640b - 192a b + 112a b)cosh(x) +--R + +--R 4 3 2 5 2 5 +--R (- 192a b + 96a b + 48a )cosh(x) - 10a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 9 4 8 3 2 5 7 +--R - 20a cosh(x) - 32a b cosh(x) + (32a b + 8a )cosh(x) +--R + +--R 2 3 4 6 4 3 2 5 +--R (128a b - 56a b)cosh(x) + (128a b - 96a b )cosh(x) +--R + +--R 5 2 3 4 4 +--R (320b - 128a b + 88a b)cosh(x) +--R + +--R 4 3 2 5 3 5 +--R (- 128a b + 64a b + 32a )cosh(x) - 20a cosh(x) +--R * +--R sinh(x) +--R + +--R 5 10 3 2 5 8 2 3 4 7 +--R - 2a cosh(x) + (16a b - 2a )cosh(x) + (32a b - 24a b)cosh(x) +--R + +--R 4 3 2 5 6 5 2 3 4 5 +--R (32a b - 32a b + 4a )cosh(x) + (64b - 32a b + 24a b)cosh(x) +--R + +--R 4 3 2 5 4 5 2 5 +--R (- 32a b + 16a b + 8a )cosh(x) - 10a cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 10 4 3 2 9 +--R 3a b sinh(x) + (14a b cosh(x) + 8a b )sinh(x) +--R + +--R 4 2 3 2 2 3 4 8 +--R (27a b cosh(x) + 40a b cosh(x) + 8a b - 5a b)sinh(x) +--R + +--R 4 3 3 2 2 2 3 4 3 2 +--R (32a b cosh(x) + 88a b cosh(x) + (48a b - 12a b)cosh(x) + 4a b ) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 4 3 2 3 2 3 4 2 +--R 30a b cosh(x) + 104a b cosh(x) + (96a b + 8a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (- 16a b + 36a b )cosh(x) - 32b + 16a b + 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 3 2 4 2 3 4 3 +--R 12a b cosh(x) + 40a b cosh(x) + (48a b + 60a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 3 2 +--R (- 64a b + 124a b )cosh(x) + (- 160b + 80a b )cosh(x) - 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 3 2 5 2 3 4 4 +--R - 26a b cosh(x) - 72a b cosh(x) + (- 80a b + 94a b)cosh(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (- 80a b + 204a b )cosh(x) + (- 320b + 144a b - 18a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 16a b - 4a b )cosh(x) + 8a b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 3 2 6 2 3 4 5 +--R - 48a b cosh(x) - 120a b cosh(x) + (- 112a b + 76a b)cosh(x) +--R + +--R 3 2 4 5 2 3 4 3 +--R 156a b cosh(x) + (- 320b + 96a b - 32a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (- 64a b + 24a b )cosh(x) + (32a b + 16a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 3 2 7 2 3 4 6 +--R - 33a b cosh(x) - 72a b cosh(x) + (- 32a b + 32a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 4 +--R (80a b + 28a b )cosh(x) + (- 160b - 16a b - 18a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 4 +--R (- 96a b + 56a b )cosh(x) + (48a b + 24a b)cosh(x) - 5a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 3 2 8 2 3 4 7 +--R - 10a b cosh(x) - 16a b cosh(x) + (16a b + 4a b)cosh(x) +--R + +--R 4 3 2 6 5 2 3 5 +--R (64a b - 28a b )cosh(x) + (- 32b - 48a b )cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 4 +--R (- 64a b + 44a b )cosh(x) + (32a b + 16a b)cosh(x) - 10a b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 10 2 3 4 8 4 3 2 7 +--R - a b cosh(x) + (8a b - a b)cosh(x) + (16a b - 12a b )cosh(x) +--R + +--R 2 3 4 6 4 3 2 5 +--R (- 16a b + 2a b)cosh(x) + (- 16a b + 12a b )cosh(x) +--R + +--R 2 3 4 4 4 2 4 +--R (8a b + 4a b)cosh(x) - 5a b cosh(x) + a b +--R / +--R 5 6 5 4 2 5 +--R 16a b sinh(x) + (96a b cosh(x) + 32a b )sinh(x) +--R + +--R 5 2 4 2 5 4 +--R (240a b cosh(x) + 160a b cosh(x) - 16a b)sinh(x) +--R + +--R 5 3 4 2 2 5 3 +--R (320a b cosh(x) + 320a b cosh(x) - 64a b cosh(x))sinh(x) +--R + +--R 5 4 4 2 3 5 2 2 +--R (240a b cosh(x) + 320a b cosh(x) - 96a b cosh(x) )sinh(x) +--R + +--R 5 5 4 2 4 5 3 +--R (96a b cosh(x) + 160a b cosh(x) - 64a b cosh(x) )sinh(x) +--R + +--R 5 6 4 2 5 5 4 +--R 16a b cosh(x) + 32a b cosh(x) - 16a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 6 6 5 5 +--R - 32a sinh(x) + (- 192a cosh(x) - 64a b)sinh(x) +--R + +--R 6 2 5 6 4 +--R (- 480a cosh(x) - 320a b cosh(x) + 32a )sinh(x) +--R + +--R 6 3 5 2 6 3 +--R (- 640a cosh(x) - 640a b cosh(x) + 128a cosh(x))sinh(x) +--R + +--R 6 4 5 3 6 2 2 +--R (- 480a cosh(x) - 640a b cosh(x) + 192a cosh(x) )sinh(x) +--R + +--R 6 5 5 4 6 3 +--R (- 192a cosh(x) - 320a b cosh(x) + 128a cosh(x) )sinh(x) +--R + +--R 6 6 5 5 6 4 +--R - 32a cosh(x) - 64a b cosh(x) + 32a cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 6 5 4 2 5 +--R - 16a b sinh(x) + (- 96a b cosh(x) - 32a b )sinh(x) +--R + +--R 5 2 4 2 5 4 +--R (- 240a b cosh(x) - 160a b cosh(x) + 16a b)sinh(x) +--R + +--R 5 3 4 2 2 5 3 +--R (- 320a b cosh(x) - 320a b cosh(x) + 64a b cosh(x))sinh(x) +--R + +--R 5 4 4 2 3 5 2 2 +--R (- 240a b cosh(x) - 320a b cosh(x) + 96a b cosh(x) )sinh(x) +--R + +--R 5 5 4 2 4 5 3 +--R (- 96a b cosh(x) - 160a b cosh(x) + 64a b cosh(x) )sinh(x) +--R + +--R 5 6 4 2 5 5 4 +--R - 16a b cosh(x) - 32a b cosh(x) + 16a b cosh(x) +--R Type: Expression Integer +--E 361 + +--S 362 of 526 +t0667:= sinh(x)/(%i+csch(x)) +--R +--R +--R sinh(x) +--R (361) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 362 + +--S 363 of 526 +r0667:= x-%i*cosh(x)-%i*cosh(x)/(1+%i*sinh(x)) +--R +--R +--R (- %i cosh(x) + x)sinh(x) - 2cosh(x) - %i x +--R (362) ------------------------------------------- +--R sinh(x) - %i +--R Type: Expression Complex Integer +--E 363 + +--S 364 of 526 +a0667:= integrate(t0667,x) +--R +--R +--R (363) +--R 2 2 +--R - %i sinh(x) + (- 2%i cosh(x) + 2x)sinh(x) - %i cosh(x) +--R + +--R (2x - 2)cosh(x) - 2%i x - 5%i +--R / +--R 2sinh(x) + 2cosh(x) - 2%i +--R Type: Union(Expression Complex Integer,...) +--E 364 + +--S 365 of 526 +m0667:= a0667-r0667 +--R +--R +--R (364) +--R 3 2 2 +--R - %i sinh(x) - sinh(x) + (%i cosh(x) + 2cosh(x) - 5%i)sinh(x) +--R + +--R 2 +--R 3cosh(x) - 2%i cosh(x) - 5 +--R / +--R 2 +--R 2sinh(x) + (2cosh(x) - 4%i)sinh(x) - 2%i cosh(x) - 2 +--R Type: Expression Complex Integer +--E 365 + +--S 366 of 526 +d0667:= D(m0667,x) +--R +--R +--R (365) +--R 5 4 +--R %i sinh(x) + (%i cosh(x) + 4)sinh(x) +--R + +--R 2 3 +--R (- %i cosh(x) + 6cosh(x) - 2%i)sinh(x) +--R + +--R 3 2 2 +--R (- %i cosh(x) - 2cosh(x) - 4%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 4 +--R (- 6cosh(x) + 3%i cosh(x) + 6cosh(x) - 3%i)sinh(x) - 2cosh(x) +--R + +--R 3 2 +--R 5%i cosh(x) + 2cosh(x) - 5%i cosh(x) +--R / +--R 4 3 +--R 2sinh(x) + (4cosh(x) - 8%i)sinh(x) +--R + +--R 2 2 +--R (2cosh(x) - 12%i cosh(x) - 12)sinh(x) +--R + +--R 2 2 +--R (- 4%i cosh(x) - 12cosh(x) + 8%i)sinh(x) - 2cosh(x) + 4%i cosh(x) + 2 +--R Type: Expression Complex Integer +--E 366 + +--S 367 of 526 +t0668:= sinh(x)^2/(%i+csch(x)) +--R +--R +--R 2 +--R sinh(x) +--R (366) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 367 + +--S 368 of 526 +r0668:= 3/2*%i*x+cosh(x)+cosh(x)/(1+%i*sinh(x))-1/2*%i*cosh(x)*sinh(x) +--R +--R +--R (367) +--R 1 2 1 3 3 +--R - - %i cosh(x)sinh(x) + (- cosh(x) + - %i x)sinh(x) - 2%i cosh(x) + - x +--R 2 2 2 2 +--R ------------------------------------------------------------------------ +--R sinh(x) - %i +--R Type: Expression Complex Fraction Integer +--E 368 + +--S 369 of 526 +a0668:= integrate(t0668,x) +--R +--R +--R (368) +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) + 4)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) + 4cosh(x) + 12%i x - %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R 4cosh(x) + (12%i x - 7%i)cosh(x) + 12x + 20 +--R / +--R 8sinh(x) + 8cosh(x) - 8%i +--R Type: Union(Expression Complex Integer,...) +--E 369 + +--S 370 of 526 +m0668:= a0668-r0668 +--R +--R +--R (369) +--R 1 4 1 3 3 +--R - - %i sinh(x) + (- %i cosh(x) + -)sinh(x) +--R 8 8 8 +--R + +--R 1 2 1 5 2 +--R (- %i cosh(x) + - cosh(x) - - %i)sinh(x) +--R 8 8 8 +--R + +--R 1 3 3 2 9 19 1 3 +--R (- - %i cosh(x) - - cosh(x) + - %i cosh(x) + --)sinh(x) - - cosh(x) +--R 8 8 8 8 8 +--R + +--R 3 2 9 5 +--R - %i cosh(x) + - cosh(x) - - %i +--R 2 8 2 +--R / +--R 2 +--R sinh(x) + (cosh(x) - 2%i)sinh(x) - %i cosh(x) - 1 +--R Type: Expression Complex Fraction Integer +--E 370 + +--S 371 of 526 +d0668:= D(m0668,x) +--R +--R +--R (370) +--R 1 6 1 5 1 2 5 7 4 +--R - %i sinh(x) + - sinh(x) + (- - %i cosh(x) - - cosh(x) + - %i)sinh(x) +--R 4 8 2 8 4 +--R + +--R 5 2 13 3 3 +--R (- - cosh(x) + -- %i cosh(x) + -)sinh(x) +--R 8 4 2 +--R + +--R 1 4 5 3 1 2 3 2 +--R (- %i cosh(x) + - cosh(x) - - %i cosh(x) + 2cosh(x) + - %i)sinh(x) +--R 4 8 2 2 +--R + +--R 1 4 13 3 15 2 13 11 +--R (- cosh(x) - -- %i cosh(x) - -- cosh(x) + -- %i cosh(x) + --)sinh(x) +--R 2 4 8 4 8 +--R + +--R 5 4 21 3 5 2 21 +--R - - %i cosh(x) - -- cosh(x) + - %i cosh(x) + -- cosh(x) +--R 4 8 4 8 +--R / +--R 4 3 +--R sinh(x) + (2cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 6%i cosh(x) - 6)sinh(x) +--R + +--R 2 2 +--R (- 2%i cosh(x) - 6cosh(x) + 4%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R Type: Expression Complex Fraction Integer +--E 371 + +--S 372 of 526 +t0669:= sinh(x)^3/(%i+csch(x)) +--R +--R +--R 3 +--R sinh(x) +--R (371) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 372 + +--S 373 of 526 +r0669:= -3/2*x+2*%i*cosh(x)-1/3*%i*cosh(x)^3+%i*cosh(x)/(1+%i*sinh(x))+_ + 1/2*cosh(x)*sinh(x) +--R +--R +--R (372) +--R 1 2 1 3 3 3 +--R - cosh(x)sinh(x) + (- - %i cosh(x) + - %i cosh(x) - - x)sinh(x) +--R 2 3 2 2 +--R + +--R 1 3 3 +--R - - cosh(x) + 3cosh(x) + - %i x +--R 3 2 +--R / +--R sinh(x) - %i +--R Type: Expression Complex Fraction Integer +--E 373 + +--S 374 of 526 +a0669:= integrate(t0669,x) +--R +--R +--R (373) +--R 4 3 +--R - %i sinh(x) + (- 4%i cosh(x) + 3)sinh(x) +--R + +--R 2 2 +--R (- 6%i cosh(x) + 3cosh(x) + 20%i)sinh(x) +--R + +--R 3 2 +--R (- 4%i cosh(x) + 9cosh(x) + 32%i cosh(x) - 36x + 3)sinh(x) +--R + +--R 4 3 2 +--R - %i cosh(x) + cosh(x) + 20%i cosh(x) + (- 36x + 39)cosh(x) + 36%i x +--R + +--R 69%i +--R / +--R 24sinh(x) + 24cosh(x) - 24%i +--R Type: Union(Expression Complex Integer,...) +--E 374 + +--S 375 of 526 +m0669:= a0669-r0669 +--R +--R +--R (374) +--R 1 5 1 1 4 +--R - -- %i sinh(x) + (- - %i cosh(x) + --)sinh(x) +--R 24 6 12 +--R + +--R 1 2 13 17 3 +--R (- - %i cosh(x) - -- cosh(x) + -- %i)sinh(x) +--R 4 24 24 +--R + +--R 1 3 3 2 5 23 2 +--R (- %i cosh(x) - - cosh(x) + -- %i cosh(x) + --)sinh(x) +--R 6 8 24 24 +--R + +--R 7 4 13 3 25 2 37 11 +--R (-- %i cosh(x) + -- cosh(x) - -- %i cosh(x) - -- cosh(x) + -- %i) +--R 24 24 24 24 4 +--R * +--R sinh(x) +--R + +--R 7 4 3 3 13 2 11 23 +--R -- cosh(x) - - %i cosh(x) - -- cosh(x) + -- %i cosh(x) + -- +--R 24 8 6 8 8 +--R / +--R 2 +--R sinh(x) + (cosh(x) - 2%i)sinh(x) - %i cosh(x) - 1 +--R Type: Expression Complex Fraction Integer +--E 375 + +--S 376 of 526 +d0669:= D(m0669,x) +--R +--R +--R (375) +--R 1 7 5 11 6 +--R - - %i sinh(x) + (- - %i cosh(x) - --)sinh(x) +--R 8 8 12 +--R + +--R 1 2 23 5 5 +--R (- - %i cosh(x) - -- cosh(x) + - %i)sinh(x) +--R 4 12 6 +--R + +--R 3 3 1 2 1 9 4 +--R (- %i cosh(x) + - cosh(x) + - %i cosh(x) - -)sinh(x) +--R 4 2 3 4 +--R + +--R 3 4 13 3 13 2 21 59 +--R (- %i cosh(x) + -- cosh(x) - -- %i cosh(x) - -- cosh(x) + -- %i) +--R 8 6 8 4 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 5 5 4 23 3 5 2 +--R - - %i cosh(x) + -- cosh(x) - -- %i cosh(x) - -- cosh(x) +--R 8 12 24 12 +--R + +--R 95 4 +--R -- %i cosh(x) - - +--R 24 3 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 5 7 4 43 3 43 2 +--R - - cosh(x) + -- %i cosh(x) + -- cosh(x) - -- %i cosh(x) +--R 4 24 12 24 +--R + +--R 10 3 +--R - -- cosh(x) + - %i +--R 3 2 +--R * +--R sinh(x) +--R + +--R 1 5 4 4 25 3 4 2 +--R - %i cosh(x) + - cosh(x) - -- %i cosh(x) - - cosh(x) + 3%i cosh(x) +--R 8 3 8 3 +--R / +--R 4 3 +--R sinh(x) + (2cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 6%i cosh(x) - 6)sinh(x) +--R + +--R 2 2 +--R (- 2%i cosh(x) - 6cosh(x) + 4%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R Type: Expression Complex Fraction Integer +--E 376 + +--S 377 of 526 +t0670:= sinh(x)^4/(%i+csch(x)) +--R +--R +--R 4 +--R sinh(x) +--R (376) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 377 + +--S 378 of 526 +r0670:= -15/8*%i*x-2*cosh(x)+1/3*cosh(x)^3-cosh(x)/(1+%i*sinh(x))+_ + 7/8*%i*cosh(x)*sinh(x)-1/4*%i*cosh(x)*sinh(x)^3 +--R +--R +--R (377) +--R 1 4 1 3 7 2 +--R - - %i cosh(x)sinh(x) - - cosh(x)sinh(x) + - %i cosh(x)sinh(x) +--R 4 4 8 +--R + +--R 1 3 9 15 1 3 +--R (- cosh(x) - - cosh(x) - -- %i x)sinh(x) - - %i cosh(x) + 3%i cosh(x) +--R 3 8 8 3 +--R + +--R 15 +--R - -- x +--R 8 +--R / +--R sinh(x) - %i +--R Type: Expression Complex Fraction Integer +--E 378 + +--S 379 of 526 +a0670:= integrate(t0670,x) +--R +--R +--R (378) +--R 5 4 +--R - 3%i sinh(x) + (- 15%i cosh(x) + 8)sinh(x) +--R + +--R 2 3 +--R (- 30%i cosh(x) + 8cosh(x) + 45%i)sinh(x) +--R + +--R 3 2 2 +--R (- 30%i cosh(x) + 48cosh(x) + 105%i cosh(x) - 160)sinh(x) +--R + +--R 4 3 2 +--R - 15%i cosh(x) + 8cosh(x) + 135%i cosh(x) - 160cosh(x) - 360%i x +--R + +--R 48%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3%i cosh(x) + 8cosh(x) + 35%i cosh(x) - 160cosh(x) +--R + +--R (- 360%i x + 288%i)cosh(x) - 360x - 552 +--R / +--R 192sinh(x) + 192cosh(x) - 192%i +--R Type: Union(Expression Complex Integer,...) +--E 379 + +--S 380 of 526 +m0670:= a0670-r0670 +--R +--R +--R (379) +--R 1 6 11 5 5 +--R - -- %i sinh(x) + (-- %i cosh(x) + ---)sinh(x) +--R 64 64 192 +--R + +--R 3 2 89 37 4 +--R (-- %i cosh(x) + --- cosh(x) + --- %i)sinh(x) +--R 32 192 192 +--R + +--R 5 3 11 2 119 115 3 +--R (- -- %i cosh(x) + -- cosh(x) - --- %i cosh(x) - ---)sinh(x) +--R 32 32 192 192 +--R + +--R 5 4 43 3 27 2 7 13 +--R (- -- %i cosh(x) - -- cosh(x) - -- %i cosh(x) - --- cosh(x) + -- %i) +--R 64 96 64 192 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 5 71 4 155 3 191 2 +--R - -- %i cosh(x) - --- cosh(x) + --- %i cosh(x) + --- cosh(x) +--R 64 192 192 192 +--R + +--R 43 21 +--R - -- %i cosh(x) - -- +--R 24 8 +--R * +--R sinh(x) +--R + +--R 1 5 7 4 33 3 13 2 3 +--R - -- cosh(x) + -- %i cosh(x) + -- cosh(x) - -- %i cosh(x) - - cosh(x) +--R 64 24 64 6 2 +--R + +--R 23 +--R -- %i +--R 8 +--R / +--R 2 +--R sinh(x) + (cosh(x) - 2%i)sinh(x) - %i cosh(x) - 1 +--R Type: Expression Complex Fraction Integer +--E 380 + +--S 381 of 526 +d0670:= D(m0670,x) +--R +--R +--R (380) +--R 3 8 1 51 7 +--R -- %i sinh(x) + (- %i cosh(x) + --)sinh(x) +--R 16 8 64 +--R + +--R 1 2 63 181 6 +--R (-- %i cosh(x) + -- cosh(x) - --- %i)sinh(x) +--R 16 64 96 +--R + +--R 1 3 15 2 205 4 5 +--R (- %i cosh(x) + -- cosh(x) - --- %i cosh(x) - -)sinh(x) +--R 4 32 96 3 +--R + +--R 3 4 5 3 2 1 89 +--R (- -- %i cosh(x) - -- cosh(x) + %i cosh(x) + -- cosh(x) - -- %i) +--R 16 32 24 32 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 73 4 101 3 227 2 +--R - - %i cosh(x) - -- cosh(x) + --- %i cosh(x) + --- cosh(x) +--R 8 64 48 64 +--R + +--R 187 673 +--R - --- %i cosh(x) - --- +--R 32 192 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 6 53 5 127 4 325 3 +--R - -- %i cosh(x) - -- cosh(x) + --- %i cosh(x) + --- cosh(x) +--R 16 64 96 192 +--R + +--R 199 2 781 17 +--R - --- %i cosh(x) - --- cosh(x) - -- %i +--R 96 192 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 6 17 5 5 4 293 3 +--R - - cosh(x) + -- %i cosh(x) - --- cosh(x) + --- %i cosh(x) +--R 8 32 192 96 +--R + +--R 293 2 43 11 +--R --- cosh(x) - -- %i cosh(x) - -- +--R 192 12 8 +--R * +--R sinh(x) +--R + +--R 1 6 5 5 67 4 195 3 +--R -- %i cosh(x) + -- cosh(x) + -- %i cosh(x) + --- cosh(x) +--R 16 64 48 64 +--R + +--R 35 2 25 +--R - -- %i cosh(x) - -- cosh(x) +--R 24 8 +--R / +--R 4 3 +--R sinh(x) + (2cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 6%i cosh(x) - 6)sinh(x) +--R + +--R 2 2 +--R (- 2%i cosh(x) - 6cosh(x) + 4%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R Type: Expression Complex Fraction Integer +--E 381 + +--S 382 of 526 +t0671:= cosh(x)/(a+b*csch(x)) +--R +--R +--R cosh(x) +--R (381) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 382 + +--S 383 of 526 +r0671:= -b*log(b+a*sinh(x))/a^2+sinh(x)/a +--R +--R +--R - b log(a sinh(x) + b) + a sinh(x) +--R (382) ---------------------------------- +--R 2 +--R a +--R Type: Expression Integer +--E 383 + +--S 384 of 526 +a0671:= integrate(t0671,x) +--R +--R +--R (383) +--R - 2a sinh(x) - 2b 2 +--R (- 2b sinh(x) - 2b cosh(x))log(-----------------) + a sinh(x) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (2a cosh(x) + 2b x)sinh(x) + a cosh(x) + 2b x cosh(x) - a +--R / +--R 2 2 +--R 2a sinh(x) + 2a cosh(x) +--R Type: Union(Expression Integer,...) +--E 384 + +--S 385 of 526 +m0671:= a0671-r0671 +--R +--R +--R (384) +--R (2b sinh(x) + 2b cosh(x))log(a sinh(x) + b) +--R + +--R - 2a sinh(x) - 2b 2 +--R (- 2b sinh(x) - 2b cosh(x))log(-----------------) - a sinh(x) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R 2b x sinh(x) + a cosh(x) + 2b x cosh(x) - a +--R / +--R 2 2 +--R 2a sinh(x) + 2a cosh(x) +--R Type: Expression Integer +--E 385 + +--S 386 of 526 +d0671:= D(m0671,x) +--R +--R +--R 2 2 +--R sinh(x) - cosh(x) + 1 +--R (385) ----------------------- +--R 2a sinh(x) + 2a cosh(x) +--R Type: Expression Integer +--E 386 + +--S 387 of 526 +t0672:= cosh(x)^2/(a+b*csch(x)) +--R +--R +--R 2 +--R cosh(x) +--R (386) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 387 + +--S 388 of 526 +r0672:= 1/2/a^3*(a^2*x+2*b^2*x+4*b*(a^2+b^2)^(1/2)*_ + atanh(1/(a^2+b^2)^(1/2)*(-b*cosh(x)+b+a*sinh(x))/sinh(x))-_ + 2*a*b*cosh(x)+a^2*cosh(x)*sinh(x)) +--R +--R +--R (387) +--R +-------+ +--R | 2 2 a sinh(x) - b cosh(x) + b 2 +--R 4b\|b + a atanh(-------------------------) + a cosh(x)sinh(x) +--R +-------+ +--R | 2 2 +--R sinh(x)\|b + a +--R + +--R 2 2 +--R - 2a b cosh(x) + (2b + a )x +--R / +--R 3 +--R 2a +--R Type: Expression Integer +--E 388 + +--S 389 of 526 +a0672:= integrate(t0672,x) +--R +--R +--R (388) +--R +-------+ +--R 2 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b + 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b + 8a )x cosh(x) - 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b + 4a )x cosh(x) - 4a b cosh(x) - a +--R / +--R 3 2 3 3 2 +--R 8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) +--R Type: Union(Expression Integer,...) +--E 389 + +--S 390 of 526 +m0672:= a0672-r0672 +--R +--R +--R (389) +--R +-------+ +--R 2 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- 16b sinh(x) - 32b cosh(x)sinh(x) - 16b cosh(x) )\|b + a +--R * +--R a sinh(x) - b cosh(x) + b +--R atanh(-------------------------) +--R +-------+ +--R | 2 2 +--R sinh(x)\|b + a +--R + +--R 2 4 3 2 2 2 +--R a sinh(x) - 4a b sinh(x) + (- 2a cosh(x) - 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (4a b cosh(x) - 4a b)sinh(x) + a cosh(x) + 4a b cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R - a +--R / +--R 3 2 3 3 2 +--R 8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) +--R Type: Expression Integer +--E 390 + +--S 391 of 526 +d0672:= D(m0672,x) +--R +--R +--R (390) +--R 3 8 3 4 4 7 +--R - a b sinh(x) + ((- 2a b - 2a )cosh(x) + 2a )sinh(x) +--R + +--R 3 4 2 2 2 3 4 3 3 +--R ((2a b - 4a )cosh(x) + (4a b - 2a b + 4a )cosh(x) + 12a b + 10a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 4 2 +--R (6a b + 2a )cosh(x) + (8a b + 4a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 4 4 +--R (40a b + 8a b + 26a b + 2a )cosh(x) + 8b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 2 2 3 4 3 +--R 8a cosh(x) + (- 4a b + 18a b - 8a )cosh(x) +--R + +--R 3 2 2 3 2 4 2 2 3 +--R (36a b + 24a b + 20a b)cosh(x) + (24b + 8a b - 6a b)cosh(x) +--R + +--R 3 3 +--R 8a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 5 2 2 3 4 4 +--R (- 6a b + 2a )cosh(x) + (- 16a b + 8a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 16a b + 16a b - 4a b - 4a )cosh(x) +--R + +--R 4 2 2 3 4 2 +--R (16b + 16a b - 8a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 4 4 +--R (32a b + 8a b + 26a b + 2a )cosh(x) + 8b - 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 6 2 2 3 4 5 +--R (- 2a b - 4a )cosh(x) + (- 4a b - 14a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 4 3 3 +--R (- 44a b - 16a b - 22a b)cosh(x) + (- 16b + 12a b)cosh(x) +--R + +--R 3 2 2 3 4 2 +--R (48a b + 24a b + 34a b + 4a )cosh(x) +--R + +--R 4 2 2 3 4 3 3 +--R (24b + 4a b - 6a b - 4a )cosh(x) - 4a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 7 2 2 3 4 6 +--R (2a b - 2a )cosh(x) + (8a b - 12a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 24a b - 24a b - 22a b + 2a )cosh(x) +--R + +--R 4 2 2 3 4 4 +--R (- 24b - 16a b + 24a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (32a b + 24a b + 22a b + 2a )cosh(x) +--R + +--R 4 2 2 3 4 2 3 3 4 +--R (24b + 8a b - 12a b - 2a )cosh(x) + (- 8a b - 2a b - 2a )cosh(x) +--R + +--R 4 +--R 2a +--R * +--R sinh(x) +--R + +--R 3 8 2 2 3 7 3 2 2 3 6 +--R a b cosh(x) + (4a b - 2a b)cosh(x) + (- 4a b - 8a b - 8a b)cosh(x) +--R + +--R 4 2 2 3 5 3 2 2 3 4 +--R (- 8b - 8a b + 10a b)cosh(x) + (8a b + 8a b + 6a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 3 3 +--R (8b + 4a b - 6a b)cosh(x) - 4a b cosh(x) - 2a b cosh(x) + a b +--R / +--R 4 6 4 5 3 2 5 5 +--R 4a b sinh(x) + ((16a b + 8a )cosh(x) + 8a b - 8a )sinh(x) +--R + +--R 4 5 2 3 2 4 5 4 4 +--R ((20a b + 32a )cosh(x) + (24a b + 24a b - 32a )cosh(x) - 24a b)sinh(x) +--R + +--R 5 3 3 2 4 5 2 +--R 48a cosh(x) + (16a b + 80a b - 48a )cosh(x) +--R + +--R 3 2 4 5 3 2 5 +--R (16a b - 72a b - 8a )cosh(x) - 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 4 3 2 4 5 3 +--R (- 20a b + 32a )cosh(x) + (- 16a b + 96a b - 32a )cosh(x) +--R + +--R 3 2 4 5 2 3 2 4 5 +--R (48a b - 72a b - 16a )cosh(x) + (- 24a b - 8a b + 16a )cosh(x) +--R + +--R 4 +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 5 3 2 4 5 4 +--R (- 16a b + 8a )cosh(x) + (- 24a b + 48a b - 8a )cosh(x) +--R + +--R 3 2 4 5 3 3 2 4 5 2 +--R (48a b - 24a b - 8a )cosh(x) + (- 24a b - 16a b + 8a )cosh(x) +--R + +--R 4 +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 6 3 2 4 5 3 2 4 +--R - 4a b cosh(x) + (- 8a b + 8a b)cosh(x) + 16a b cosh(x) +--R + +--R 3 2 4 3 4 2 +--R (- 8a b - 8a b)cosh(x) + 4a b cosh(x) +--R Type: Expression Integer +--E 391 + +--S 392 of 526 +t0673:= cosh(x)^3/(a+b*csch(x)) +--R +--R +--R 3 +--R cosh(x) +--R (391) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 392 + +--S 393 of 526 +r0673:= -b*(a^2+b^2)*log(b+a*sinh(x))/a^4+(a^2+b^2)*sinh(x)/a^3-_ + 1/2*b*sinh(x)^2/a^2+1/3*sinh(x)^3/a +--R +--R +--R (392) +--R 3 2 3 3 2 2 +--R (- 6b - 6a b)log(a sinh(x) + b) + 2a sinh(x) - 3a b sinh(x) +--R + +--R 2 3 +--R (6a b + 6a )sinh(x) +--R / +--R 4 +--R 6a +--R Type: Expression Integer +--E 393 + +--S 394 of 526 +a0673:= integrate(t0673,x) +--R +--R +--R (393) +--R 3 2 3 3 2 2 +--R (- 24b - 24a b)sinh(x) + (- 72b - 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 72b - 72a b)cosh(x) sinh(x) + (- 24b - 24a b)cosh(x) +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b + 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 20a cosh(x) - 30a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 +--R (24b + 24a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 15a cosh(x) - 30a b cosh(x) + (72a b + 54a )cosh(x) +--R + +--R 3 2 2 3 +--R (72b + 72a b)x cosh(x) - 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (72b + 72a b)x cosh(x) + (- 24a b - 18a )cosh(x) - 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R (24b + 24a b)x cosh(x) + (- 12a b - 9a )cosh(x) - 3a b cosh(x) - a +--R / +--R 4 3 4 2 4 2 4 3 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) +--R Type: Union(Expression Integer,...) +--E 394 + +--S 395 of 526 +m0673:= a0673-r0673 +--R +--R +--R (394) +--R 3 2 3 3 2 2 +--R (24b + 24a b)sinh(x) + (72b + 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (72b + 72a b)cosh(x) sinh(x) + (24b + 24a b)cosh(x) +--R * +--R log(a sinh(x) + b) +--R + +--R 3 2 3 3 2 2 +--R (- 24b - 24a b)sinh(x) + (- 72b - 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 72b - 72a b)cosh(x) sinh(x) + (- 24b - 24a b)cosh(x) +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 6 3 2 5 +--R - 7a sinh(x) + (- 18a cosh(x) + 9a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (- 9a cosh(x) + 21a b cosh(x) - 12a b - 15a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 12a cosh(x) + 6a b cosh(x) + (- 24a b - 36a )cosh(x) +--R + +--R 3 2 +--R (24b + 24a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 +--R 15a cosh(x) - 18a b cosh(x) - 18a cosh(x) +--R + +--R 3 2 2 3 +--R (72b + 72a b)x cosh(x) - 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (24a b + 12a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (72b + 72a b)x cosh(x) + (- 24a b - 18a )cosh(x) - 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R (24b + 24a b)x cosh(x) + (- 12a b - 9a )cosh(x) - 3a b cosh(x) - a +--R / +--R 4 3 4 2 4 2 4 3 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) +--R Type: Expression Integer +--E 395 + +--S 396 of 526 +d0673:= D(m0673,x) +--R +--R +--R (395) +--R 2 6 2 5 +--R a sinh(x) + (- 2a cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 9a cosh(x) - 2a b cosh(x) + 4b + 3a )sinh(x) +--R + +--R 2 3 2 2 2 3 +--R (- 4a cosh(x) + 4a b cosh(x) + (8b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 2 2 +--R (7a cosh(x) + 4a b cosh(x) - 6a cosh(x) + 4b + 3a )sinh(x) +--R + +--R 2 5 4 2 2 3 +--R 6a cosh(x) - 2a b cosh(x) + (- 8b - 12a )cosh(x) +--R + +--R 2 2 +--R (8b + 6a )cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 6 5 2 2 4 2 2 2 +--R a cosh(x) - 2a b cosh(x) + (- 4b - 5a )cosh(x) + (4b + 3a )cosh(x) +--R + +--R 2 +--R 2a b cosh(x) + a +--R / +--R 3 3 3 2 3 2 3 3 +--R 8a sinh(x) + 24a cosh(x)sinh(x) + 24a cosh(x) sinh(x) + 8a cosh(x) +--R Type: Expression Integer +--E 396 + +--S 397 of 526 +t0674:= cosh(x)^4/(a+b*csch(x)) +--R +--R +--R 4 +--R cosh(x) +--R (396) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 397 + +--S 398 of 526 +r0674:= -5/8*x/a-1/2*b^2*x/a^3+(a^2+b^2)^2*x/a^5+_ + 2*b*(a^2+b^2)^(3/2)*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^5-_ + b*cosh(x)/a^2-b^3*cosh(x)/a^4-1/3*b*cosh(x)^3/a^2+_ + 5/8*cosh(x)*sinh(x)/a+1/2*b^2*cosh(x)*sinh(x)/a^3+_ + 1/4*cosh(x)*sinh(x)^3/a +--R +--R +--R (397) +--R x +--R +-------+ b tanh(-) - a +--R 3 2 | 2 2 2 4 3 +--R (- 48b - 48a b)\|b + a atanh(-------------) + 6a cosh(x)sinh(x) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 4 3 3 3 3 +--R (12a b + 15a )cosh(x)sinh(x) - 8a b cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 4 2 2 4 +--R (24b + 36a b + 9a )x +--R / +--R 5 +--R 24a +--R Type: Expression Integer +--E 398 + +--S 399 of 526 +a0674:= integrate(t0674,x) +--R +--R +--R (398) +--R 3 2 4 3 2 3 +--R (192b + 192a b)sinh(x) + (768b + 768a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 3 +--R (1152b + 1152a b)cosh(x) sinh(x) + (768b + 768a b)cosh(x) sinh(x) +--R + +--R 3 2 4 +--R (192b + 192a b)cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 168a cosh(x) - 168a b cosh(x) + (144a b + 144a )cosh(x) - 96a b +--R + +--R 3 +--R - 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b - 600a b)cosh(x) + (192b + 288a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b + 480a )cosh(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 960a b - 1200a b)cosh(x) + (768b + 1152a b + 288a )x cosh(x) +--R + +--R 3 3 +--R - 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 3 4 2 2 4 2 +--R (- 960a b - 1200a b)cosh(x) + (1152b + 1728a b + 432a )x cosh(x) +--R + +--R 3 3 2 2 4 +--R (- 288a b - 360a b)cosh(x) - 24a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 3 3 4 4 2 2 4 3 +--R (- 480a b - 600a b)cosh(x) + (768b + 1152a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (- 288a b - 360a b)cosh(x) + (- 48a b - 48a )cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b - 120a b)cosh(x) + (192b + 288a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (- 96a b - 120a b)cosh(x) + (- 24a b - 24a )cosh(x) - 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R Type: Union(Expression Integer,...) +--E 399 + +--S 400 of 526 +m0674:= a0674-r0674 +--R +--R +--R (399) +--R 3 2 4 3 2 3 +--R (192b + 192a b)sinh(x) + (768b + 768a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 3 +--R (1152b + 1152a b)cosh(x) sinh(x) + (768b + 768a b)cosh(x) sinh(x) +--R + +--R 3 2 4 +--R (192b + 192a b)cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 3 2 4 3 2 3 +--R (384b + 384a b)sinh(x) + (1536b + 1536a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (2304b + 2304a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (1536b + 1536a b)cosh(x) sinh(x) + (384b + 384a b)cosh(x) +--R * +--R x +--R +-------+ b tanh(-) - a +--R | 2 2 2 +--R \|b + a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (- 24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (- 108a cosh(x) - 56a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R - 120a cosh(x) - 168a b cosh(x) + (48a b + 24a )cosh(x) - 96a b +--R + +--R 3 +--R - 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 216a b cosh(x) + (- 24a b - 120a )cosh(x) +--R + +--R 3 3 +--R (- 288a b - 408a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 120a cosh(x) - 24a b cosh(x) + (- 96a b - 240a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (- 192a b - 432a b)cosh(x) - 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) + 216a b cosh(x) + (- 24a b - 120a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 4 +--R (192a b - 48a b)cosh(x) + (- 288a b - 360a b)cosh(x) - 24a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) + 200a b cosh(x) + (48a b + 24a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (288a b + 168a b)cosh(x) + (- 288a b - 360a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b - 48a )cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) + 56a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (96a b + 72a b)cosh(x) + (- 96a b - 120a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b - 24a )cosh(x) - 8a b cosh(x) - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R Type: Expression Integer +--E 400 + +--S 401 of 526 +d0674:= D(m0674,x) +--R +--R +--R (400) +--R 4 10 4 3 2 9 +--R - 3a b sinh(x) + (- 14a b cosh(x) - 8a b )sinh(x) +--R + +--R 4 2 3 2 2 3 4 8 +--R (- 27a b cosh(x) - 40a b cosh(x) - 8a b - 3a b)sinh(x) +--R + +--R 4 3 3 2 2 2 3 4 +--R - 32a b cosh(x) - 88a b cosh(x) + (- 48a b - 20a b)cosh(x) +--R + +--R 3 2 +--R - 4a b +--R * +--R 7 +--R sinh(x) +--R + +--R 4 4 3 2 3 2 3 4 2 +--R - 30a b cosh(x) - 104a b cosh(x) + (- 96a b - 40a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (16a b - 4a b )cosh(x) + 32b + 48a b + 22a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 3 2 4 2 3 4 3 +--R - 12a b cosh(x) - 40a b cosh(x) + (- 48a b - 28a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (64a b + 4a b )cosh(x) + (160b + 240a b + 112a b)cosh(x) +--R + +--R 3 2 +--R 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 3 2 5 2 3 4 4 +--R 26a b cosh(x) + 72a b cosh(x) + (80a b - 14a b)cosh(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (80a b - 44a b )cosh(x) + (320b + 496a b + 250a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (16a b + 36a b )cosh(x) - 8a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 3 2 6 2 3 4 5 +--R 48a b cosh(x) + 120a b cosh(x) + (112a b - 44a b)cosh(x) +--R + +--R 3 2 4 5 2 3 4 3 +--R - 156a b cosh(x) + (320b + 544a b + 320a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (64a b + 104a b )cosh(x) + (- 32a b - 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 3 2 7 2 3 4 6 +--R 33a b cosh(x) + 72a b cosh(x) + (32a b - 64a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 4 +--R (- 80a b - 188a b )cosh(x) + (160b + 336a b + 250a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 4 +--R (96a b + 136a b )cosh(x) + (- 48a b - 72a b)cosh(x) - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 3 2 8 2 3 4 7 +--R 10a b cosh(x) + 16a b cosh(x) + (- 16a b - 36a b)cosh(x) +--R + +--R 4 3 2 6 5 2 3 4 5 +--R (- 64a b - 100a b )cosh(x) + (32b + 112a b + 112a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (64a b + 84a b )cosh(x) + (- 32a b - 48a b)cosh(x) +--R + +--R 4 +--R - 6a b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 10 2 3 4 8 +--R a b cosh(x) + (- 8a b - 7a b)cosh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (- 16a b - 20a b )cosh(x) + (16a b + 22a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 4 4 2 +--R (16a b + 20a b )cosh(x) + (- 8a b - 12a b)cosh(x) - 3a b cosh(x) +--R + +--R 4 +--R - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 10 5 4 9 +--R 6a sinh(x) + (28a cosh(x) + 16a b)sinh(x) +--R + +--R 5 2 4 3 2 5 8 +--R (54a cosh(x) + 80a b cosh(x) + 16a b + 6a )sinh(x) +--R + +--R 5 3 4 2 3 2 5 4 +--R (64a cosh(x) + 176a b cosh(x) + (96a b + 40a )cosh(x) + 8a b) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 4 3 3 2 5 2 +--R 60a cosh(x) + 208a b cosh(x) + (192a b + 80a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (- 32a b + 8a b)cosh(x) - 32a b - 32a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 4 4 3 2 5 3 +--R 24a cosh(x) + 80a b cosh(x) + (96a b + 56a )cosh(x) +--R + +--R 2 3 4 2 4 3 2 5 +--R (- 128a b - 8a b)cosh(x) + (- 128a b - 96a b - 32a )cosh(x) +--R + +--R 5 2 3 4 +--R 64b + 128a b + 56a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 6 4 5 3 2 5 4 +--R - 52a cosh(x) - 144a b cosh(x) + (- 160a b + 28a )cosh(x) +--R + +--R 2 3 4 3 4 3 2 5 2 +--R (- 160a b + 88a b)cosh(x) + (- 160a b - 32a b - 20a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (320b + 608a b + 248a b)cosh(x) - 32a b - 48a b - 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 7 4 6 3 2 5 5 +--R - 96a cosh(x) - 240a b cosh(x) + (- 224a b + 88a )cosh(x) +--R + +--R 4 4 3 2 3 +--R 312a b cosh(x) + 192a b cosh(x) +--R + +--R 5 2 3 4 2 +--R (640b + 1152a b + 432a b)cosh(x) +--R + +--R 4 3 2 5 +--R (- 128a b - 192a b - 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 8 4 7 3 2 5 6 +--R - 66a cosh(x) - 144a b cosh(x) + (- 64a b + 128a )cosh(x) +--R + +--R 2 3 4 5 4 3 2 5 4 +--R (160a b + 376a b)cosh(x) + (160a b + 288a b - 20a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (640b + 1088a b + 368a b)cosh(x) +--R + +--R 4 3 2 5 2 5 +--R (- 192a b - 288a b - 48a )cosh(x) + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 9 4 8 3 2 5 7 +--R - 20a cosh(x) - 32a b cosh(x) + (32a b + 72a )cosh(x) +--R + +--R 2 3 4 6 4 3 2 5 5 +--R (128a b + 200a b)cosh(x) + (128a b + 160a b - 32a )cosh(x) +--R + +--R 5 2 3 4 4 +--R (320b + 512a b + 152a b)cosh(x) +--R + +--R 4 3 2 5 3 5 +--R (- 128a b - 192a b - 32a )cosh(x) + 12a cosh(x) +--R * +--R sinh(x) +--R + +--R 5 10 3 2 5 8 2 3 4 7 +--R - 2a cosh(x) + (16a b + 14a )cosh(x) + (32a b + 40a b)cosh(x) +--R + +--R 4 3 2 5 6 5 2 3 4 5 +--R (32a b + 32a b - 12a )cosh(x) + (64b + 96a b + 24a b)cosh(x) +--R + +--R 4 3 2 5 4 5 2 5 +--R (- 32a b - 48a b - 8a )cosh(x) + 6a cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 10 4 3 2 9 +--R 3a b sinh(x) + (14a b cosh(x) + 8a b )sinh(x) +--R + +--R 4 2 3 2 2 3 4 8 +--R (27a b cosh(x) + 40a b cosh(x) + 8a b + 3a b)sinh(x) +--R + +--R 4 3 3 2 2 2 3 4 3 2 +--R (32a b cosh(x) + 88a b cosh(x) + (48a b + 20a b)cosh(x) + 4a b ) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 4 3 2 3 2 3 4 2 +--R 30a b cosh(x) + 104a b cosh(x) + (96a b + 40a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (- 16a b + 4a b )cosh(x) - 32b - 48a b - 22a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 3 2 4 2 3 4 3 +--R 12a b cosh(x) + 40a b cosh(x) + (48a b + 28a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (- 64a b - 4a b )cosh(x) + (- 160b - 240a b - 112a b)cosh(x) +--R + +--R 3 2 +--R - 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 3 2 5 2 3 4 4 +--R - 26a b cosh(x) - 72a b cosh(x) + (- 80a b + 14a b)cosh(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (- 80a b + 44a b )cosh(x) + (- 320b - 496a b - 250a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 16a b - 36a b )cosh(x) + 8a b + 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 3 2 6 2 3 4 5 +--R - 48a b cosh(x) - 120a b cosh(x) + (- 112a b + 44a b)cosh(x) +--R + +--R 3 2 4 5 2 3 4 3 +--R 156a b cosh(x) + (- 320b - 544a b - 320a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (- 64a b - 104a b )cosh(x) + (32a b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 3 2 7 2 3 4 6 +--R - 33a b cosh(x) - 72a b cosh(x) + (- 32a b + 64a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 4 +--R (80a b + 188a b )cosh(x) + (- 160b - 336a b - 250a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 4 +--R (- 96a b - 136a b )cosh(x) + (48a b + 72a b)cosh(x) + 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 3 2 8 2 3 4 7 +--R - 10a b cosh(x) - 16a b cosh(x) + (16a b + 36a b)cosh(x) +--R + +--R 4 3 2 6 5 2 3 4 5 +--R (64a b + 100a b )cosh(x) + (- 32b - 112a b - 112a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 4 +--R (- 64a b - 84a b )cosh(x) + (32a b + 48a b)cosh(x) + 6a b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 10 2 3 4 8 4 3 2 7 +--R - a b cosh(x) + (8a b + 7a b)cosh(x) + (16a b + 20a b )cosh(x) +--R + +--R 2 3 4 6 4 3 2 5 +--R (- 16a b - 22a b)cosh(x) + (- 16a b - 20a b )cosh(x) +--R + +--R 2 3 4 4 4 2 4 +--R (8a b + 12a b)cosh(x) + 3a b cosh(x) + a b +--R / +--R 5 6 5 4 2 5 +--R 16a b sinh(x) + (96a b cosh(x) + 32a b )sinh(x) +--R + +--R 5 2 4 2 5 4 +--R (240a b cosh(x) + 160a b cosh(x) - 16a b)sinh(x) +--R + +--R 5 3 4 2 2 5 3 +--R (320a b cosh(x) + 320a b cosh(x) - 64a b cosh(x))sinh(x) +--R + +--R 5 4 4 2 3 5 2 2 +--R (240a b cosh(x) + 320a b cosh(x) - 96a b cosh(x) )sinh(x) +--R + +--R 5 5 4 2 4 5 3 +--R (96a b cosh(x) + 160a b cosh(x) - 64a b cosh(x) )sinh(x) +--R + +--R 5 6 4 2 5 5 4 +--R 16a b cosh(x) + 32a b cosh(x) - 16a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 6 6 5 5 +--R - 32a sinh(x) + (- 192a cosh(x) - 64a b)sinh(x) +--R + +--R 6 2 5 6 4 +--R (- 480a cosh(x) - 320a b cosh(x) + 32a )sinh(x) +--R + +--R 6 3 5 2 6 3 +--R (- 640a cosh(x) - 640a b cosh(x) + 128a cosh(x))sinh(x) +--R + +--R 6 4 5 3 6 2 2 +--R (- 480a cosh(x) - 640a b cosh(x) + 192a cosh(x) )sinh(x) +--R + +--R 6 5 5 4 6 3 +--R (- 192a cosh(x) - 320a b cosh(x) + 128a cosh(x) )sinh(x) +--R + +--R 6 6 5 5 6 4 +--R - 32a cosh(x) - 64a b cosh(x) + 32a cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 6 5 4 2 5 +--R - 16a b sinh(x) + (- 96a b cosh(x) - 32a b )sinh(x) +--R + +--R 5 2 4 2 5 4 +--R (- 240a b cosh(x) - 160a b cosh(x) + 16a b)sinh(x) +--R + +--R 5 3 4 2 2 5 3 +--R (- 320a b cosh(x) - 320a b cosh(x) + 64a b cosh(x))sinh(x) +--R + +--R 5 4 4 2 3 5 2 2 +--R (- 240a b cosh(x) - 320a b cosh(x) + 96a b cosh(x) )sinh(x) +--R + +--R 5 5 4 2 4 5 3 +--R (- 96a b cosh(x) - 160a b cosh(x) + 64a b cosh(x) )sinh(x) +--R + +--R 5 6 4 2 5 5 4 +--R - 16a b cosh(x) - 32a b cosh(x) + 16a b cosh(x) +--R Type: Expression Integer +--E 401 + +--S 402 of 526 +t0675:= cosh(x)/(%i+csch(x)) +--R +--R +--R cosh(x) +--R (401) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 402 + +--S 403 of 526 +r0675:= log(-%i+sinh(x))-%i*sinh(x) +--R +--R +--R (402) log(sinh(x) - %i) - %i sinh(x) +--R Type: Expression Complex Integer +--E 403 + +--S 404 of 526 +a0675:= integrate(t0675,x) +--R +--R +--R (403) +--R 2 +--R (4sinh(x) + 4cosh(x))log(sinh(x) + cosh(x) - %i) - %i sinh(x) +--R + +--R 2 +--R (- 2%i cosh(x) - 2x)sinh(x) - %i cosh(x) - 2x cosh(x) + %i +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Union(Expression Complex Integer,...) +--E 404 + +--S 405 of 526 +m0675:= a0675-r0675 +--R +--R +--R (404) +--R (4sinh(x) + 4cosh(x))log(sinh(x) + cosh(x) - %i) +--R + +--R 2 +--R (- 2sinh(x) - 2cosh(x))log(sinh(x) - %i) + %i sinh(x) - 2x sinh(x) +--R + +--R 2 +--R - %i cosh(x) - 2x cosh(x) + %i +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Expression Complex Integer +--E 405 + +--S 406 of 526 +d0675:= D(m0675,x) +--R +--R +--R (405) +--R 4 3 2 2 +--R - %i sinh(x) - %i cosh(x)sinh(x) + (%i cosh(x) + cosh(x))sinh(x) +--R + +--R 3 3 2 +--R (%i cosh(x) - %i cosh(x))sinh(x) - cosh(x) - %i cosh(x) + cosh(x) + %i +--R / +--R 3 2 +--R 2sinh(x) + (4cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (2cosh(x) - 6%i cosh(x) - 2)sinh(x) - 2%i cosh(x) - 2cosh(x) +--R Type: Expression Complex Integer +--E 406 + +--S 407 of 526 +t0676:= cosh(x)^2/(%i+csch(x)) +--R +--R +--R 2 +--R cosh(x) +--R (406) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 407 + +--S 408 of 526 +r0676:= 1/2*%i*x+cosh(x)-1/2*%i*cosh(x)*sinh(x) +--R +--R +--R 1 1 +--R (407) - - %i cosh(x)sinh(x) + cosh(x) + - %i x +--R 2 2 +--R Type: Expression Complex Fraction Integer +--E 408 + +--S 409 of 526 +a0676:= integrate(t0676,x) +--R +--R +--R - %i cosh(x)sinh(x) + 2cosh(x) + %i x +--R (408) ------------------------------------- +--R 2 +--R Type: Union(Expression Complex Integer,...) +--E 409 + +--S 410 of 526 +m0676:= a0676-r0676 +--R +--R +--R (409) 0 +--R Type: Expression Complex Fraction Integer +--E 410 + +--S 411 of 526 +d0676:= D(m0676,x) +--R +--R +--R (410) 0 +--R Type: Expression Complex Fraction Integer +--E 411 + +--S 412 of 526 +t0677:= cosh(x)^4/(%i+csch(x)) +--R +--R +--R 4 +--R cosh(x) +--R (411) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 412 + +--S 413 of 526 +r0677:= 1/8*%i*x+1/3*cosh(x)^3-1/8*%i*cosh(x)*sinh(x)-1/4*%i*cosh(x)*sinh(x)^3 +--R +--R +--R 1 3 1 1 3 1 +--R (412) - - %i cosh(x)sinh(x) - - %i cosh(x)sinh(x) + - cosh(x) + - %i x +--R 4 8 3 8 +--R Type: Expression Complex Fraction Integer +--E 413 + +--S 414 of 526 +a0677:= integrate(t0677,x) +--R +--R +--R (413) +--R 3 2 3 +--R - 3%i cosh(x)sinh(x) + 6cosh(x)sinh(x) - 3%i cosh(x) sinh(x) +--R + +--R 3 +--R 2cosh(x) + 6cosh(x) + 3%i x +--R / +--R 24 +--R Type: Union(Expression Complex Integer,...) +--E 414 + +--S 415 of 526 +m0677:= a0677-r0677 +--R +--R +--R (414) +--R 1 3 1 2 +--R - %i cosh(x)sinh(x) + - cosh(x)sinh(x) +--R 8 4 +--R + +--R 1 3 1 1 3 1 +--R (- - %i cosh(x) + - %i cosh(x))sinh(x) - - cosh(x) + - cosh(x) +--R 8 8 4 4 +--R Type: Expression Complex Fraction Integer +--E 415 + +--S 416 of 526 +d0677:= D(m0677,x) +--R +--R +--R (415) +--R 1 4 1 3 1 2 1 2 1 +--R - %i sinh(x) + - sinh(x) + - %i sinh(x) + (- - cosh(x) + -)sinh(x) +--R 8 4 8 4 4 +--R + +--R 1 4 1 2 +--R - - %i cosh(x) + - %i cosh(x) +--R 8 8 +--R Type: Expression Complex Fraction Integer +--E 416 + +--S 417 of 526 +t0678:= tanh(x)/(a+b*csch(x)) +--R +--R +--R tanh(x) +--R (416) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 417 + +--S 418 of 526 +r0678:= -1/2*(2*a*b*atan(sinh(x))-a^2*log(cosh(x)^2)-_ + 2*b^2*log(b+a*sinh(x)))/a/(a^2+b^2) +--R +--R +--R 2 2 2 +--R 2b log(a sinh(x) + b) + a log(cosh(x) ) - 2a b atan(sinh(x)) +--R (417) ------------------------------------------------------------ +--R 2 3 +--R 2a b + 2a +--R Type: Expression Integer +--E 418 + +--S 419 of 526 +a0678:= integrate(t0678,x) +--R +--R +--R (418) +--R 2 2cosh(x) 2 - 2a sinh(x) - 2b +--R a log(- -----------------) + b log(-----------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 2a b atan(sinh(x) + cosh(x)) + (- b - a )x +--R / +--R 2 3 +--R a b + a +--R Type: Union(Expression Integer,...) +--E 419 + +--S 420 of 526 +m0678:= a0678-r0678 +--R +--R +--R (419) +--R 2 2 2 2 2cosh(x) +--R - 2b log(a sinh(x) + b) - a log(cosh(x) ) + 2a log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 - 2a sinh(x) - 2b +--R 2b log(-----------------) - 4a b atan(sinh(x) + cosh(x)) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R 2a b atan(sinh(x)) + (- 2b - 2a )x +--R / +--R 2 3 +--R 2a b + 2a +--R Type: Expression Integer +--E 420 + +--S 421 of 526 +d0678:= D(m0678,x) +--R +--R +--R (420) +--R 3 2 2 +--R - 2b sinh(x) - b cosh(x)sinh(x) + (2b cosh(x) - 2b)sinh(x) +--R + +--R 3 +--R b cosh(x) - b cosh(x) +--R / +--R 2 2 4 2 2 3 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((b + a )cosh(x) + 2b + 2a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b + a )cosh(x) + b + a +--R Type: Expression Integer +--E 421 + +--S 422 of 526 +t0679:= tanh(x)^2/(a+b*csch(x)) +--R +--R +--R 2 +--R tanh(x) +--R (421) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 422 + +--S 423 of 526 +r0679:= x/a+2*b^3*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a/_ + (a^2+b^2)^(3/2)+b*sech(x)/(a^2+b^2)-a*tanh(x)/(a^2+b^2) +--R +--R +--R (422) +--R x +--R b tanh(-) - a +--R 3 2 +--R - 2b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (- a tanh(x) + a b sech(x) + (b + a )x)\|b + a +--R / +--R +-------+ +--R 2 3 | 2 2 +--R (a b + a )\|b + a +--R Type: Expression Integer +--E 423 + +--S 424 of 526 +a0679:= integrate(t0679,x) +--R +--R +--R (423) +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 2 2 2 2 +--R (b + a )x sinh(x) + ((2b + 2a )x cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (b + a )x cosh(x) + 2a b cosh(x) + (b + a )x + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 2 2 3 2 3 2 +--R (a b + a )sinh(x) + (2a b + 2a )cosh(x)sinh(x) + (a b + a )cosh(x) +--R + +--R 2 3 +--R a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression Integer,...) +--E 424 + +--S 425 of 526 +m0679:= a0679-r0679 +--R +--R +--R (424) +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R x +--R b tanh(-) - a +--R 3 2 3 3 2 3 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) + 2b )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a )tanh(x) +--R + +--R 2 +--R - a b sech(x)sinh(x) + (- 2a b cosh(x)sech(x) + 2a b)sinh(x) +--R + +--R 2 2 +--R (- a b cosh(x) - a b)sech(x) + 2a b cosh(x) + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 2 2 3 2 3 2 +--R (a b + a )sinh(x) + (2a b + 2a )cosh(x)sinh(x) + (a b + a )cosh(x) +--R + +--R 2 3 +--R a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression Integer +--E 425 + +--S 426 of 526 +d0679:= D(m0679,x) +--R +--R +--R (425) +--R 2 6 2 2 5 +--R - a b sinh(x) + (- 6a b cosh(x) - 2a b )sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 15a b cosh(x) - 10a b cosh(x) - a b)sinh(x) +--R + +--R 2 3 2 2 2 2 +--R (- 20a b cosh(x) - 20a b cosh(x) - 4a b cosh(x) - 4a b ) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R - 15a b cosh(x) - 20a b cosh(x) - 6a b cosh(x) +--R + +--R 2 2 +--R - 12a b cosh(x) + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R - 6a b cosh(x) - 10a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 2 +--R - 12a b cosh(x) + 2a b cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - a b cosh(x) - 2a b cosh(x) - a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 2 +--R a b cosh(x) - 2a b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 2 5 +--R 2a sinh(x) + (12a cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 3 4 +--R (30a cosh(x) + 20a b cosh(x) + 2a )sinh(x) +--R + +--R 3 3 2 2 3 2 3 +--R (40a cosh(x) + 40a b cosh(x) + 8a cosh(x) + 8a b)sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 30a cosh(x) + 40a b cosh(x) + 12a cosh(x) + 24a b cosh(x) +--R + +--R 3 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 3 3 2 2 +--R 12a cosh(x) + 20a b cosh(x) + 8a cosh(x) + 24a b cosh(x) +--R + +--R 3 2 +--R - 4a cosh(x) + 4a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 4 2 3 +--R 2a cosh(x) + 4a b cosh(x) + 2a cosh(x) + 8a b cosh(x) +--R + +--R 3 2 2 3 +--R - 2a cosh(x) + 4a b cosh(x) - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R a b sinh(x) + (6a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 2 2 4 +--R (15a b cosh(x) + 10a b cosh(x) + a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R (20a b cosh(x) + 20a b cosh(x) + 4a b cosh(x) + 4a b )sinh(x) +--R + +--R 2 4 2 3 2 2 2 +--R 15a b cosh(x) + 20a b cosh(x) + 6a b cosh(x) + 12a b cosh(x) +--R + +--R 2 +--R - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 6a b cosh(x) + 10a b cosh(x) + 4a b cosh(x) + 12a b cosh(x) +--R + +--R 2 2 +--R - 2a b cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 2 +--R - a b cosh(x) + 2a b cosh(x) - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 2 3 5 +--R a b sech(x)sinh(x) + (6a b cosh(x) + 2b )sech(x)sinh(x) +--R + +--R 2 2 3 2 4 +--R (15a b cosh(x) + 10b cosh(x) + a b )sech(x)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (20a b cosh(x) + 20b cosh(x) + 4a b cosh(x) + 4b )sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R 15a b cosh(x) + 20b cosh(x) + 6a b cosh(x) + 12b cosh(x) +--R + +--R 2 +--R - a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 6a b cosh(x) + 10b cosh(x) + 4a b cosh(x) + 12b cosh(x) +--R + +--R 2 3 +--R - 2a b cosh(x) + 2b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R a b cosh(x) + 2b cosh(x) + a b cosh(x) + 4b cosh(x) +--R + +--R 2 2 3 2 +--R - a b cosh(x) + 2b cosh(x) - a b +--R * +--R sech(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R - 2a b sech(x)sinh(x) + (- 12a b cosh(x) - 4a b )sech(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 30a b cosh(x) - 20a b cosh(x) - 2a b)sech(x)sinh(x) +--R + +--R 2 3 2 2 2 2 +--R (- 40a b cosh(x) - 40a b cosh(x) - 8a b cosh(x) - 8a b ) +--R * +--R 3 +--R sech(x)sinh(x) +--R + +--R 2 4 2 3 2 2 +--R - 30a b cosh(x) - 40a b cosh(x) - 12a b cosh(x) +--R + +--R 2 2 +--R - 24a b cosh(x) + 2a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 2 4 2 3 +--R - 12a b cosh(x) - 20a b cosh(x) - 8a b cosh(x) +--R + +--R 2 2 2 2 +--R - 24a b cosh(x) + 4a b cosh(x) - 4a b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 2 5 2 4 +--R - 2a b cosh(x) - 4a b cosh(x) - 2a b cosh(x) +--R + +--R 2 3 2 2 2 2 +--R - 8a b cosh(x) + 2a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R sech(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 3 5 +--R - a b sech(x)sinh(x) + (- 6a b cosh(x) - 2b )sech(x)sinh(x) +--R + +--R 2 2 3 2 4 +--R (- 15a b cosh(x) - 10b cosh(x) - a b )sech(x)sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (- 20a b cosh(x) - 20b cosh(x) - 4a b cosh(x) - 4b )sech(x)sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R - 15a b cosh(x) - 20b cosh(x) - 6a b cosh(x) - 12b cosh(x) +--R + +--R 2 +--R a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R - 6a b cosh(x) - 10b cosh(x) - 4a b cosh(x) - 12b cosh(x) +--R + +--R 2 3 +--R 2a b cosh(x) - 2b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R - a b cosh(x) - 2b cosh(x) - a b cosh(x) - 4b cosh(x) +--R + +--R 2 2 3 2 +--R a b cosh(x) - 2b cosh(x) + a b +--R * +--R sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 6 3 2 5 +--R (b + a b)sinh(x) + (6b + 6a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((15b + 15a b)cosh(x) - 3b - 3a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((20b + 20a b)cosh(x) + (- 12b - 12a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((15b + 15a b)cosh(x) + (- 18b - 18a b)cosh(x) + 3b + 3a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (6b + 6a b)cosh(x) + (- 12b - 12a b)cosh(x) +--R + +--R 3 2 +--R (6b + 6a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R (b + a b)cosh(x) + (- 3b - 3a b)cosh(x) + (3b + 3a b)cosh(x) +--R + +--R 3 2 +--R - b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 3 5 +--R - 2a sinh(x) + (- 12a cosh(x) + 4b )sinh(x) +--R + +--R 3 2 3 2 3 4 +--R (- 30a cosh(x) + 20b cosh(x) + 8a b + 6a )sinh(x) +--R + +--R 3 3 3 2 2 3 3 +--R (- 40a cosh(x) + 40b cosh(x) + (32a b + 24a )cosh(x) + 8b ) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 3 3 2 3 2 +--R - 30a cosh(x) + 40b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 3 +--R 24b cosh(x) - 8a b - 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 3 4 2 3 3 +--R - 12a cosh(x) + 20b cosh(x) + (32a b + 24a )cosh(x) +--R + +--R 3 2 2 3 3 +--R 24b cosh(x) + (- 16a b - 12a )cosh(x) + 4b +--R * +--R sinh(x) +--R + +--R 3 6 3 5 2 3 4 3 3 +--R - 2a cosh(x) + 4b cosh(x) + (8a b + 6a )cosh(x) + 8b cosh(x) +--R + +--R 2 3 2 3 3 +--R (- 8a b - 6a )cosh(x) + 4b cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 6 3 2 5 +--R (- b - a b)sinh(x) + (- 6b - 6a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 15b - 15a b)cosh(x) + 3b + 3a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 20b - 20a b)cosh(x) + (12b + 12a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R ((- 15b - 15a b)cosh(x) + (18b + 18a b)cosh(x) - 3b - 3a b)sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 6b - 6a b)cosh(x) + (12b + 12a b)cosh(x) +--R + +--R 3 2 +--R (- 6b - 6a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 3 +--R (- b - a b)cosh(x) + (3b + 3a b)cosh(x) + (- 3b - 3a b)cosh(x) + b +--R + +--R 2 +--R a b +--R / +--R 3 3 6 3 3 4 2 2 5 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2b + 2a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R ((15a b + 15a b)cosh(x) + (10b + 10a b )cosh(x) + a b + a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (20a b + 20a b)cosh(x) + (20b + 20a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (4a b + 4a b)cosh(x) + 4b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 4 2 2 3 +--R (15a b + 15a b)cosh(x) + (20b + 20a b )cosh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (6a b + 6a b)cosh(x) + (12b + 12a b )cosh(x) - a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 4 2 2 4 +--R (6a b + 6a b)cosh(x) + (10b + 10a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (4a b + 4a b)cosh(x) + (12b + 12a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (- 2a b - 2a b)cosh(x) + 2b + 2a b +--R * +--R sinh(x) +--R + +--R 3 3 6 4 2 2 5 3 3 4 +--R (a b + a b)cosh(x) + (2b + 2a b )cosh(x) + (a b + a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 4 2 2 +--R (4b + 4a b )cosh(x) + (- a b - a b)cosh(x) + (2b + 2a b )cosh(x) +--R + +--R 3 3 +--R - a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 6 +--R (- 2a b - 2a )sinh(x) +--R + +--R 2 2 4 3 3 5 +--R ((- 12a b - 12a )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 2 2 4 2 3 3 2 2 +--R (- 30a b - 30a )cosh(x) + (- 20a b - 20a b)cosh(x) - 2a b +--R + +--R 4 +--R - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 4 3 3 3 2 +--R (- 40a b - 40a )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (- 8a b - 8a )cosh(x) - 8a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 4 3 3 3 +--R (- 30a b - 30a )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 2 2 4 2 3 3 2 2 4 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 24a b)cosh(x) + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 5 3 3 4 +--R (- 12a b - 12a )cosh(x) + (- 20a b - 20a b)cosh(x) +--R + +--R 2 2 4 3 3 3 2 +--R (- 8a b - 8a )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (4a b + 4a )cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 2 4 6 3 3 5 +--R (- 2a b - 2a )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 2 4 4 3 3 3 +--R (- 2a b - 2a )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 2 2 4 2 3 3 2 2 4 +--R (2a b + 2a )cosh(x) + (- 4a b - 4a b)cosh(x) + 2a b + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 6 3 3 4 2 2 5 +--R (- a b - a b)sinh(x) + ((- 6a b - 6a b)cosh(x) - 2b - 2a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R ((- 15a b - 15a b)cosh(x) + (- 10b - 10a b )cosh(x) - a b - a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (- 20a b - 20a b)cosh(x) + (- 20b - 20a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (- 4a b - 4a b)cosh(x) - 4b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 4 2 2 3 +--R (- 15a b - 15a b)cosh(x) + (- 20b - 20a b )cosh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (- 6a b - 6a b)cosh(x) + (- 12b - 12a b )cosh(x) + a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 4 2 2 4 +--R (- 6a b - 6a b)cosh(x) + (- 10b - 10a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (- 4a b - 4a b)cosh(x) + (- 12b - 12a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (2a b + 2a b)cosh(x) - 2b - 2a b +--R * +--R sinh(x) +--R + +--R 3 3 6 4 2 2 5 3 3 4 +--R (- a b - a b)cosh(x) + (- 2b - 2a b )cosh(x) + (- a b - a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 4 2 2 +--R (- 4b - 4a b )cosh(x) + (a b + a b)cosh(x) + (- 2b - 2a b )cosh(x) +--R + +--R 3 3 +--R a b + a b +--R Type: Expression Integer +--E 426 + +--S 427 of 526 +t0680:= tanh(x)^3/(a+b*csch(x)) +--R +--R +--R 3 +--R tanh(x) +--R (426) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 427 + +--S 428 of 526 +r0680:= -1/2*(b*atan(sinh(x))*a^3*cosh(x)^2+3*b^3*atan(sinh(x))*a*cosh(x)^2-_ + a^4*log(cosh(x)^2)*cosh(x)^2-2*a^2*log(cosh(x)^2)*b^2*cosh(x)^2-_ + 2*b^4*log(b+a*sinh(x))*cosh(x)^2-a^4-a^2*b^2-b*sinh(x)*a^3-_ + b^3*sinh(x)*a)/cosh(x)^2/a/(a^2+b^2)^2 +--R +--R +--R (427) +--R 4 2 2 2 4 2 2 +--R 2b cosh(x) log(a sinh(x) + b) + (2a b + a )cosh(x) log(cosh(x) ) +--R + +--R 3 3 2 3 3 2 2 4 +--R (- 3a b - a b)cosh(x) atan(sinh(x)) + (a b + a b)sinh(x) + a b + a +--R / +--R 4 3 2 5 2 +--R (2a b + 4a b + 2a )cosh(x) +--R Type: Expression Integer +--E 428 + +--S 429 of 526 +a0680:= integrate(t0680,x) +--R +--R +--R (428) +--R 2 2 4 4 2 2 4 3 +--R (2a b + a )sinh(x) + (8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 4 2 2 2 4 2 +--R ((12a b + 6a )cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 2 4 3 2 2 4 +--R ((8a b + 4a )cosh(x) + (8a b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 +--R (2a b + a )cosh(x) + (4a b + 2a )cosh(x) + 2a b + a +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 4 4 3 4 2 4 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 4 3 3 3 +--R (- 3a b - a b)sinh(x) + (- 12a b - 4a b)cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 2 +--R ((- 18a b - 6a b)cosh(x) - 6a b - 2a b)sinh(x) +--R + +--R 3 3 3 3 3 +--R ((- 12a b - 4a b)cosh(x) + (- 12a b - 4a b)cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 3 3 +--R (- 3a b - a b)cosh(x) + (- 6a b - 2a b)cosh(x) - 3a b - a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 4 2 2 4 4 +--R (- b - 2a b - a )x sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R ((- 4b - 8a b - 4a )x cosh(x) + a b + a b)sinh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (- 6b - 12a b - 6a )x cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 +--R (- 2b - 4a b - 2a )x + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 4b - 8a b - 4a )x cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((- 4b - 8a b - 4a )x + 4a b + 4a )cosh(x) - a b - a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- b - 2a b - a )x cosh(x) + (a b + a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 3 3 +--R ((- 2b - 4a b - 2a )x + 2a b + 2a )cosh(x) + (- a b - a b)cosh(x) +--R + +--R 4 2 2 4 +--R (- b - 2a b - a )x +--R / +--R 4 3 2 5 4 4 3 2 5 3 +--R (a b + 2a b + a )sinh(x) + (4a b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 2 +--R ((6a b + 12a b + 6a )cosh(x) + 2a b + 4a b + 2a )sinh(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((4a b + 8a b + 4a )cosh(x) + (4a b + 8a b + 4a )cosh(x))sinh(x) +--R + +--R 4 3 2 5 4 4 3 2 5 2 4 +--R (a b + 2a b + a )cosh(x) + (2a b + 4a b + 2a )cosh(x) + a b +--R + +--R 3 2 5 +--R 2a b + a +--R Type: Union(Expression Integer,...) +--E 429 + +--S 430 of 526 +m0680:= a0680-r0680 +--R +--R +--R (429) +--R 4 2 4 4 3 3 +--R - 2b cosh(x) sinh(x) - 8b cosh(x) sinh(x) +--R + +--R 4 4 4 2 2 +--R (- 12b cosh(x) - 4b cosh(x) )sinh(x) +--R + +--R 4 5 4 3 4 6 4 4 +--R (- 8b cosh(x) - 8b cosh(x) )sinh(x) - 2b cosh(x) - 4b cosh(x) +--R + +--R 4 2 +--R - 2b cosh(x) +--R * +--R log(a sinh(x) + b) +--R + +--R 2 2 4 2 4 2 2 4 3 3 +--R (- 2a b - a )cosh(x) sinh(x) + (- 8a b - 4a )cosh(x) sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 +--R ((- 12a b - 6a )cosh(x) + (- 4a b - 2a )cosh(x) )sinh(x) +--R + +--R 2 2 4 5 2 2 4 3 +--R ((- 8a b - 4a )cosh(x) + (- 8a b - 4a )cosh(x) )sinh(x) +--R + +--R 2 2 4 6 2 2 4 4 +--R (- 2a b - a )cosh(x) + (- 4a b - 2a )cosh(x) +--R + +--R 2 2 4 2 +--R (- 2a b - a )cosh(x) +--R * +--R 2 +--R log(cosh(x) ) +--R + +--R 2 2 4 2 4 2 2 4 3 3 +--R (4a b + 2a )cosh(x) sinh(x) + (16a b + 8a )cosh(x) sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 +--R ((24a b + 12a )cosh(x) + (8a b + 4a )cosh(x) )sinh(x) +--R + +--R 2 2 4 5 2 2 4 3 +--R ((16a b + 8a )cosh(x) + (16a b + 8a )cosh(x) )sinh(x) +--R + +--R 2 2 4 6 2 2 4 4 2 2 4 2 +--R (4a b + 2a )cosh(x) + (8a b + 4a )cosh(x) + (4a b + 2a )cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 2 4 4 3 3 +--R 2b cosh(x) sinh(x) + 8b cosh(x) sinh(x) +--R + +--R 4 4 4 2 2 +--R (12b cosh(x) + 4b cosh(x) )sinh(x) +--R + +--R 4 5 4 3 4 6 4 4 +--R (8b cosh(x) + 8b cosh(x) )sinh(x) + 2b cosh(x) + 4b cosh(x) +--R + +--R 4 2 +--R 2b cosh(x) +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 2 4 3 3 3 3 +--R (- 6a b - 2a b)cosh(x) sinh(x) + (- 24a b - 8a b)cosh(x) sinh(x) +--R + +--R 3 3 4 3 3 2 2 +--R ((- 36a b - 12a b)cosh(x) + (- 12a b - 4a b)cosh(x) )sinh(x) +--R + +--R 3 3 5 3 3 3 +--R ((- 24a b - 8a b)cosh(x) + (- 24a b - 8a b)cosh(x) )sinh(x) +--R + +--R 3 3 6 3 3 4 +--R (- 6a b - 2a b)cosh(x) + (- 12a b - 4a b)cosh(x) +--R + +--R 3 3 2 +--R (- 6a b - 2a b)cosh(x) +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 3 2 4 3 3 3 3 +--R (3a b + a b)cosh(x) sinh(x) + (12a b + 4a b)cosh(x) sinh(x) +--R + +--R 3 3 4 3 3 2 2 +--R ((18a b + 6a b)cosh(x) + (6a b + 2a b)cosh(x) )sinh(x) +--R + +--R 3 3 5 3 3 3 +--R ((12a b + 4a b)cosh(x) + (12a b + 4a b)cosh(x) )sinh(x) +--R + +--R 3 3 6 3 3 4 3 3 2 +--R (3a b + a b)cosh(x) + (6a b + 2a b)cosh(x) + (3a b + a b)cosh(x) +--R * +--R atan(sinh(x)) +--R + +--R 3 3 5 +--R (- a b - a b)sinh(x) +--R + +--R 4 2 2 4 2 3 3 2 2 4 +--R ((- 2b - 4a b - 2a )x cosh(x) + (- 4a b - 4a b)cosh(x) - a b - a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 8b - 16a b - 8a )x cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (- 4a b - 4a )cosh(x) - 2a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 12b - 24a b - 12a )x cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 +--R ((- 4b - 8a b - 4a )x - 2a b - 2a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (- 4a b - 4a b)cosh(x) - 2a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (- 8b - 16a b - 8a )x cosh(x) + (5a b + 5a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 +--R ((- 8b - 16a b - 8a )x + 4a b + 4a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 4a b - 4a b)cosh(x) + (- 4a b - 4a )cosh(x) - a b - a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (- 2b - 4a b - 2a )x cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 4 3 3 3 +--R ((- 4b - 8a b - 4a )x + 3a b + 3a )cosh(x) + (- 2a b - 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 2 2 4 +--R ((- 2b - 4a b - 2a )x - 2a b - 2a )cosh(x) - a b - a +--R / +--R 4 3 2 5 2 4 +--R (2a b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 3 2 5 3 3 +--R (8a b + 16a b + 8a )cosh(x) sinh(x) +--R + +--R 4 3 2 5 4 4 3 2 5 2 +--R ((12a b + 24a b + 12a )cosh(x) + (4a b + 8a b + 4a )cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 5 5 4 3 2 5 3 +--R ((8a b + 16a b + 8a )cosh(x) + (8a b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 3 2 5 6 4 3 2 5 4 +--R (2a b + 4a b + 2a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 4 3 2 5 2 +--R (2a b + 4a b + 2a )cosh(x) +--R Type: Expression Integer +--E 430 + +--S 431 of 526 +d0680:= D(m0680,x) +--R +--R +--R (430) +--R 3 2 10 3 2 2 3 9 +--R (2b + 2a b)sinh(x) + ((12b + 12a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 8 +--R ((29b + 29a b)cosh(x) + (12a b + 12a )cosh(x) + 8b + 8a b)sinh(x) +--R + +--R 3 2 3 2 3 2 +--R (26b + 30a b)cosh(x) + (30a b + 30a )cosh(x) +--R + +--R 3 2 2 3 +--R (36b + 36a b)cosh(x) + 8a b + 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 22b - 4a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (62b + 62a b)cosh(x) + (36a b + 36a )cosh(x) + 12b + 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 70b - 42a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (38b + 50a b)cosh(x) + (66a b + 66a )cosh(x) +--R + +--R 3 2 2 3 +--R (36b + 36a b)cosh(x) + 12a b + 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 6 2 3 5 +--R (- 48b - 38a b)cosh(x) + (- 36a b - 36a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 28b + 10a b)cosh(x) + (64a b + 64a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (36b + 36a b)cosh(x) + (36a b + 36a )cosh(x) + 8b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 7 2 3 6 +--R (14b - 6a b)cosh(x) + (- 30a b - 30a )cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 64b - 24a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 2b + 10a b)cosh(x) + (42a b + 42a )cosh(x) +--R + +--R 3 2 2 3 +--R (12b + 12a b)cosh(x) + 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 8 2 3 7 +--R (36b + 10a b)cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 3 2 6 2 3 5 +--R (- 42b - 30a b)cosh(x) + (- 28a b - 28a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 14b + 8a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (2b + 2a b)cosh(x) + (12a b + 12a )cosh(x) + 2b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 9 3 2 7 +--R (18b + 6a b)cosh(x) + (- 10b - 14a b)cosh(x) +--R + +--R 2 3 6 3 2 5 +--R (- 30a b - 30a )cosh(x) + (6b + 18a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (22a b + 22a )cosh(x) + (- 14b - 10a b)cosh(x) +--R + +--R 2 3 2 2 3 +--R (6a b + 6a )cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 10 2 8 2 3 7 +--R (3b + a b)cosh(x) - 2a b cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 3 2 6 2 3 5 3 2 4 +--R (6b + 8a b)cosh(x) + (8a b + 8a )cosh(x) + (- 8b - 6a b)cosh(x) +--R + +--R 3 2 2 +--R (- b - a b)cosh(x) +--R / +--R 4 2 2 4 3 8 +--R (2b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 4 7 +--R (12b + 24a b + 12a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 6 +--R ((30b + 60a b + 30a )cosh(x) + (8b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 5 +--R ((40b + 80a b + 40a )cosh(x) + (36b + 72a b + 36a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 7 4 2 2 4 5 +--R (30b + 60a b + 30a )cosh(x) + (66b + 132a b + 66a )cosh(x) +--R + +--R 4 2 2 4 3 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (64b + 128a b + 64a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (36b + 72a b + 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (42b + 84a b + 42a )cosh(x) + (8b + 16a b + 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (24b + 48a b + 24a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (6b + 12a b + 6a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (6b + 12a b + 6a )cosh(x) + (2b + 4a b + 2a )cosh(x) +--R Type: Expression Integer +--E 431 + +--S 432 of 526 +t0681:= tanh(x)^4/(a+b*csch(x)) +--R +--R +--R 4 +--R tanh(x) +--R (431) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 432 + +--S 433 of 526 +r0681:= x/a+2*b^5*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a/_ + (a^2+b^2)^(5/2)+b*(a^2+2*b^2)*sech(x)/(a^2+b^2)^2-_ + b*sech(x)^3/(3*a^2+3*b^2)+a*tanh(x)/(a^2+b^2)-_ + a*(2*a^2+3*b^2)*tanh(x)/(a^2+b^2)^2-a*tanh(x)^3/(3*a^2+3*b^2) +--R +--R +--R (432) +--R x +--R b tanh(-) - a +--R 5 2 +--R - 6b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 4 3 2 2 4 +--R (- a b - a )tanh(x) + (- 6a b - 3a )tanh(x) +--R + +--R 3 3 3 3 3 4 2 2 4 +--R (- a b - a b)sech(x) + (6a b + 3a b)sech(x) + (3b + 6a b + 3a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 3 2 5 | 2 2 +--R (3a b + 6a b + 3a )\|b + a +--R Type: Expression Integer +--E 433 + +--S 434 of 526 +a0681:= integrate(t0681,x) +--R +--R +--R (433) +--R 5 6 5 5 5 2 5 4 +--R 3b sinh(x) + 18b cosh(x)sinh(x) + (45b cosh(x) + 9b )sinh(x) +--R + +--R 5 3 5 3 +--R (60b cosh(x) + 36b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (45b cosh(x) + 54b cosh(x) + 9b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (18b cosh(x) + 36b cosh(x) + 18b cosh(x))sinh(x) + 3b cosh(x) +--R + +--R 5 4 5 2 5 +--R 9b cosh(x) + 9b cosh(x) + 3b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 4 2 2 4 6 +--R (3b + 6a b + 3a )x sinh(x) +--R + +--R 4 2 2 4 3 3 5 +--R ((18b + 36a b + 18a )x cosh(x) + 12a b + 6a b)sinh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (45b + 90a b + 45a )x cosh(x) + (60a b + 30a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 +--R (9b + 18a b + 9a )x + 18a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (60b + 120a b + 60a )x cosh(x) + (120a b + 60a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((36b + 72a b + 36a )x + 72a b + 48a )cosh(x) + 16a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (45b + 90a b + 45a )x cosh(x) + (120a b + 60a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 +--R ((54b + 108a b + 54a )x + 108a b + 72a )cosh(x) +--R + +--R 3 3 4 2 2 4 2 2 4 +--R (48a b + 12a b)cosh(x) + (9b + 18a b + 9a )x + 24a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (18b + 36a b + 18a )x cosh(x) + (60a b + 30a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 +--R ((36b + 72a b + 36a )x + 72a b + 48a )cosh(x) +--R + +--R 3 3 2 +--R (48a b + 12a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((18b + 36a b + 18a )x + 48a b + 24a )cosh(x) + 12a b + 6a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (3b + 6a b + 3a )x cosh(x) + (12a b + 6a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 4 +--R ((9b + 18a b + 9a )x + 18a b + 12a )cosh(x) +--R + +--R 3 3 3 +--R (16a b + 4a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 +--R ((9b + 18a b + 9a )x + 24a b + 12a )cosh(x) +--R + +--R 3 3 4 2 2 4 2 2 4 +--R (12a b + 6a b)cosh(x) + (3b + 6a b + 3a )x + 14a b + 8a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 2 5 6 4 3 2 5 5 +--R (3a b + 6a b + 3a )sinh(x) + (18a b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R ((45a b + 90a b + 45a )cosh(x) + 9a b + 18a b + 9a )sinh(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((60a b + 120a b + 60a )cosh(x) + (36a b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 5 4 +--R (45a b + 90a b + 45a )cosh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (54a b + 108a b + 54a )cosh(x) + 9a b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 5 5 4 3 2 5 3 +--R (18a b + 36a b + 18a )cosh(x) + (36a b + 72a b + 36a )cosh(x) +--R + +--R 4 3 2 5 +--R (18a b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 5 6 4 3 2 5 4 +--R (3a b + 6a b + 3a )cosh(x) + (9a b + 18a b + 9a )cosh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (9a b + 18a b + 9a )cosh(x) + 3a b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression Integer,...) +--E 434 + +--S 435 of 526 +m0681:= a0681-r0681 +--R +--R +--R (434) +--R 5 6 5 5 5 2 5 4 +--R 3b sinh(x) + 18b cosh(x)sinh(x) + (45b cosh(x) + 9b )sinh(x) +--R + +--R 5 3 5 3 +--R (60b cosh(x) + 36b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (45b cosh(x) + 54b cosh(x) + 9b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (18b cosh(x) + 36b cosh(x) + 18b cosh(x))sinh(x) + 3b cosh(x) +--R + +--R 5 4 5 2 5 +--R 9b cosh(x) + 9b cosh(x) + 3b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 5 6 5 5 5 2 5 4 +--R 6b sinh(x) + 36b cosh(x)sinh(x) + (90b cosh(x) + 18b )sinh(x) +--R + +--R 5 3 5 3 +--R (120b cosh(x) + 72b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (90b cosh(x) + 108b cosh(x) + 18b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (36b cosh(x) + 72b cosh(x) + 36b cosh(x))sinh(x) + 6b cosh(x) +--R + +--R 5 4 5 2 5 +--R 18b cosh(x) + 18b cosh(x) + 6b +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 4 6 2 2 4 5 +--R (a b + a )sinh(x) + (6a b + 6a )cosh(x)sinh(x) +--R + +--R 2 2 4 2 2 2 4 4 +--R ((15a b + 15a )cosh(x) + 3a b + 3a )sinh(x) +--R + +--R 2 2 4 3 2 2 4 3 +--R ((20a b + 20a )cosh(x) + (12a b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 +--R (15a b + 15a )cosh(x) + (18a b + 18a )cosh(x) + 3a b +--R + +--R 4 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 5 2 2 4 3 +--R (6a b + 6a )cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 4 +--R (6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 6 2 2 4 4 +--R (a b + a )cosh(x) + (3a b + 3a )cosh(x) +--R + +--R 2 2 4 2 2 2 4 +--R (3a b + 3a )cosh(x) + a b + a +--R * +--R 3 +--R tanh(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (6a b + 3a )sinh(x) + (36a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 4 2 2 2 4 4 +--R ((90a b + 45a )cosh(x) + 18a b + 9a )sinh(x) +--R + +--R 2 2 4 3 2 2 4 3 +--R ((120a b + 60a )cosh(x) + (72a b + 36a )cosh(x))sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 +--R (90a b + 45a )cosh(x) + (108a b + 54a )cosh(x) + 18a b +--R + +--R 4 +--R 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 5 2 2 4 3 +--R (36a b + 18a )cosh(x) + (72a b + 36a )cosh(x) +--R + +--R 2 2 4 +--R (36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 6 2 2 4 4 +--R (6a b + 3a )cosh(x) + (18a b + 9a )cosh(x) +--R + +--R 2 2 4 2 2 2 4 +--R (18a b + 9a )cosh(x) + 6a b + 3a +--R * +--R tanh(x) +--R + +--R 3 3 3 3 3 6 +--R ((a b + a b)sech(x) + (- 6a b - 3a b)sech(x))sinh(x) +--R + +--R 3 3 3 3 3 +--R (6a b + 6a b)cosh(x)sech(x) + (- 36a b - 18a b)cosh(x)sech(x) +--R + +--R 3 3 +--R 12a b + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 3 2 3 3 3 +--R ((15a b + 15a b)cosh(x) + 3a b + 3a b)sech(x) +--R + +--R 3 3 2 3 3 +--R ((- 90a b - 45a b)cosh(x) - 18a b - 9a b)sech(x) +--R + +--R 3 3 2 2 4 +--R (60a b + 30a b)cosh(x) + 18a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 3 3 3 +--R ((20a b + 20a b)cosh(x) + (12a b + 12a b)cosh(x))sech(x) +--R + +--R 3 3 3 3 3 +--R ((- 120a b - 60a b)cosh(x) + (- 72a b - 36a b)cosh(x))sech(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (120a b + 60a b)cosh(x) + (72a b + 48a )cosh(x) + 16a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 3 3 2 3 +--R (15a b + 15a b)cosh(x) + (18a b + 18a b)cosh(x) + 3a b +--R + +--R 3 +--R 3a b +--R * +--R 3 +--R sech(x) +--R + +--R 3 3 4 3 3 2 +--R (- 90a b - 45a b)cosh(x) + (- 108a b - 54a b)cosh(x) +--R + +--R 3 3 +--R - 18a b - 9a b +--R * +--R sech(x) +--R + +--R 3 3 3 2 2 4 2 +--R (120a b + 60a b)cosh(x) + (108a b + 72a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (48a b + 12a b)cosh(x) + 24a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 3 3 3 +--R (6a b + 6a b)cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 3 3 +--R (6a b + 6a b)cosh(x) +--R * +--R 3 +--R sech(x) +--R + +--R 3 3 5 3 3 3 +--R (- 36a b - 18a b)cosh(x) + (- 72a b - 36a b)cosh(x) +--R + +--R 3 3 +--R (- 36a b - 18a b)cosh(x) +--R * +--R sech(x) +--R + +--R 3 3 4 2 2 4 3 +--R (60a b + 30a b)cosh(x) + (72a b + 48a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (48a b + 12a b)cosh(x) + (48a b + 24a )cosh(x) + 12a b + 6a b +--R * +--R sinh(x) +--R + +--R 3 3 6 3 3 4 +--R (a b + a b)cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 3 3 2 3 3 +--R (3a b + 3a b)cosh(x) + a b + a b +--R * +--R 3 +--R sech(x) +--R + +--R 3 3 6 3 3 4 +--R (- 6a b - 3a b)cosh(x) + (- 18a b - 9a b)cosh(x) +--R + +--R 3 3 2 3 3 +--R (- 18a b - 9a b)cosh(x) - 6a b - 3a b +--R * +--R sech(x) +--R + +--R 3 3 5 2 2 4 4 +--R (12a b + 6a b)cosh(x) + (18a b + 12a )cosh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (16a b + 4a b)cosh(x) + (24a b + 12a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (12a b + 6a b)cosh(x) + 14a b + 8a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 2 5 6 4 3 2 5 5 +--R (3a b + 6a b + 3a )sinh(x) + (18a b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R ((45a b + 90a b + 45a )cosh(x) + 9a b + 18a b + 9a )sinh(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((60a b + 120a b + 60a )cosh(x) + (36a b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 5 4 +--R (45a b + 90a b + 45a )cosh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (54a b + 108a b + 54a )cosh(x) + 9a b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 5 5 4 3 2 5 3 +--R (18a b + 36a b + 18a )cosh(x) + (36a b + 72a b + 36a )cosh(x) +--R + +--R 4 3 2 5 +--R (18a b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 5 6 4 3 2 5 4 +--R (3a b + 6a b + 3a )cosh(x) + (9a b + 18a b + 9a )cosh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (9a b + 18a b + 9a )cosh(x) + 3a b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression Integer +--E 435 + +--S 436 of 526 +--d0681:= D(m0681,x) +--E 436 + +--S 437 of 526 +t0682:= tanh(x)/(%i+csch(x)) +--R +--R +--R tanh(x) +--R (435) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 437 + +--S 438 of 526 +r0682:= -3/4*%i*log(-%i+sinh(x))-1/4*%i*log(%i+sinh(x))+1/(2*%i-2*sinh(x)) +--R +--R +--R (436) +--R 1 1 +--R (- - %i sinh(x) - -)log(sinh(x) + %i) +--R 4 4 +--R + +--R 3 3 1 +--R (- - %i sinh(x) - -)log(sinh(x) - %i) - - +--R 4 4 2 +--R / +--R sinh(x) - %i +--R Type: Expression Complex Fraction Integer +--E 438 + +--S 439 of 526 +a0682:= integrate(t0682,x) +--R +--R +--R (437) +--R 2 2 +--R (%i sinh(x) + (2%i cosh(x) + 2)sinh(x) + %i cosh(x) + 2cosh(x) - %i) +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R 2 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) - 4)sinh(x) - 2%i cosh(x) - 4cosh(x) +--R + +--R 2%i +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R 2%i x sinh(x) + (4%i x cosh(x) + 4x - 2)sinh(x) + 2%i x cosh(x) +--R + +--R (4x - 2)cosh(x) - 2%i x +--R / +--R 2 2 +--R 2sinh(x) + (4cosh(x) - 4%i)sinh(x) + 2cosh(x) - 4%i cosh(x) - 2 +--R Type: Union(Expression Complex Integer,...) +--E 439 + +--S 440 of 526 +m0682:= a0682-r0682 +--R +--R +--R (438) +--R 1 3 1 3 2 +--R - %i sinh(x) + (- %i cosh(x) + -)sinh(x) +--R 4 2 4 +--R + +--R 1 2 3 1 2 1 1 +--R (- %i cosh(x) + cosh(x) - - %i)sinh(x) + - cosh(x) - - %i cosh(x) - - +--R 4 4 4 2 4 +--R * +--R log(sinh(x) + %i) +--R + +--R 3 3 3 9 2 +--R - %i sinh(x) + (- %i cosh(x) + -)sinh(x) +--R 4 2 4 +--R + +--R 3 2 9 3 2 3 +--R (- %i cosh(x) + 3cosh(x) - - %i)sinh(x) + - cosh(x) - - %i cosh(x) +--R 4 4 4 2 +--R + +--R 3 +--R - - +--R 4 +--R * +--R log(sinh(x) - %i) +--R + +--R 1 3 3 2 +--R - %i sinh(x) + (%i cosh(x) + -)sinh(x) +--R 2 2 +--R + +--R 1 2 3 1 2 1 +--R (- %i cosh(x) + 2cosh(x) - - %i)sinh(x) + - cosh(x) - %i cosh(x) - - +--R 2 2 2 2 +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R 3 2 +--R - %i sinh(x) + (- 2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (- %i cosh(x) - 4cosh(x) + 3%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 1 2 +--R %i x sinh(x) + (2%i x cosh(x) + 3x - -)sinh(x) +--R 2 +--R + +--R 2 1 2 +--R (%i x cosh(x) + 4x cosh(x) - 3%i x)sinh(x) + (x + -)cosh(x) +--R 2 +--R + +--R 1 +--R - 2%i x cosh(x) - x - - +--R 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) - 3%i)sinh(x) + (cosh(x) - 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R - %i cosh(x) - 2cosh(x) + %i +--R Type: Expression Complex Fraction Integer +--E 440 + +--S 441 of 526 +d0682:= D(m0682,x) +--R +--R +--R (439) +--R 8 7 +--R - %i sinh(x) + (- 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 6 2 5 +--R (- 5%i cosh(x) - 8cosh(x) + %i)sinh(x) + (- 4cosh(x) - 5)sinh(x) +--R + +--R 4 3 2 4 +--R (5%i cosh(x) + 6cosh(x) - 6%i cosh(x) - 12cosh(x) + 5%i)sinh(x) +--R + +--R 5 4 3 2 +--R (4%i cosh(x) + 7cosh(x) - 8%i cosh(x) - 6cosh(x) + 8%i cosh(x) - 1) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R %i cosh(x) + 2cosh(x) - 3%i cosh(x) + 2cosh(x) + %i cosh(x) +--R + +--R - 4cosh(x) + 3%i +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (cosh(x) - 4%i cosh(x) - 2cosh(x) + 4%i cosh(x) + 1)sinh(x) +--R + +--R 4 2 +--R - 2%i cosh(x) + 2%i cosh(x) +--R / +--R 7 2 6 +--R cosh(x)sinh(x) + (4cosh(x) - 3%i cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (6cosh(x) - 10%i cosh(x) - cosh(x))sinh(x) +--R + +--R 4 3 2 4 +--R (4cosh(x) - 12%i cosh(x) - 2cosh(x) - 5%i cosh(x))sinh(x) +--R + +--R 5 4 2 3 +--R (cosh(x) - 6%i cosh(x) - 12%i cosh(x) - 5cosh(x))sinh(x) +--R + +--R 5 4 3 2 +--R (- %i cosh(x) + 2cosh(x) - 12%i cosh(x) - 8cosh(x) - %i cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R (cosh(x) - 6%i cosh(x) - 6cosh(x) - 2%i cosh(x) - 3cosh(x))sinh(x) +--R + +--R 5 4 2 +--R - %i cosh(x) - 2cosh(x) - 2cosh(x) + %i cosh(x) +--R Type: Expression Complex Fraction Integer +--E 441 + +--S 442 of 526 +t0683:= tanh(x)^2/(%i+csch(x)) +--R +--R +--R 2 +--R tanh(x) +--R (440) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 442 + +--S 443 of 526 +r0683:= 1/3/cosh(x)^3*(4*%i*sinh(x)*cosh(x)^2-_ + %i*sinh(x)+1-3*%i*x*cosh(x)^3-3*cosh(x)^2) +--R +--R +--R 2 3 2 +--R (4%i cosh(x) - %i)sinh(x) - 3%i x cosh(x) - 3cosh(x) + 1 +--R (441) ----------------------------------------------------------- +--R 3 +--R 3cosh(x) +--R Type: Expression Complex Integer +--E 443 + +--S 444 of 526 +a0683:= integrate(t0683,x) +--R +--R +--R (442) +--R 2 2 +--R 2%i sinh(x) + ((- 3%i x - 4%i)cosh(x) + 1)sinh(x) + 2%i cosh(x) +--R + +--R (- 3x - 4)cosh(x) +--R / +--R 3cosh(x)sinh(x) - 3%i cosh(x) +--R Type: Union(Expression Complex Integer,...) +--E 444 + +--S 445 of 526 +m0683:= a0683-r0683 +--R +--R +--R (443) +--R 2 2 3 4 +--R (- 2%i cosh(x) + %i)sinh(x) - 4%i cosh(x) sinh(x) + 2%i cosh(x) +--R + +--R 3 2 +--R - 4cosh(x) - 3%i cosh(x) + %i +--R / +--R 3 3 +--R 3cosh(x) sinh(x) - 3%i cosh(x) +--R Type: Expression Complex Integer +--E 445 + +--S 446 of 526 +d0683:= D(m0683,x) +--R +--R +--R (444) +--R 2 4 2 3 +--R (2%i cosh(x) - 3%i)sinh(x) + (2cosh(x) - 3)sinh(x) +--R + +--R 2 2 4 2 +--R (4%i cosh(x) - 3%i)sinh(x) + (- 2cosh(x) + 5cosh(x) - 3)sinh(x) +--R + +--R 6 4 2 +--R - 2%i cosh(x) + 3%i cosh(x) - %i cosh(x) +--R / +--R 4 2 4 4 +--R 3cosh(x) sinh(x) - 6%i cosh(x) sinh(x) - 3cosh(x) +--R Type: Expression Complex Integer +--E 446 + +--S 447 of 526 +t0684:= tanh(x)^3/(%i+csch(x)) +--R +--R +--R 3 +--R tanh(x) +--R (445) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 447 + +--S 448 of 526 +r0684:= -11/16*%i*log(-%i+sinh(x))-5/16*%i*log(%i+sinh(x))-_ + 1/8*%i/(%i-sinh(x))^2+3/(4*%i-4*sinh(x))+1/(8*%i+8*sinh(x)) +--R +--R +--R (446) +--R 5 3 5 2 5 5 +--R (- -- %i sinh(x) - -- sinh(x) - -- %i sinh(x) - --)log(sinh(x) + %i) +--R 16 16 16 16 +--R + +--R 11 3 11 2 11 11 +--R (- -- %i sinh(x) - -- sinh(x) - -- %i sinh(x) - --)log(sinh(x) - %i) +--R 16 16 16 16 +--R + +--R 5 2 3 3 +--R - - sinh(x) - - %i sinh(x) - - +--R 8 8 4 +--R / +--R 3 2 +--R sinh(x) - %i sinh(x) + sinh(x) - %i +--R Type: Expression Complex Fraction Integer +--E 448 + +--S 449 of 526 +a0684:= integrate(t0684,x) +--R +--R +--R (447) +--R 6 5 +--R 3%i sinh(x) + (18%i cosh(x) + 6)sinh(x) +--R + +--R 2 4 +--R (45%i cosh(x) + 30cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 3 +--R (60%i cosh(x) + 60cosh(x) + 12%i cosh(x) + 12)sinh(x) +--R + +--R 4 3 2 +--R (45%i cosh(x) + 60cosh(x) + 18%i cosh(x) + 36cosh(x) - 3%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 18%i cosh(x) + 30cosh(x) + 12%i cosh(x) + 36cosh(x) +--R + +--R - 6%i cosh(x) + 6 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 3%i cosh(x) + 6cosh(x) + 3%i cosh(x) + 12cosh(x) - 3%i cosh(x) +--R + +--R 6cosh(x) - 3%i +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R 6 5 +--R - 8%i sinh(x) + (- 48%i cosh(x) - 16)sinh(x) +--R + +--R 2 4 +--R (- 120%i cosh(x) - 80cosh(x) - 8%i)sinh(x) +--R + +--R 3 2 3 +--R (- 160%i cosh(x) - 160cosh(x) - 32%i cosh(x) - 32)sinh(x) +--R + +--R 4 3 2 +--R (- 120%i cosh(x) - 160cosh(x) - 48%i cosh(x) - 96cosh(x) + 8%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 48%i cosh(x) - 80cosh(x) - 32%i cosh(x) - 96cosh(x) +--R + +--R 16%i cosh(x) - 16 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 8%i cosh(x) - 16cosh(x) - 8%i cosh(x) - 32cosh(x) +--R + +--R 2 +--R 8%i cosh(x) - 16cosh(x) + 8%i +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 6 5 +--R 8%i x sinh(x) + (48%i x cosh(x) + 16x - 10)sinh(x) +--R + +--R 2 4 +--R (120%i x cosh(x) + (80x - 50)cosh(x) + 8%i x - 12%i)sinh(x) +--R + +--R 3 2 +--R 160%i x cosh(x) + (160x - 100)cosh(x) + (32%i x - 48%i)cosh(x) +--R + +--R 32x - 28 +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 120%i x cosh(x) + (160x - 100)cosh(x) + (48%i x - 72%i)cosh(x) +--R + +--R (96x - 84)cosh(x) - 8%i x + 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R 48%i x cosh(x) + (80x - 50)cosh(x) + (32%i x - 48%i)cosh(x) +--R + +--R 2 +--R (96x - 84)cosh(x) + (- 16%i x + 24%i)cosh(x) + 16x - 10 +--R * +--R sinh(x) +--R + +--R 6 5 4 +--R 8%i x cosh(x) + (16x - 10)cosh(x) + (8%i x - 12%i)cosh(x) +--R + +--R 3 2 +--R (32x - 28)cosh(x) + (- 8%i x + 12%i)cosh(x) + (16x - 10)cosh(x) - 8%i x +--R / +--R 6 5 +--R 8sinh(x) + (48cosh(x) - 16%i)sinh(x) +--R + +--R 2 4 +--R (120cosh(x) - 80%i cosh(x) + 8)sinh(x) +--R + +--R 3 2 3 +--R (160cosh(x) - 160%i cosh(x) + 32cosh(x) - 32%i)sinh(x) +--R + +--R 4 3 2 2 +--R (120cosh(x) - 160%i cosh(x) + 48cosh(x) - 96%i cosh(x) - 8)sinh(x) +--R + +--R 5 4 3 2 +--R 48cosh(x) - 80%i cosh(x) + 32cosh(x) - 96%i cosh(x) - 16cosh(x) +--R + +--R - 16%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 8cosh(x) - 16%i cosh(x) + 8cosh(x) - 32%i cosh(x) - 8cosh(x) +--R + +--R - 16%i cosh(x) - 8 +--R Type: Union(Expression Complex Integer,...) +--E 449 + +--S 450 of 526 +m0684:= a0684-r0684 +--R +--R +--R (448) +--R 5 9 15 15 8 +--R -- %i sinh(x) + (-- %i cosh(x) + --)sinh(x) +--R 16 8 16 +--R + +--R 75 2 7 +--R (-- %i cosh(x) + 5cosh(x))sinh(x) +--R 16 +--R + +--R 25 3 175 2 5 6 +--R (-- %i cosh(x) + --- cosh(x) + -)sinh(x) +--R 4 16 2 +--R + +--R 75 4 25 3 5 2 15 +--R (-- %i cosh(x) + -- cosh(x) + -- %i cosh(x) + 10cosh(x) - -- %i) +--R 16 2 16 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 15 5 125 4 5 3 265 2 +--R -- %i cosh(x) + --- cosh(x) + - %i cosh(x) + --- cosh(x) +--R 8 16 4 16 +--R + +--R 25 15 +--R - -- %i cosh(x) + -- +--R 4 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 6 5 5 15 4 3 +--R -- %i cosh(x) + - cosh(x) + -- %i cosh(x) + 15cosh(x) +--R 16 2 8 +--R + +--R 135 2 5 +--R - --- %i cosh(x) + 5cosh(x) - - %i +--R 16 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 6 5 5 65 4 25 3 +--R -- cosh(x) + - %i cosh(x) + -- cosh(x) - -- %i cosh(x) +--R 16 4 8 4 +--R + +--R 85 2 +--R -- cosh(x) - 5%i cosh(x) +--R 16 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 6 5 5 45 4 5 3 +--R -- %i cosh(x) + - cosh(x) - -- %i cosh(x) + - cosh(x) +--R 16 2 16 2 +--R + +--R 65 2 15 +--R - -- %i cosh(x) - -- %i +--R 16 16 +--R * +--R sinh(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R -- cosh(x) - - %i cosh(x) + -- cosh(x) - - %i cosh(x) +--R 16 8 16 4 +--R + +--R 5 2 5 5 +--R - -- cosh(x) - - %i cosh(x) - -- +--R 16 8 16 +--R * +--R log(sinh(x) + %i) +--R + +--R 11 9 33 33 8 +--R -- %i sinh(x) + (-- %i cosh(x) + --)sinh(x) +--R 16 8 16 +--R + +--R 165 2 7 +--R (--- %i cosh(x) + 11cosh(x))sinh(x) +--R 16 +--R + +--R 55 3 385 2 11 6 +--R (-- %i cosh(x) + --- cosh(x) + --)sinh(x) +--R 4 16 2 +--R + +--R 165 4 55 3 11 2 +--R --- %i cosh(x) + -- cosh(x) + -- %i cosh(x) + 22cosh(x) +--R 16 2 16 +--R + +--R 33 +--R - -- %i +--R 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 33 5 275 4 11 3 583 2 +--R -- %i cosh(x) + --- cosh(x) + -- %i cosh(x) + --- cosh(x) +--R 8 16 4 16 +--R + +--R 55 33 +--R - -- %i cosh(x) + -- +--R 4 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 6 11 5 33 4 3 +--R -- %i cosh(x) + -- cosh(x) + -- %i cosh(x) + 33cosh(x) +--R 16 2 8 +--R + +--R 297 2 11 +--R - --- %i cosh(x) + 11cosh(x) - -- %i +--R 16 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 11 6 11 5 143 4 55 3 +--R -- cosh(x) + -- %i cosh(x) + --- cosh(x) - -- %i cosh(x) +--R 16 4 8 4 +--R + +--R 187 2 +--R --- cosh(x) - 11%i cosh(x) +--R 16 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 6 11 5 99 4 11 3 +--R -- %i cosh(x) + -- cosh(x) - -- %i cosh(x) + -- cosh(x) +--R 16 2 16 2 +--R + +--R 143 2 33 +--R - --- %i cosh(x) - -- %i +--R 16 16 +--R * +--R sinh(x) +--R + +--R 11 6 11 5 11 4 11 3 +--R -- cosh(x) - -- %i cosh(x) + -- cosh(x) - -- %i cosh(x) +--R 16 8 16 4 +--R + +--R 11 2 11 11 +--R - -- cosh(x) - -- %i cosh(x) - -- +--R 16 8 16 +--R * +--R log(sinh(x) - %i) +--R + +--R 3 9 9 9 8 +--R - %i sinh(x) + (- %i cosh(x) + -)sinh(x) +--R 8 4 8 +--R + +--R 45 2 7 +--R (-- %i cosh(x) + 6cosh(x))sinh(x) +--R 8 +--R + +--R 15 3 105 2 6 +--R (-- %i cosh(x) + --- cosh(x) + 3)sinh(x) +--R 2 8 +--R + +--R 45 4 3 3 2 9 +--R (-- %i cosh(x) + 15cosh(x) + - %i cosh(x) + 12cosh(x) - - %i) +--R 8 8 4 +--R * +--R 5 +--R sinh(x) +--R + +--R 9 5 75 4 3 3 159 2 +--R - %i cosh(x) + -- cosh(x) + - %i cosh(x) + --- cosh(x) +--R 4 8 2 8 +--R + +--R 15 9 +--R - -- %i cosh(x) + - +--R 2 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 6 5 9 4 3 +--R - %i cosh(x) + 3cosh(x) + - %i cosh(x) + 18cosh(x) +--R 8 4 +--R + +--R 81 2 +--R - -- %i cosh(x) + 6cosh(x) - 3%i +--R 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 5 39 4 15 3 +--R - cosh(x) + - %i cosh(x) + -- cosh(x) - -- %i cosh(x) +--R 8 2 4 2 +--R + +--R 51 2 +--R -- cosh(x) - 6%i cosh(x) +--R 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 27 4 3 +--R - %i cosh(x) + 3cosh(x) - -- %i cosh(x) + 3cosh(x) +--R 8 8 +--R + +--R 39 2 9 +--R - -- %i cosh(x) - - %i +--R 8 8 +--R * +--R sinh(x) +--R + +--R 3 6 3 5 3 4 3 3 3 2 +--R - cosh(x) - - %i cosh(x) + - cosh(x) - - %i cosh(x) - - cosh(x) +--R 8 4 8 2 8 +--R + +--R 3 3 +--R - - %i cosh(x) - - +--R 4 8 +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R 9 8 +--R - %i sinh(x) + (- 6%i cosh(x) - 3)sinh(x) +--R + +--R 2 7 +--R (- 15%i cosh(x) - 16cosh(x))sinh(x) +--R + +--R 3 2 6 +--R (- 20%i cosh(x) - 35cosh(x) - 8)sinh(x) +--R + +--R 4 3 2 +--R (- 15%i cosh(x) - 40cosh(x) - %i cosh(x) - 32cosh(x) + 6%i) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 6%i cosh(x) - 25cosh(x) - 4%i cosh(x) - 53cosh(x) +--R + +--R 20%i cosh(x) - 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - %i cosh(x) - 8cosh(x) - 6%i cosh(x) - 48cosh(x) +--R + +--R 2 +--R 27%i cosh(x) - 16cosh(x) + 8%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - cosh(x) - 4%i cosh(x) - 26cosh(x) + 20%i cosh(x) +--R + +--R 2 +--R - 17cosh(x) + 16%i cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - %i cosh(x) - 8cosh(x) + 9%i cosh(x) - 8cosh(x) +--R + +--R 2 +--R 13%i cosh(x) + 3%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - cosh(x) + 2%i cosh(x) - cosh(x) + 4%i cosh(x) + cosh(x) +--R + +--R 2%i cosh(x) + 1 +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 9 5 8 +--R %i x sinh(x) + (6%i x cosh(x) + 3x - -)sinh(x) +--R 8 +--R + +--R 2 5 9 7 +--R (15%i x cosh(x) + (16x - -)cosh(x) - - %i)sinh(x) +--R 2 8 +--R + +--R 3 25 2 15 33 6 +--R (20%i x cosh(x) + (35x - --)cosh(x) - -- %i cosh(x) + 8x - --)sinh(x) +--R 8 4 8 +--R + +--R 4 3 27 2 +--R 15%i x cosh(x) + 40x cosh(x) + (%i x - -- %i)cosh(x) +--R 8 +--R + +--R 9 +--R (32x - 12)cosh(x) - 6%i x + - %i +--R 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 5 25 4 3 3 +--R 6%i x cosh(x) + (25x + --)cosh(x) + (4%i x + - %i)cosh(x) +--R 8 2 +--R + +--R 19 2 1 25 +--R (53x - --)cosh(x) + (- 20%i x + - %i)cosh(x) + 6x - -- +--R 2 4 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 5 33 4 +--R %i x cosh(x) + (8x + -)cosh(x) + (6%i x + -- %i)cosh(x) +--R 2 8 +--R + +--R 3 19 2 17 +--R (48x + 3)cosh(x) + (- 27%i x - -- %i)cosh(x) + (16x - --)cosh(x) +--R 4 2 +--R + +--R 13 +--R - 8%i x + -- %i +--R 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 6 9 5 63 4 +--R (x + -)cosh(x) + (4%i x + - %i)cosh(x) + (26x + --)cosh(x) +--R 8 4 8 +--R + +--R 3 77 2 +--R (- 20%i x - 6%i)cosh(x) + (17x - --)cosh(x) +--R 8 +--R + +--R 15 3 +--R (- 16%i x + -- %i)cosh(x) - - +--R 4 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 19 4 +--R (%i x + - %i)cosh(x) + (8x + 4)cosh(x) + (- 9%i x - -- %i)cosh(x) +--R 8 8 +--R + +--R 3 21 2 5 +--R (8x - 5)cosh(x) + (- 13%i x + -- %i)cosh(x) + cosh(x) - 3%i x - - %i +--R 8 8 +--R * +--R sinh(x) +--R + +--R 3 6 1 5 3 4 +--R (x + -)cosh(x) + (- 2%i x - - %i)cosh(x) + (x - -)cosh(x) +--R 4 4 4 +--R + +--R 1 3 3 2 1 +--R (- 4%i x + - %i)cosh(x) + (- x + -)cosh(x) + (- 2%i x - - %i)cosh(x) +--R 2 4 4 +--R + +--R 3 +--R - x - - +--R 4 +--R / +--R 9 8 2 7 +--R sinh(x) + (6cosh(x) - 3%i)sinh(x) + (15cosh(x) - 16%i cosh(x))sinh(x) +--R + +--R 3 2 6 +--R (20cosh(x) - 35%i cosh(x) - 8%i)sinh(x) +--R + +--R 4 3 2 5 +--R (15cosh(x) - 40%i cosh(x) + cosh(x) - 32%i cosh(x) - 6)sinh(x) +--R + +--R 5 4 3 2 +--R 6cosh(x) - 25%i cosh(x) + 4cosh(x) - 53%i cosh(x) - 20cosh(x) +--R + +--R - 6%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) - 8%i cosh(x) + 6cosh(x) - 48%i cosh(x) - 27cosh(x) +--R + +--R - 16%i cosh(x) - 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - %i cosh(x) + 4cosh(x) - 26%i cosh(x) - 20cosh(x) +--R + +--R 2 +--R - 17%i cosh(x) - 16cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R (cosh(x) - 8%i cosh(x) - 9cosh(x) - 8%i cosh(x) - 13cosh(x) - 3) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - %i cosh(x) - 2cosh(x) - %i cosh(x) - 4cosh(x) + %i cosh(x) +--R + +--R - 2cosh(x) + %i +--R Type: Expression Complex Fraction Integer +--E 450 + +--S 451 of 526 +d0684:= D(m0684,x) +--R +--R +--R (449) +--R 14 13 +--R - %i sinh(x) + (- 8%i cosh(x) - 3)sinh(x) +--R + +--R 2 12 +--R (- 27%i cosh(x) - 20cosh(x) - 2%i)sinh(x) +--R + +--R 3 2 11 +--R (- 48%i cosh(x) - 54cosh(x) - 12%i cosh(x) - 14)sinh(x) +--R + +--R 4 3 2 10 +--R (- 42%i cosh(x) - 70cosh(x) - 32%i cosh(x) - 76cosh(x) + 5%i)sinh(x) +--R + +--R 4 3 2 9 +--R (- 28cosh(x) - 52%i cosh(x) - 162cosh(x) + 20%i cosh(x) - 25)sinh(x) +--R + +--R 6 5 4 3 +--R 42%i cosh(x) + 42cosh(x) - 60%i cosh(x) - 158cosh(x) +--R + +--R 2 +--R 34%i cosh(x) - 120cosh(x) + 20%i +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 48%i cosh(x) + 70cosh(x) - 52%i cosh(x) - 40cosh(x) +--R + +--R 3 2 +--R 32%i cosh(x) - 218cosh(x) + 72%i cosh(x) - 20 +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 27%i cosh(x) + 46cosh(x) - 32%i cosh(x) + 56cosh(x) +--R + +--R 4 3 2 +--R 8%i cosh(x) - 166cosh(x) + 90%i cosh(x) - 88cosh(x) + 25%i +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 8%i cosh(x) + 15cosh(x) - 12%i cosh(x) + 54cosh(x) +--R + +--R 5 4 3 2 +--R - 28%i cosh(x) - 6cosh(x) + 44%i cosh(x) - 158cosh(x) +--R + +--R 80%i cosh(x) - 5 +--R * +--R 5 +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R %i cosh(x) + 2cosh(x) - 2%i cosh(x) + 18cosh(x) - 42%i cosh(x) +--R + +--R 5 4 3 2 +--R 74cosh(x) + 6%i cosh(x) - 134cosh(x) + 87%i cosh(x) - 20cosh(x) +--R + +--R 14%i +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 2cosh(x) - 24%i cosh(x) + 48cosh(x) - 4%i cosh(x) - 28cosh(x) +--R + +--R 3 2 +--R 24%i cosh(x) - 40cosh(x) + 36%i cosh(x) + 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 5%i cosh(x) + 12cosh(x) - 10%i cosh(x) + 36cosh(x) +--R + +--R 4 3 2 +--R - 18%i cosh(x) - 52cosh(x) + 38%i cosh(x) + 4cosh(x) + 3%i +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) - 8%i cosh(x) + 24cosh(x) - 12%i cosh(x) - 34cosh(x) +--R + +--R 3 2 +--R 16%i cosh(x) + 8cosh(x) + 4%i cosh(x) + 1 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 2%i cosh(x) + 4cosh(x) - 2%i cosh(x) - 8cosh(x) + 2%i cosh(x) +--R + +--R 3 2 +--R 4cosh(x) + 2%i cosh(x) +--R / +--R 13 2 12 +--R cosh(x)sinh(x) + (8cosh(x) - 3%i cosh(x))sinh(x) +--R + +--R 3 2 11 +--R (28cosh(x) - 22%i cosh(x) + 2cosh(x))sinh(x) +--R + +--R 4 3 2 10 +--R (56cosh(x) - 70%i cosh(x) + 14cosh(x) - 14%i cosh(x))sinh(x) +--R + +--R 5 4 3 2 +--R (70cosh(x) - 126%i cosh(x) + 44cosh(x) - 86%i cosh(x) - 5cosh(x)) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 56cosh(x) - 140%i cosh(x) + 82cosh(x) - 230%i cosh(x) +--R + +--R 2 +--R - 26cosh(x) - 25%i cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 28cosh(x) - 98%i cosh(x) + 100cosh(x) - 352%i cosh(x) +--R + +--R 3 2 +--R - 56cosh(x) - 124%i cosh(x) - 20cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 8cosh(x) - 42%i cosh(x) + 82cosh(x) - 340%i cosh(x) - 64cosh(x) +--R + +--R 3 2 +--R - 268%i cosh(x) - 84cosh(x) - 20%i cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R cosh(x) - 10%i cosh(x) + 44cosh(x) - 214%i cosh(x) - 40cosh(x) +--R + +--R 4 3 2 +--R - 332%i cosh(x) - 152cosh(x) - 76%i cosh(x) - 25cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - %i cosh(x) + 14cosh(x) - 86%i cosh(x) - 10cosh(x) +--R + +--R 5 4 3 2 +--R - 260%i cosh(x) - 156cosh(x) - 124%i cosh(x) - 76cosh(x) +--R + +--R - 5%i cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R 2cosh(x) - 20%i cosh(x) + 4cosh(x) - 134%i cosh(x) - 100cosh(x) +--R + +--R 4 3 2 +--R - 112%i cosh(x) - 100cosh(x) - 14%i cosh(x) - 14cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - 2%i cosh(x) + 4cosh(x) - 46%i cosh(x) - 42cosh(x) +--R + +--R 5 4 3 2 +--R - 60%i cosh(x) - 72cosh(x) - 14%i cosh(x) - 26cosh(x) + 2%i cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R cosh(x) - 10%i cosh(x) - 12cosh(x) - 18%i cosh(x) - 30cosh(x) +--R + +--R 4 3 2 +--R - 6%i cosh(x) - 20cosh(x) + 2%i cosh(x) - 3cosh(x) +--R * +--R sinh(x) +--R + +--R 9 8 7 6 4 +--R - %i cosh(x) - 2cosh(x) - 2%i cosh(x) - 6cosh(x) - 6cosh(x) +--R + +--R 3 2 +--R 2%i cosh(x) - 2cosh(x) + %i cosh(x) +--R Type: Expression Complex Fraction Integer +--E 451 + +--S 452 of 526 +t0685:= tanh(x)^4/(%i+csch(x)) +--R +--R +--R 4 +--R tanh(x) +--R (450) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 452 + +--S 453 of 526 +r0685:= 1/15/cosh(x)^5*(23*%i*cosh(x)^4*sinh(x)-11*%i*cosh(x)^2*sinh(x)+_ + 3*%i*sinh(x)+10*cosh(x)^2-3-15*cosh(x)^4-15*%i*x*cosh(x)^5) +--R +--R +--R (451) +--R 4 2 5 +--R (23%i cosh(x) - 11%i cosh(x) + 3%i)sinh(x) - 15%i x cosh(x) +--R + +--R 4 2 +--R - 15cosh(x) + 10cosh(x) - 3 +--R / +--R 5 +--R 15cosh(x) +--R Type: Expression Complex Integer +--E 453 + +--S 454 of 526 +a0685:= integrate(t0685,x) +--R +--R +--R (452) +--R 4 3 +--R 23%i sinh(x) + ((- 60%i x - 92%i)cosh(x) + 16)sinh(x) +--R + +--R 2 2 +--R (138%i cosh(x) + (- 90x - 138)cosh(x) + 16%i)sinh(x) +--R + +--R 3 2 +--R ((- 60%i x - 92%i)cosh(x) + 48cosh(x) + (- 60%i x - 92%i)cosh(x) + 8) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R 23%i cosh(x) + (- 30x - 46)cosh(x) + 16%i cosh(x) +--R + +--R (- 90x - 138)cosh(x) + 25%i +--R / +--R 3 2 +--R 60cosh(x)sinh(x) - 90%i cosh(x)sinh(x) +--R + +--R 3 3 +--R (60cosh(x) + 60cosh(x))sinh(x) - 30%i cosh(x) - 90%i cosh(x) +--R Type: Union(Expression Complex Integer,...) +--E 454 + +--S 455 of 526 +m0685:= a0685-r0685 +--R +--R +--R (453) +--R 4 2 4 +--R (- 69%i cosh(x) + 44%i cosh(x) - 12%i)sinh(x) +--R + +--R 5 4 2 3 +--R (- 92%i cosh(x) - 62cosh(x) + 26cosh(x) - 6)sinh(x) +--R + +--R 6 5 4 2 +--R (46%i cosh(x) - 138cosh(x) - 122%i cosh(x) + 92%i cosh(x) - 30%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 92%i cosh(x) + 62cosh(x) - 92%i cosh(x) - 88cosh(x) +--R + +--R 2 +--R 32cosh(x) - 6 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 23%i cosh(x) - 46cosh(x) - 14%i cosh(x) - 138cosh(x) - 45%i cosh(x) +--R + +--R 2 +--R 54%i cosh(x) - 18%i +--R / +--R 5 3 5 2 +--R 60cosh(x) sinh(x) - 90%i cosh(x) sinh(x) +--R + +--R 7 5 7 5 +--R (60cosh(x) + 60cosh(x) )sinh(x) - 30%i cosh(x) - 90%i cosh(x) +--R Type: Expression Complex Integer +--E 455 + +--S 456 of 526 +d0685:= D(m0685,x) +--R +--R +--R (454) +--R 4 2 8 +--R (138%i cosh(x) - 264%i cosh(x) + 120%i)sinh(x) +--R + +--R 4 2 7 +--R (331cosh(x) - 552cosh(x) + 240)sinh(x) +--R + +--R 6 4 2 6 +--R (368%i cosh(x) - 156%i cosh(x) - 438%i cosh(x) + 330%i)sinh(x) +--R + +--R 6 4 2 5 +--R (427cosh(x) + 657cosh(x) - 1476cosh(x) + 750)sinh(x) +--R + +--R 8 6 4 2 +--R - 460%i cosh(x) + 704%i cosh(x) - 976%i cosh(x) + 30%i cosh(x) +--R + +--R 300%i +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (- 735cosh(x) + 670cosh(x) + 329cosh(x) - 1356cosh(x) + 780)sinh(x) +--R + +--R 8 6 4 2 +--R 532%i cosh(x) + 218%i cosh(x) - 874%i cosh(x) + 258%i cosh(x) +--R + +--R 90%i +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 23cosh(x) + 337cosh(x) - 185cosh(x) + 33cosh(x) - 432cosh(x) +--R + +--R 270 +--R * +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 46%i cosh(x) - 80%i cosh(x) + 20%i cosh(x) + 214%i cosh(x) +--R + +--R 4 2 +--R - 162%i cosh(x) + 54%i cosh(x) +--R / +--R 6 6 6 5 +--R 120cosh(x) sinh(x) - 360%i cosh(x) sinh(x) +--R + +--R 8 6 4 +--R (240cosh(x) - 30cosh(x) )sinh(x) +--R + +--R 8 6 3 +--R (- 480%i cosh(x) - 720%i cosh(x) )sinh(x) +--R + +--R 10 8 6 2 +--R (120cosh(x) + 60cosh(x) - 420cosh(x) )sinh(x) +--R + +--R 10 8 6 +--R (- 120%i cosh(x) - 480%i cosh(x) - 360%i cosh(x) )sinh(x) +--R + +--R 10 8 6 +--R - 30cosh(x) - 180cosh(x) - 270cosh(x) +--R Type: Expression Complex Integer +--E 456 + +--S 457 of 526 +t0686:= coth(x)/(a+b*csch(x)) +--R +--R +--R coth(x) +--R (455) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 457 + +--S 458 of 526 +r0686:= log(b+a*sinh(x))/a +--R +--R +--R log(a sinh(x) + b) +--R (456) ------------------ +--R a +--R Type: Expression Integer +--E 458 + +--S 459 of 526 +a0686:= integrate(t0686,x) +--R +--R +--R - 2a sinh(x) - 2b +--R log(-----------------) - x +--R sinh(x) - cosh(x) +--R (457) -------------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 459 + +--S 460 of 526 +m0686:= a0686-r0686 +--R +--R +--R - 2a sinh(x) - 2b +--R - log(a sinh(x) + b) + log(-----------------) - x +--R sinh(x) - cosh(x) +--R (458) ------------------------------------------------- +--R a +--R Type: Expression Integer +--E 460 + +--S 461 of 526 +d0686:= D(m0686,x) +--R +--R +--R (459) 0 +--R Type: Expression Integer +--E 461 + +--S 462 of 526 +t0687:= coth(x)^2/(a+b*csch(x)) +--R +--R +--R 2 +--R coth(x) +--R (460) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 462 + +--S 463 of 526 +r0687:= x/a-acoth(cosh(x))/b+_ + 2*(a^2+b^2)^(1/2)*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a/b +--R +--R +--R x +--R +-------+ b tanh(-) - a +--R | 2 2 2 +--R - 2\|b + a atanh(-------------) - a acoth(cosh(x)) + b x +--R +-------+ +--R | 2 2 +--R \|b + a +--R (461) ---------------------------------------------------------- +--R a b +--R Type: Expression Integer +--E 463 + +--S 464 of 526 +a0687:= integrate(t0687,x) +--R +--R +--R (462) +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R - a log(sinh(x) + cosh(x) + 1) + a log(sinh(x) + cosh(x) - 1) + b x +--R / +--R a b +--R Type: Union(Expression Integer,...) +--E 464 + +--S 465 of 526 +m0687:= a0687-r0687 +--R +--R +--R (463) +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R - a log(sinh(x) + cosh(x) + 1) + a log(sinh(x) + cosh(x) - 1) +--R + +--R x +--R +-------+ b tanh(-) - a +--R | 2 2 2 +--R 2\|b + a atanh(-------------) + a acoth(cosh(x)) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R a b +--R Type: Expression Integer +--E 465 + +--S 466 of 526 +d0687:= D(m0687,x) +--R +--R +--R (464) +--R 5 +--R - a b sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((b + a )cosh(x) - 4a b cosh(x) - 3b - a )sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((4b + 4a )cosh(x) - 4a b cosh(x) + (- 10b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R (6b + 6a )cosh(x) + 2a b cosh(x) + (- 10b - 8a )cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 4 2 2 3 +--R (4b + 4a )cosh(x) + 5a b cosh(x) + (- 2b - 8a )cosh(x) +--R + +--R 2 2 2 +--R - 6a b cosh(x) + (- 2b + 4a )cosh(x) + a b +--R * +--R sinh(x) +--R + +--R 2 2 6 5 2 2 4 +--R (b + a )cosh(x) + 2a b cosh(x) + (b - 3a )cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - 4a b cosh(x) + (- b + 3a )cosh(x) + 2a b cosh(x) - b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 5 2 4 +--R 2a sinh(x) + (8a cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R ((4b + 12a )cosh(x) + 12a b cosh(x) - 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 2 +--R (12b + 8a )cosh(x) + 4a b cosh(x) + (- 12b - 8a )cosh(x) +--R + +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R (12b + 2a )cosh(x) - 12a b cosh(x) + (- 16b - 4a )cosh(x) +--R + +--R 2 2 +--R 12a b cosh(x) + 4b + 2a +--R * +--R sinh(x) +--R + +--R 2 5 4 2 3 2 2 +--R 4b cosh(x) - 8a b cosh(x) - 8b cosh(x) + 8a b cosh(x) + 4b cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 2 2 2 2 2 4 +--R a b sinh(x) + ((- b - a )cosh(x) + 4a b cosh(x) + 3b + a )sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 4b - 4a )cosh(x) + 4a b cosh(x) + (10b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R (- 6b - 6a )cosh(x) - 2a b cosh(x) + (10b + 8a )cosh(x) +--R + +--R 2 +--R 2a b cosh(x) - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 4 2 2 3 +--R (- 4b - 4a )cosh(x) - 5a b cosh(x) + (2b + 8a )cosh(x) +--R + +--R 2 2 2 +--R 6a b cosh(x) + (2b - 4a )cosh(x) - a b +--R * +--R sinh(x) +--R + +--R 2 2 6 5 2 2 4 +--R (- b - a )cosh(x) - 2a b cosh(x) + (- b + 3a )cosh(x) +--R + +--R 3 2 2 2 2 2 +--R 4a b cosh(x) + (b - 3a )cosh(x) - 2a b cosh(x) + b + a +--R / +--R 2 2 2 4 +--R (a b cosh(x) - a b )sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (4a b cosh(x) + 2b cosh(x) - 4a b cosh(x) - 2b )sinh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R (6a b cosh(x) + 6b cosh(x) - 8a b cosh(x) - 6b cosh(x) + 2a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 4a b cosh(x) + 6b cosh(x) - 8a b cosh(x) - 8b cosh(x) +--R + +--R 2 3 +--R 4a b cosh(x) + 2b +--R * +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R a b cosh(x) + 2b cosh(x) - 3a b cosh(x) - 4b cosh(x) +--R + +--R 2 2 3 2 +--R 3a b cosh(x) + 2b cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 4 +--R (- 2a b cosh(x) + 2a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R (- 8a b cosh(x) - 4a b cosh(x) + 8a b cosh(x) + 4a b )sinh(x) +--R + +--R 2 4 2 3 2 2 +--R - 12a b cosh(x) - 12a b cosh(x) + 16a b cosh(x) +--R + +--R 2 2 +--R 12a b cosh(x) - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R - 8a b cosh(x) - 12a b cosh(x) + 16a b cosh(x) +--R + +--R 2 2 2 2 +--R 16a b cosh(x) - 8a b cosh(x) - 4a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 2a b cosh(x) - 4a b cosh(x) + 6a b cosh(x) + 8a b cosh(x) +--R + +--R 2 2 2 2 +--R - 6a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 2 2 4 +--R (- a b cosh(x) + a b )sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (- 4a b cosh(x) - 2b cosh(x) + 4a b cosh(x) + 2b )sinh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R (- 6a b cosh(x) - 6b cosh(x) + 8a b cosh(x) + 6b cosh(x) - 2a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R - 4a b cosh(x) - 6b cosh(x) + 8a b cosh(x) + 8b cosh(x) +--R + +--R 2 3 +--R - 4a b cosh(x) - 2b +--R * +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R - a b cosh(x) - 2b cosh(x) + 3a b cosh(x) + 4b cosh(x) +--R + +--R 2 2 3 2 +--R - 3a b cosh(x) - 2b cosh(x) + a b +--R Type: Expression Integer +--E 466 + +--S 467 of 526 +t0688:= coth(x)^3/(a+b*csch(x)) +--R +--R +--R 3 +--R coth(x) +--R (465) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 467 + +--S 468 of 526 +r0688:= -csch(x)/b-a*log(sinh(x))/b^2+(a^2+b^2)*log(b+a*sinh(x))/b^2/a +--R +--R +--R 2 2 2 +--R (b + a )log(a sinh(x) + b) - a log(sinh(x)) - a b csch(x) +--R (466) ---------------------------------------------------------- +--R 2 +--R a b +--R Type: Expression Integer +--E 468 + +--S 469 of 526 +a0688:= integrate(t0688,x) +--R +--R +--R (467) +--R 2 2 2 2 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a ) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) +--R + +--R 2 2 +--R - b - a +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 +--R - b x sinh(x) + (- 2b x cosh(x) - 2a b)sinh(x) - b x cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) + b x +--R / +--R 2 2 2 2 2 2 +--R a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) - a b +--R Type: Union(Expression Integer,...) +--E 469 + +--S 470 of 526 +m0688:= a0688-r0688 +--R +--R +--R (468) +--R 2 2 2 2 2 +--R (- b - a )sinh(x) + (- 2b - 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- b - a )cosh(x) + b + a +--R * +--R log(a sinh(x) + b) +--R + +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a )log(sinh(x)) +--R + +--R 2 2 2 2 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a ) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) +--R + +--R 2 2 +--R - b - a +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (a b csch(x) - b x)sinh(x) +--R + +--R 2 +--R (2a b cosh(x)csch(x) - 2b x cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (a b cosh(x) - a b)csch(x) - b x cosh(x) - 2a b cosh(x) + b x +--R / +--R 2 2 2 2 2 2 +--R a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) - a b +--R Type: Expression Integer +--E 470 + +--S 471 of 526 +d0688:= D(m0688,x) +--R +--R +--R (469) +--R 4 3 +--R - coth(x)csch(x)sinh(x) + (- 4cosh(x)coth(x)csch(x) + 2)sinh(x) +--R + +--R 2 2 +--R ((- 6cosh(x) + 2)coth(x)csch(x) + 6cosh(x))sinh(x) +--R + +--R 3 2 +--R ((- 4cosh(x) + 4cosh(x))coth(x)csch(x) + 6cosh(x) + 2)sinh(x) +--R + +--R 4 2 3 +--R (- cosh(x) + 2cosh(x) - 1)coth(x)csch(x) + 2cosh(x) + 2cosh(x) +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) - 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) - 4b cosh(x))sinh(x) + b cosh(x) - 2b cosh(x) + b +--R Type: Expression Integer +--E 471 + +--S 472 of 526 +t0689:= coth(x)^4/(a+b*csch(x)) +--R +--R +--R 4 +--R coth(x) +--R (470) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 472 + +--S 473 of 526 +r0689:= x/a-a^2*acoth(cosh(x))/b^3-3/2*acoth(cosh(x))/b+_ + 2*(a^2+b^2)^(3/2)*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a/b^3+_ + a*coth(x)/b^2-1/2*coth(x)*csch(x)/b +--R +--R +--R (471) +--R x +--R +-------+ b tanh(-) - a +--R 2 2 | 2 2 2 +--R (- 4b - 4a )\|b + a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 2 3 +--R (- 3a b - 2a )acoth(cosh(x)) - a b coth(x)csch(x) + 2a b coth(x) + 2b x +--R / +--R 3 +--R 2a b +--R Type: Expression Integer +--E 473 + +--S 474 of 526 +a0689:= integrate(t0689,x) +--R +--R +--R (472) +--R 2 2 4 2 2 3 +--R (2b + 2a )sinh(x) + (8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 12a )cosh(x) - 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 8a )cosh(x) + (- 8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + 2a )cosh(x) + (- 4b - 4a )cosh(x) + 2b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 3 4 2 3 3 +--R (- 3a b - 2a )sinh(x) + (- 12a b - 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 18a b - 12a )cosh(x) + 6a b + 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 12a b - 8a )cosh(x) + (12a b + 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 3a b - 2a )cosh(x) + (6a b + 4a )cosh(x) - 3a b - 2a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 3 4 2 3 3 +--R (3a b + 2a )sinh(x) + (12a b + 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((18a b + 12a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((12a b + 8a )cosh(x) + (- 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (3a b + 2a )cosh(x) + (- 6a b - 4a )cosh(x) + 3a b + 2a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 4 3 2 3 +--R 2b x sinh(x) + (8b x cosh(x) - 2a b )sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (12b x cosh(x) - 6a b cosh(x) - 4b x + 4a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (8b x cosh(x) - 6a b cosh(x) + (- 8b x + 8a b)cosh(x) - 2a b )sinh(x) +--R + +--R 3 4 2 3 3 2 2 2 +--R 2b x cosh(x) - 2a b cosh(x) + (- 4b x + 4a b)cosh(x) - 2a b cosh(x) +--R + +--R 3 2 +--R 2b x - 4a b +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a b sinh(x) + 8a b cosh(x)sinh(x) + (12a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (8a b cosh(x) - 8a b cosh(x))sinh(x) + 2a b cosh(x) - 4a b cosh(x) +--R + +--R 3 +--R 2a b +--R Type: Union(Expression Integer,...) +--E 474 + +--S 475 of 526 +m0689:= a0689-r0689 +--R +--R +--R (473) +--R 2 2 4 2 2 3 +--R (2b + 2a )sinh(x) + (8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 12a )cosh(x) - 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 8a )cosh(x) + (- 8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + 2a )cosh(x) + (- 4b - 4a )cosh(x) + 2b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 3 4 2 3 3 +--R (- 3a b - 2a )sinh(x) + (- 12a b - 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 18a b - 12a )cosh(x) + 6a b + 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 12a b - 8a )cosh(x) + (12a b + 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 3a b - 2a )cosh(x) + (6a b + 4a )cosh(x) - 3a b - 2a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 3 4 2 3 3 +--R (3a b + 2a )sinh(x) + (12a b + 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((18a b + 12a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((12a b + 8a )cosh(x) + (- 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (3a b + 2a )cosh(x) + (- 6a b - 4a )cosh(x) + 3a b + 2a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 4 2 2 3 +--R (4b + 4a )sinh(x) + (16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b + 24a )cosh(x) - 8b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b + 16a )cosh(x) + (- 16b - 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b + 4a )cosh(x) + (- 8b - 8a )cosh(x) + 4b + 4a +--R * +--R x +--R +-------+ b tanh(-) - a +--R | 2 2 2 +--R \|b + a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 4 2 3 3 +--R (3a b + 2a )sinh(x) + (12a b + 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((18a b + 12a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((12a b + 8a )cosh(x) + (- 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (3a b + 2a )cosh(x) + (- 6a b - 4a )cosh(x) + 3a b + 2a +--R * +--R acoth(cosh(x)) +--R + +--R 2 2 4 +--R (a b coth(x)csch(x) - 2a b coth(x))sinh(x) +--R + +--R 2 2 2 3 +--R (4a b cosh(x)coth(x)csch(x) - 8a b cosh(x)coth(x) - 2a b )sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) - 2a b )coth(x)csch(x) +--R + +--R 2 2 2 2 2 +--R (- 12a b cosh(x) + 4a b)coth(x) - 6a b cosh(x) + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (4a b cosh(x) - 4a b cosh(x))coth(x)csch(x) +--R + +--R 2 3 2 2 2 +--R (- 8a b cosh(x) + 8a b cosh(x))coth(x) - 6a b cosh(x) +--R + +--R 2 2 +--R 8a b cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (a b cosh(x) - 2a b cosh(x) + a b )coth(x)csch(x) +--R + +--R 2 4 2 2 2 2 3 +--R (- 2a b cosh(x) + 4a b cosh(x) - 2a b)coth(x) - 2a b cosh(x) +--R + +--R 2 2 2 2 +--R 4a b cosh(x) - 2a b cosh(x) - 4a b +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a b sinh(x) + 8a b cosh(x)sinh(x) + (12a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (8a b cosh(x) - 8a b cosh(x))sinh(x) + 2a b cosh(x) - 4a b cosh(x) +--R + +--R 3 +--R 2a b +--R Type: Expression Integer +--E 475 + +--S 476 of 526 +--d0689:= D(m0689,x) +--E 476 + +--S 477 of 526 +t0690:= coth(x)/(%i+csch(x)) +--R +--R +--R coth(x) +--R (474) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 477 + +--S 478 of 526 +r0690:= -%i*log(1+%i*sinh(x)) +--R +--R +--R (475) - %i log(%i sinh(x) + 1) +--R Type: Expression Complex Integer +--E 478 + +--S 479 of 526 +a0690:= integrate(t0690,x) +--R +--R +--R (476) - 2%i log(sinh(x) + cosh(x) - %i) + %i x +--R Type: Union(Expression Complex Integer,...) +--E 479 + +--S 480 of 526 +m0690:= a0690-r0690 +--R +--R +--R (477) - 2%i log(sinh(x) + cosh(x) - %i) + %i log(%i sinh(x) + 1) + %i x +--R Type: Expression Complex Integer +--E 480 + +--S 481 of 526 +d0690:= D(m0690,x) +--R +--R +--R 2 2 +--R - %i sinh(x) + %i cosh(x) - %i +--R (478) -------------------------------------------------- +--R 2 +--R sinh(x) + (cosh(x) - 2%i)sinh(x) - %i cosh(x) - 1 +--R Type: Expression Complex Integer +--E 481 + +--S 482 of 526 +t0691:= coth(x)^2/(%i+csch(x)) +--R +--R +--R 2 +--R coth(x) +--R (479) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 482 + +--S 483 of 526 +r0691:= -%i*x-acoth(cosh(x)) +--R +--R +--R (480) - acoth(cosh(x)) - %i x +--R Type: Expression Complex Integer +--E 483 + +--S 484 of 526 +a0691:= integrate(t0691,x) +--R +--R +--R (481) - log(sinh(x) + cosh(x) + 1) + log(sinh(x) + cosh(x) - 1) - %i x +--R Type: Union(Expression Complex Integer,...) +--E 484 + +--S 485 of 526 +m0691:= a0691-r0691 +--R +--R +--R (482) +--R - log(sinh(x) + cosh(x) + 1) + log(sinh(x) + cosh(x) - 1) + acoth(cosh(x)) +--R Type: Expression Complex Integer +--E 485 + +--S 486 of 526 +d0691:= D(m0691,x) +--R +--R +--R (483) +--R 3 2 2 3 +--R - sinh(x) - 2cosh(x)sinh(x) + (cosh(x) - 1)sinh(x) + 2cosh(x) +--R + +--R - 2cosh(x) +--R / +--R 2 2 3 4 +--R (cosh(x) - 1)sinh(x) + (2cosh(x) - 2cosh(x))sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x) + 1 +--R Type: Expression Complex Integer +--E 486 + +--S 487 of 526 +t0692:= coth(x)^3/(%i+csch(x)) +--R +--R +--R 3 +--R coth(x) +--R (484) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 487 + +--S 488 of 526 +r0692:= -csch(x)-%i*log(sinh(x)) +--R +--R +--R (485) - %i log(sinh(x)) - csch(x) +--R Type: Expression Complex Integer +--E 488 + +--S 489 of 526 +a0692:= integrate(t0692,x) +--R +--R +--R (486) +--R 2 2 +--R (- %i sinh(x) - 2%i cosh(x)sinh(x) - %i cosh(x) + %i) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R %i x sinh(x) + (2%i x cosh(x) - 2)sinh(x) + %i x cosh(x) - 2cosh(x) +--R + +--R - %i x +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Union(Expression Complex Integer,...) +--E 489 + +--S 490 of 526 +m0692:= a0692-r0692 +--R +--R +--R (487) +--R 2 2 +--R (%i sinh(x) + 2%i cosh(x)sinh(x) + %i cosh(x) - %i)log(sinh(x)) +--R + +--R 2 2 +--R (- %i sinh(x) - 2%i cosh(x)sinh(x) - %i cosh(x) + %i) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (csch(x) + %i x)sinh(x) + (2cosh(x)csch(x) + 2%i x cosh(x) - 2)sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 1)csch(x) + %i x cosh(x) - 2cosh(x) - %i x +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Expression Complex Integer +--E 490 + +--S 491 of 526 +d0692:= D(m0692,x) +--R +--R +--R (488) +--R 4 3 +--R - coth(x)csch(x)sinh(x) + (- 4cosh(x)coth(x)csch(x) + 2)sinh(x) +--R + +--R 2 2 +--R ((- 6cosh(x) + 2)coth(x)csch(x) + 6cosh(x))sinh(x) +--R + +--R 3 2 +--R ((- 4cosh(x) + 4cosh(x))coth(x)csch(x) + 6cosh(x) + 2)sinh(x) +--R + +--R 4 2 3 +--R (- cosh(x) + 2cosh(x) - 1)coth(x)csch(x) + 2cosh(x) + 2cosh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Expression Complex Integer +--E 491 + +--S 492 of 526 +t0693:= coth(x)^4/(%i+csch(x)) +--R +--R +--R 4 +--R coth(x) +--R (489) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 492 + +--S 493 of 526 +r0693:= -%i*x-1/2*acoth(cosh(x))+%i*coth(x)-1/2*coth(x)*csch(x) +--R +--R +--R - acoth(cosh(x)) - coth(x)csch(x) + 2%i coth(x) - 2%i x +--R (490) ------------------------------------------------------- +--R 2 +--R Type: Expression Complex Integer +--E 493 + +--S 494 of 526 +a0693:= integrate(t0693,x) +--R +--R +--R (491) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) - cosh(x) + 2cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 3 +--R - 2%i x sinh(x) + (- 8%i x cosh(x) - 2)sinh(x) +--R + +--R 2 2 +--R (- 12%i x cosh(x) - 6cosh(x) + 4%i x + 4%i)sinh(x) +--R + +--R 3 2 +--R (- 8%i x cosh(x) - 6cosh(x) + (8%i x + 8%i)cosh(x) - 2)sinh(x) +--R + +--R 4 3 2 +--R - 2%i x cosh(x) - 2cosh(x) + (4%i x + 4%i)cosh(x) - 2cosh(x) - 2%i x +--R + +--R - 4%i +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Union(Expression Complex Integer,...) +--E 494 + +--S 495 of 526 +m0693:= a0693-r0693 +--R +--R +--R (492) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) - cosh(x) + 2cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R acoth(cosh(x)) +--R + +--R 4 +--R (coth(x)csch(x) - 2%i coth(x))sinh(x) +--R + +--R 3 +--R (4cosh(x)coth(x)csch(x) - 8%i cosh(x)coth(x) - 2)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) - 2)coth(x)csch(x) + (- 12%i cosh(x) + 4%i)coth(x) +--R + +--R - 6cosh(x) + 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 3 +--R (4cosh(x) - 4cosh(x))coth(x)csch(x) +--R + +--R 3 2 +--R (- 8%i cosh(x) + 8%i cosh(x))coth(x) - 6cosh(x) + 8%i cosh(x) - 2 +--R * +--R sinh(x) +--R + +--R 4 2 +--R (cosh(x) - 2cosh(x) + 1)coth(x)csch(x) +--R + +--R 4 2 3 2 +--R (- 2%i cosh(x) + 4%i cosh(x) - 2%i)coth(x) - 2cosh(x) + 4%i cosh(x) +--R + +--R - 2cosh(x) - 4%i +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Expression Complex Integer +--E 495 + +--S 496 of 526 +d0693:= D(m0693,x) +--R +--R +--R (493) +--R 7 +--R - sinh(x) +--R + +--R 2 2 2 +--R ((- 2cosh(x) + 2)coth(x) + cosh(x) - 1)csch(x) +--R + +--R 2 2 2 +--R (2%i cosh(x) - 2%i)coth(x) - 2%i cosh(x) - 6cosh(x) + 2%i +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 3 +--R ((- 12cosh(x) + 12cosh(x))coth(x) + 6cosh(x) - 6cosh(x))csch(x) +--R + +--R 3 2 3 2 +--R (12%i cosh(x) - 12%i cosh(x))coth(x) - 12%i cosh(x) - 11cosh(x) +--R + +--R 12%i cosh(x) - 1 +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 2 4 2 +--R (- 30cosh(x) + 36cosh(x) - 6)coth(x) + 15cosh(x) - 18cosh(x) +--R + +--R 3 +--R * +--R csch(x) +--R + +--R 4 2 2 4 +--R (30%i cosh(x) - 36%i cosh(x) + 6%i)coth(x) - 30%i cosh(x) +--R + +--R 2 +--R 28%i cosh(x) - 8cosh(x) + 2%i +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 40cosh(x) + 64cosh(x) - 24cosh(x))coth(x) + 20cosh(x) +--R + +--R 3 +--R - 32cosh(x) + 12cosh(x) +--R * +--R csch(x) +--R + +--R 5 3 2 +--R (40%i cosh(x) - 64%i cosh(x) + 24%i cosh(x))coth(x) +--R + +--R 5 4 3 2 +--R - 40%i cosh(x) + 25cosh(x) + 32%i cosh(x) - 14cosh(x) +--R + +--R 8%i cosh(x) - 11 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (- 30cosh(x) + 66cosh(x) - 42cosh(x) + 6)coth(x) + 15cosh(x) +--R + +--R 4 2 +--R - 33cosh(x) + 21cosh(x) - 3 +--R * +--R csch(x) +--R + +--R 6 4 2 2 +--R (30%i cosh(x) - 66%i cosh(x) + 42%i cosh(x) - 6%i)coth(x) +--R + +--R 6 5 4 3 +--R - 30%i cosh(x) + 34cosh(x) + 18%i cosh(x) - 4cosh(x) +--R + +--R 2 +--R 14%i cosh(x) - 30cosh(x) - 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (- 12cosh(x) + 36cosh(x) - 36cosh(x) + 12cosh(x))coth(x) +--R + +--R 7 5 3 +--R 6cosh(x) - 18cosh(x) + 18cosh(x) - 6cosh(x) +--R * +--R csch(x) +--R + +--R 7 5 3 +--R (12%i cosh(x) - 36%i cosh(x) + 36%i cosh(x) - 12%i cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 +--R - 12%i cosh(x) + 19cosh(x) + 4%i cosh(x) + 7cosh(x) +--R + +--R 3 2 +--R 12%i cosh(x) - 23cosh(x) - 4%i cosh(x) - 3 +--R * +--R sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 2cosh(x) + 8cosh(x) - 12cosh(x) + 8cosh(x) - 2)coth(x) +--R + +--R 8 6 4 2 +--R cosh(x) - 4cosh(x) + 6cosh(x) - 4cosh(x) + 1 +--R * +--R csch(x) +--R + +--R 8 6 4 2 +--R (2%i cosh(x) - 8%i cosh(x) + 12%i cosh(x) - 8%i cosh(x) + 2%i) +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 5 4 3 +--R - 2%i cosh(x) + 4cosh(x) + 4cosh(x) + 4%i cosh(x) - 4cosh(x) +--R + +--R - 4cosh(x) - 2%i +--R / +--R 2 6 3 5 +--R (2cosh(x) - 2)sinh(x) + (12cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (30cosh(x) - 36cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (40cosh(x) - 64cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (30cosh(x) - 66cosh(x) + 42cosh(x) - 6)sinh(x) +--R + +--R 7 5 3 8 +--R (12cosh(x) - 36cosh(x) + 36cosh(x) - 12cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) + 12cosh(x) - 8cosh(x) + 2 +--R Type: Expression Complex Integer +--E 496 + +--S 497 of 526 +t0694:= sech(x)/(a+b*csch(x)) +--R +--R +--R sech(x) +--R (494) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 497 + +--S 498 of 526 +r0694:= 1/2*(2*a*atan(sinh(x))+b*log(cosh(x)^2)-2*b*log(b+a*sinh(x)))/(a^2+b^2) +--R +--R +--R 2 +--R - 2b log(a sinh(x) + b) + b log(cosh(x) ) + 2a atan(sinh(x)) +--R (495) ------------------------------------------------------------ +--R 2 2 +--R 2b + 2a +--R Type: Expression Integer +--E 498 + +--S 499 of 526 +a0694:= integrate(t0694,x) +--R +--R +--R (496) +--R 2cosh(x) - 2a sinh(x) - 2b +--R b log(- -----------------) - b log(-----------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R + +--R 2a atan(sinh(x) + cosh(x)) +--R / +--R 2 2 +--R b + a +--R Type: Union(Expression Integer,...) +--E 499 + +--S 500 of 526 +m0694:= a0694-r0694 +--R +--R +--R (497) +--R 2 2cosh(x) +--R 2b log(a sinh(x) + b) - b log(cosh(x) ) + 2b log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2a sinh(x) - 2b +--R - 2b log(-----------------) + 4a atan(sinh(x) + cosh(x)) - 2a atan(sinh(x)) +--R sinh(x) - cosh(x) +--R / +--R 2 2 +--R 2b + 2a +--R Type: Expression Integer +--E 500 + +--S 501 of 526 +d0694:= D(m0694,x) +--R +--R +--R (498) +--R 3 2 2 +--R 2a sinh(x) + a cosh(x)sinh(x) + (- 2a cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R - a cosh(x) + a cosh(x) +--R / +--R 2 2 4 2 2 3 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((b + a )cosh(x) + 2b + 2a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b + a )cosh(x) + b + a +--R Type: Expression Integer +--E 501 + +--S 502 of 526 +t0695:= sech(x)^2/(a+b*csch(x)) +--R +--R +--R 2 +--R sech(x) +--R (499) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 502 + +--S 503 of 526 +r0695:= 2*a*b*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ + b*sech(x)/(a^2+b^2)+a*tanh(x)/(a^2+b^2) +--R +--R +--R x +--R b tanh(-) - a +-------+ +--R 2 | 2 2 +--R - 2a b atanh(-------------) + (a tanh(x) - b sech(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (500) --------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 503 + +--S 504 of 526 +a0695:= integrate(t0695,x) +--R +--R +--R (501) +--R 2 2 +--R (a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) + a b) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R +-------+ +--R | 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|b + a +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) + b +--R + +--R 2 +--R a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression Integer,...) +--E 504 + +--S 505 of 526 +m0695:= a0695-r0695 +--R +--R +--R (502) +--R 2 2 +--R (a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) + a b) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 2 +--R (2a b sinh(x) + 4a b cosh(x)sinh(x) + 2a b cosh(x) + 2a b) +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a)tanh(x) +--R + +--R 2 +--R b sech(x)sinh(x) + (2b cosh(x)sech(x) - 2b)sinh(x) +--R + +--R 2 +--R (b cosh(x) + b)sech(x) - 2b cosh(x) - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) + b +--R + +--R 2 +--R a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression Integer +--E 505 + +--S 506 of 526 +d0695:= D(m0695,x) +--R +--R +--R (503) +--R 2 6 2 2 5 +--R a b sinh(x) + (6a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 2 2 4 +--R (15a b cosh(x) + 10a b cosh(x) + a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R (20a b cosh(x) + 20a b cosh(x) + 4a b cosh(x) + 4a b )sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 15a b cosh(x) + 20a b cosh(x) + 6a b cosh(x) +--R + +--R 2 2 +--R 12a b cosh(x) - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 6a b cosh(x) + 10a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 2 +--R 12a b cosh(x) - 2a b cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 2 +--R - a b cosh(x) + 2a b cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 2 5 +--R - 2a sinh(x) + (- 12a cosh(x) - 4a b)sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 30a cosh(x) - 20a b cosh(x) - 2a )sinh(x) +--R + +--R 3 3 2 2 3 2 3 +--R (- 40a cosh(x) - 40a b cosh(x) - 8a cosh(x) - 8a b)sinh(x) +--R + +--R 3 4 2 3 3 2 +--R - 30a cosh(x) - 40a b cosh(x) - 12a cosh(x) +--R + +--R 2 3 +--R - 24a b cosh(x) + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 3 3 +--R - 12a cosh(x) - 20a b cosh(x) - 8a cosh(x) +--R + +--R 2 2 3 2 +--R - 24a b cosh(x) + 4a cosh(x) - 4a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 4 2 3 +--R - 2a cosh(x) - 4a b cosh(x) - 2a cosh(x) - 8a b cosh(x) +--R + +--R 3 2 2 3 +--R 2a cosh(x) - 4a b cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R - a b sinh(x) + (- 6a b cosh(x) - 2a b )sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 15a b cosh(x) - 10a b cosh(x) - a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R (- 20a b cosh(x) - 20a b cosh(x) - 4a b cosh(x) - 4a b )sinh(x) +--R + +--R 2 4 2 3 2 2 2 +--R - 15a b cosh(x) - 20a b cosh(x) - 6a b cosh(x) - 12a b cosh(x) +--R + +--R 2 +--R a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 6a b cosh(x) - 10a b cosh(x) - 4a b cosh(x) - 12a b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - a b cosh(x) - 2a b cosh(x) - a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 2 +--R a b cosh(x) - 2a b cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 2 3 5 +--R - a b sech(x)sinh(x) + (- 6a b cosh(x) - 2b )sech(x)sinh(x) +--R + +--R 2 2 3 2 4 +--R (- 15a b cosh(x) - 10b cosh(x) - a b )sech(x)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (- 20a b cosh(x) - 20b cosh(x) - 4a b cosh(x) - 4b )sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R - 15a b cosh(x) - 20b cosh(x) - 6a b cosh(x) - 12b cosh(x) +--R + +--R 2 +--R a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R - 6a b cosh(x) - 10b cosh(x) - 4a b cosh(x) - 12b cosh(x) +--R + +--R 2 3 +--R 2a b cosh(x) - 2b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R - a b cosh(x) - 2b cosh(x) - a b cosh(x) - 4b cosh(x) +--R + +--R 2 2 3 2 +--R a b cosh(x) - 2b cosh(x) + a b +--R * +--R sech(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R 2a b sech(x)sinh(x) + (12a b cosh(x) + 4a b )sech(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (30a b cosh(x) + 20a b cosh(x) + 2a b)sech(x)sinh(x) +--R + +--R 2 3 2 2 2 2 +--R (40a b cosh(x) + 40a b cosh(x) + 8a b cosh(x) + 8a b )sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 30a b cosh(x) + 40a b cosh(x) + 12a b cosh(x) +--R + +--R 2 2 +--R 24a b cosh(x) - 2a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 12a b cosh(x) + 20a b cosh(x) + 8a b cosh(x) +--R + +--R 2 2 2 2 +--R 24a b cosh(x) - 4a b cosh(x) + 4a b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R 2a b cosh(x) + 4a b cosh(x) + 2a b cosh(x) + 8a b cosh(x) +--R + +--R 2 2 2 2 +--R - 2a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R sech(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 3 5 +--R a b sech(x)sinh(x) + (6a b cosh(x) + 2b )sech(x)sinh(x) +--R + +--R 2 2 3 2 4 +--R (15a b cosh(x) + 10b cosh(x) + a b )sech(x)sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (20a b cosh(x) + 20b cosh(x) + 4a b cosh(x) + 4b )sech(x)sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R 15a b cosh(x) + 20b cosh(x) + 6a b cosh(x) + 12b cosh(x) +--R + +--R 2 +--R - a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 6a b cosh(x) + 10b cosh(x) + 4a b cosh(x) + 12b cosh(x) +--R + +--R 2 3 +--R - 2a b cosh(x) + 2b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R a b cosh(x) + 2b cosh(x) + a b cosh(x) + 4b cosh(x) +--R + +--R 2 2 3 2 +--R - a b cosh(x) + 2b cosh(x) - a b +--R * +--R sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 4 3 2 3 +--R (4b + 4a b)sinh(x) + (16b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 +--R ((24b + 24a b)cosh(x) - 4b - 4a b)sinh(x) +--R + +--R 3 2 3 3 2 +--R ((16b + 16a b)cosh(x) + (- 8b - 8a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 +--R (4b + 4a b)cosh(x) + (- 4b - 4a b)cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 2 5 +--R 2a sinh(x) + (12a cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (30a cosh(x) + 20a b cosh(x) - 8a b - 6a )sinh(x) +--R + +--R 3 3 2 2 2 3 2 +--R (40a cosh(x) + 40a b cosh(x) + (- 32a b - 24a )cosh(x) + 8a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 30a cosh(x) + 40a b cosh(x) + (- 48a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R 24a b cosh(x) + 8a b + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 12a cosh(x) + 20a b cosh(x) + (- 32a b - 24a )cosh(x) +--R + +--R 2 2 2 3 2 +--R 24a b cosh(x) + (16a b + 12a )cosh(x) + 4a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 2 3 +--R 2a cosh(x) + 4a b cosh(x) + (- 8a b - 6a )cosh(x) + 8a b cosh(x) +--R + +--R 2 3 2 2 3 +--R (8a b + 6a )cosh(x) + 4a b cosh(x) - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 4 3 2 3 +--R (- 4b - 4a b)sinh(x) + (- 16b - 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 +--R ((- 24b - 24a b)cosh(x) + 4b + 4a b)sinh(x) +--R + +--R 3 2 3 3 2 +--R ((- 16b - 16a b)cosh(x) + (8b + 8a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 +--R (- 4b - 4a b)cosh(x) + (4b + 4a b)cosh(x) +--R / +--R 3 3 6 3 3 4 2 2 5 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2b + 2a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R ((15a b + 15a b)cosh(x) + (10b + 10a b )cosh(x) + a b + a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (20a b + 20a b)cosh(x) + (20b + 20a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (4a b + 4a b)cosh(x) + 4b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 4 2 2 3 +--R (15a b + 15a b)cosh(x) + (20b + 20a b )cosh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (6a b + 6a b)cosh(x) + (12b + 12a b )cosh(x) - a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 4 2 2 4 +--R (6a b + 6a b)cosh(x) + (10b + 10a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (4a b + 4a b)cosh(x) + (12b + 12a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (- 2a b - 2a b)cosh(x) + 2b + 2a b +--R * +--R sinh(x) +--R + +--R 3 3 6 4 2 2 5 3 3 4 +--R (a b + a b)cosh(x) + (2b + 2a b )cosh(x) + (a b + a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 4 2 2 +--R (4b + 4a b )cosh(x) + (- a b - a b)cosh(x) + (2b + 2a b )cosh(x) +--R + +--R 3 3 +--R - a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 6 +--R (- 2a b - 2a )sinh(x) +--R + +--R 2 2 4 3 3 5 +--R ((- 12a b - 12a )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 2 2 4 2 3 3 2 2 +--R (- 30a b - 30a )cosh(x) + (- 20a b - 20a b)cosh(x) - 2a b +--R + +--R 4 +--R - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 4 3 3 3 2 +--R (- 40a b - 40a )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (- 8a b - 8a )cosh(x) - 8a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 4 3 3 3 +--R (- 30a b - 30a )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 2 2 4 2 3 3 2 2 4 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 24a b)cosh(x) + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 5 3 3 4 +--R (- 12a b - 12a )cosh(x) + (- 20a b - 20a b)cosh(x) +--R + +--R 2 2 4 3 3 3 2 +--R (- 8a b - 8a )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (4a b + 4a )cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 2 4 6 3 3 5 +--R (- 2a b - 2a )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 2 4 4 3 3 3 +--R (- 2a b - 2a )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 2 2 4 2 3 3 2 2 4 +--R (2a b + 2a )cosh(x) + (- 4a b - 4a b)cosh(x) + 2a b + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 6 3 3 4 2 2 5 +--R (- a b - a b)sinh(x) + ((- 6a b - 6a b)cosh(x) - 2b - 2a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R ((- 15a b - 15a b)cosh(x) + (- 10b - 10a b )cosh(x) - a b - a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (- 20a b - 20a b)cosh(x) + (- 20b - 20a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (- 4a b - 4a b)cosh(x) - 4b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 4 2 2 3 +--R (- 15a b - 15a b)cosh(x) + (- 20b - 20a b )cosh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (- 6a b - 6a b)cosh(x) + (- 12b - 12a b )cosh(x) + a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 4 2 2 4 +--R (- 6a b - 6a b)cosh(x) + (- 10b - 10a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (- 4a b - 4a b)cosh(x) + (- 12b - 12a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (2a b + 2a b)cosh(x) - 2b - 2a b +--R * +--R sinh(x) +--R + +--R 3 3 6 4 2 2 5 3 3 4 +--R (- a b - a b)cosh(x) + (- 2b - 2a b )cosh(x) + (- a b - a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 4 2 2 +--R (- 4b - 4a b )cosh(x) + (a b + a b)cosh(x) + (- 2b - 2a b )cosh(x) +--R + +--R 3 3 +--R a b + a b +--R Type: Expression Integer +--E 506 + +--S 507 of 526 +t0696:= sech(x)^3/(a+b*csch(x)) +--R +--R +--R 3 +--R sech(x) +--R (504) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 507 + +--S 508 of 526 +r0696:= 1/2*(-a*b^2*atan(sinh(x))*cosh(x)^2+a^3*atan(sinh(x))*cosh(x)^2+_ + a^2*b*log(cosh(x)^2)*cosh(x)^2-2*a^2*b*log(b+a*sinh(x))*cosh(x)^2-_ + a^2*b-b^3+a^3*sinh(x)+b^2*a*sinh(x))/cosh(x)^2/(a^2+b^2)^2 +--R +--R +--R (505) +--R 2 2 2 2 2 +--R - 2a b cosh(x) log(a sinh(x) + b) + a b cosh(x) log(cosh(x) ) +--R + +--R 2 3 2 2 3 3 2 +--R (- a b + a )cosh(x) atan(sinh(x)) + (a b + a )sinh(x) - b - a b +--R / +--R 4 2 2 4 2 +--R (2b + 4a b + 2a )cosh(x) +--R Type: Expression Integer +--E 508 + +--S 509 of 526 +a0696:= integrate(t0696,x) +--R +--R +--R (506) +--R 2 4 2 3 2 2 2 2 +--R a b sinh(x) + 4a b cosh(x)sinh(x) + (6a b cosh(x) + 2a b)sinh(x) +--R + +--R 2 3 2 2 4 2 2 +--R (4a b cosh(x) + 4a b cosh(x))sinh(x) + a b cosh(x) + 2a b cosh(x) +--R + +--R 2 +--R a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 4 2 3 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 6a b cosh(x) - 2a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (- 4a b cosh(x) - 4a b cosh(x))sinh(x) - a b cosh(x) +--R + +--R 2 2 2 +--R - 2a b cosh(x) - a b +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 4 2 3 3 +--R (- a b + a )sinh(x) + (- 4a b + 4a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 6a b + 6a )cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 4a b + 4a )cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- a b + a )cosh(x) + (- 2a b + 2a )cosh(x) - a b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 3 2 3 3 2 2 +--R (a b + a )sinh(x) + ((3a b + 3a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 3 2 3 2 2 3 +--R ((3a b + 3a )cosh(x) + (- 4b - 4a b)cosh(x) - a b - a )sinh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (a b + a )cosh(x) + (- 2b - 2a b)cosh(x) + (- a b - a )cosh(x) +--R / +--R 4 2 2 4 4 4 2 2 4 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 2 +--R ((6b + 12a b + 6a )cosh(x) + 2b + 4a b + 2a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((4b + 8a b + 4a )cosh(x) + (4b + 8a b + 4a )cosh(x))sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 4 2 2 4 +--R (b + 2a b + a )cosh(x) + (2b + 4a b + 2a )cosh(x) + b + 2a b + a +--R Type: Union(Expression Integer,...) +--E 509 + +--S 510 of 526 +m0696:= a0696-r0696 +--R +--R +--R (507) +--R 2 2 4 2 3 3 +--R 2a b cosh(x) sinh(x) + 8a b cosh(x) sinh(x) +--R + +--R 2 4 2 2 2 +--R (12a b cosh(x) + 4a b cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 6 +--R (8a b cosh(x) + 8a b cosh(x) )sinh(x) + 2a b cosh(x) +--R + +--R 2 4 2 2 +--R 4a b cosh(x) + 2a b cosh(x) +--R * +--R log(a sinh(x) + b) +--R + +--R 2 2 4 2 3 3 +--R - a b cosh(x) sinh(x) - 4a b cosh(x) sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 6a b cosh(x) - 2a b cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 6 +--R (- 4a b cosh(x) - 4a b cosh(x) )sinh(x) - a b cosh(x) +--R + +--R 2 4 2 2 +--R - 2a b cosh(x) - a b cosh(x) +--R * +--R 2 +--R log(cosh(x) ) +--R + +--R 2 2 4 2 3 3 +--R 2a b cosh(x) sinh(x) + 8a b cosh(x) sinh(x) +--R + +--R 2 4 2 2 2 +--R (12a b cosh(x) + 4a b cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 6 +--R (8a b cosh(x) + 8a b cosh(x) )sinh(x) + 2a b cosh(x) +--R + +--R 2 4 2 2 +--R 4a b cosh(x) + 2a b cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 3 3 +--R - 2a b cosh(x) sinh(x) - 8a b cosh(x) sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 12a b cosh(x) - 4a b cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 6 +--R (- 8a b cosh(x) - 8a b cosh(x) )sinh(x) - 2a b cosh(x) +--R + +--R 2 4 2 2 +--R - 4a b cosh(x) - 2a b cosh(x) +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 4 2 3 3 3 +--R (- 2a b + 2a )cosh(x) sinh(x) + (- 8a b + 8a )cosh(x) sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R ((- 12a b + 12a )cosh(x) + (- 4a b + 4a )cosh(x) )sinh(x) +--R + +--R 2 3 5 2 3 3 +--R ((- 8a b + 8a )cosh(x) + (- 8a b + 8a )cosh(x) )sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b + 2a )cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 2 3 2 +--R (- 2a b + 2a )cosh(x) +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 4 2 3 3 3 +--R (a b - a )cosh(x) sinh(x) + (4a b - 4a )cosh(x) sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R ((6a b - 6a )cosh(x) + (2a b - 2a )cosh(x) )sinh(x) +--R + +--R 2 3 5 2 3 3 +--R ((4a b - 4a )cosh(x) + (4a b - 4a )cosh(x) )sinh(x) +--R + +--R 2 3 6 2 3 4 2 3 2 +--R (a b - a )cosh(x) + (2a b - 2a )cosh(x) + (a b - a )cosh(x) +--R * +--R atan(sinh(x)) +--R + +--R 2 3 5 2 3 3 2 4 +--R (- a b - a )sinh(x) + ((- 4a b - 4a )cosh(x) + b + a b)sinh(x) +--R + +--R 2 3 2 3 2 2 3 3 +--R ((- 4a b - 4a )cosh(x) + (4b + 4a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (2a b + 2a )cosh(x) + (2b + 2a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 +--R 2b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 +--R (5a b + 5a )cosh(x) + (- 4b - 4a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 4a b - 4a )cosh(x) + (4b + 4a b)cosh(x) - a b - a +--R * +--R sinh(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R (2a b + 2a )cosh(x) + (- 3b - 3a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (2b + 2a b)cosh(x) + b + a b +--R / +--R 4 2 2 4 2 4 +--R (2b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 3 3 +--R (8b + 16a b + 8a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 2 +--R ((12b + 24a b + 12a )cosh(x) + (4b + 8a b + 4a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R ((8b + 16a b + 8a )cosh(x) + (8b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (2b + 4a b + 2a )cosh(x) + (4b + 8a b + 4a )cosh(x) +--R + +--R 4 2 2 4 2 +--R (2b + 4a b + 2a )cosh(x) +--R Type: Expression Integer +--E 510 + +--S 511 of 526 +d0696:= D(m0696,x) +--R +--R +--R (508) +--R 2 3 10 2 3 3 2 9 +--R (2a b + 2a )sinh(x) + ((12a b + 12a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 3 2 3 2 2 3 8 +--R ((29a b + 29a )cosh(x) + (- 12b - 12a b)cosh(x) + 8a b + 8a )sinh(x) +--R + +--R 2 3 3 3 2 2 +--R (30a b + 34a )cosh(x) + (- 30b - 30a b)cosh(x) +--R + +--R 2 3 3 2 +--R (36a b + 36a )cosh(x) - 8b - 8a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 +--R (- 4a b + 14a )cosh(x) + (- 32b - 32a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (62a b + 62a )cosh(x) + (- 36b - 36a b)cosh(x) + 12a b + 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 5 3 2 4 +--R (- 42a b - 14a )cosh(x) + (2b + 2a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (50a b + 62a )cosh(x) + (- 66b - 66a b)cosh(x) +--R + +--R 2 3 3 2 +--R (36a b + 36a )cosh(x) - 12b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 6 3 2 5 +--R (- 38a b - 28a )cosh(x) + (36b + 36a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (10a b + 48a )cosh(x) + (- 64b - 64a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (36a b + 36a )cosh(x) + (- 36b - 36a b)cosh(x) + 8a b + 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 7 3 2 6 +--R (- 6a b - 26a )cosh(x) + (30b + 30a b)cosh(x) +--R + +--R 2 3 5 3 2 4 +--R (- 24a b + 16a )cosh(x) + (- 20b - 20a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (10a b + 22a )cosh(x) + (- 42b - 42a b)cosh(x) +--R + +--R 2 3 3 2 +--R (12a b + 12a )cosh(x) - 8b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 8 3 2 7 +--R (10a b - 16a )cosh(x) + (8b + 8a b)cosh(x) +--R + +--R 2 3 6 3 2 5 +--R (- 30a b - 18a )cosh(x) + (28b + 28a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (8a b + 30a )cosh(x) + (- 32b - 32a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (2a b + 2a )cosh(x) + (- 12b - 12a b)cosh(x) + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 9 2 3 7 +--R (6a b - 6a )cosh(x) + (- 14a b - 18a )cosh(x) +--R + +--R 3 2 6 2 3 5 +--R (30b + 30a b)cosh(x) + (18a b + 30a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 22b - 22a b)cosh(x) + (- 10a b - 6a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 6b - 6a b)cosh(x) - 2b - 2a b +--R * +--R sinh(x) +--R + +--R 2 3 10 2 3 8 3 2 7 +--R (a b - a )cosh(x) + (- 2a b - 4a )cosh(x) + (8b + 8a b)cosh(x) +--R + +--R 2 3 6 3 2 5 2 3 4 +--R (8a b + 10a )cosh(x) + (- 8b - 8a b)cosh(x) + (- 6a b - 4a )cosh(x) +--R + +--R 2 3 2 +--R (- a b - a )cosh(x) +--R / +--R 4 2 2 4 3 8 +--R (2b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 4 7 +--R (12b + 24a b + 12a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 6 +--R ((30b + 60a b + 30a )cosh(x) + (8b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 5 +--R ((40b + 80a b + 40a )cosh(x) + (36b + 72a b + 36a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 7 4 2 2 4 5 +--R (30b + 60a b + 30a )cosh(x) + (66b + 132a b + 66a )cosh(x) +--R + +--R 4 2 2 4 3 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (64b + 128a b + 64a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (36b + 72a b + 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (42b + 84a b + 42a )cosh(x) + (8b + 16a b + 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (24b + 48a b + 24a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (6b + 12a b + 6a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (6b + 12a b + 6a )cosh(x) + (2b + 4a b + 2a )cosh(x) +--R Type: Expression Integer +--E 511 + +--S 512 of 526 +t0697:= sech(x)^4/(a+b*csch(x)) +--R +--R +--R 4 +--R sech(x) +--R (509) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 512 + +--S 513 of 526 +r0697:= 2*a^3*b*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-_ + a^2*b*sech(x)/(a^2+b^2)^2-b*sech(x)^3/(3*a^2+3*b^2)-_ + a*b^2*tanh(x)/(a^2+b^2)^2+a*tanh(x)/(a^2+b^2)-a*tanh(x)^3/(3*a^2+3*b^2) +--R +--R +--R (510) +--R x +--R b tanh(-) - a +--R 3 2 +--R - 6a b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 3 3 3 2 3 +--R (- a b - a )tanh(x) + 3a tanh(x) + (- b - a b)sech(x) +--R + +--R 2 +--R - 3a b sech(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression Integer +--E 513 + +--S 514 of 526 +a0697:= integrate(t0697,x) +--R +--R +--R (511) +--R 3 6 3 5 +--R 3a b sinh(x) + 18a b cosh(x)sinh(x) +--R + +--R 3 2 3 4 +--R (45a b cosh(x) + 9a b)sinh(x) +--R + +--R 3 3 3 3 +--R (60a b cosh(x) + 36a b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (45a b cosh(x) + 54a b cosh(x) + 9a b)sinh(x) +--R + +--R 3 5 3 3 3 +--R (18a b cosh(x) + 36a b cosh(x) + 18a b cosh(x))sinh(x) +--R + +--R 3 6 3 4 3 2 3 +--R 3a b cosh(x) + 9a b cosh(x) + 9a b cosh(x) + 3a b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 5 2 2 4 +--R - 6a b sinh(x) + (- 30a b cosh(x) + 6a b )sinh(x) +--R + +--R 2 2 2 3 2 3 +--R (- 60a b cosh(x) + 24a b cosh(x) - 8b - 20a b)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R - 60a b cosh(x) + 36a b cosh(x) + (- 24b - 60a b)cosh(x) +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 3 3 2 2 +--R - 30a b cosh(x) + 24a b cosh(x) + (- 24b - 60a b)cosh(x) +--R + +--R 3 2 +--R - 24a cosh(x) - 6a b +--R * +--R sinh(x) +--R + +--R 2 5 2 4 3 2 3 +--R - 6a b cosh(x) + 6a b cosh(x) + (- 8b - 20a b)cosh(x) +--R + +--R 3 2 2 2 3 +--R - 12a cosh(x) - 6a b cosh(x) + 2a b - 4a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 2 2 4 6 4 2 2 4 5 +--R (3b + 6a b + 3a )sinh(x) + (18b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 4 +--R ((45b + 90a b + 45a )cosh(x) + 9b + 18a b + 9a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((60b + 120a b + 60a )cosh(x) + (36b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (45b + 90a b + 45a )cosh(x) + (54b + 108a b + 54a )cosh(x) +--R + +--R 4 2 2 4 +--R 9b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (18b + 36a b + 18a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 +--R (18b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (3b + 6a b + 3a )cosh(x) + (9b + 18a b + 9a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (9b + 18a b + 9a )cosh(x) + 3b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression Integer,...) +--E 514 + +--S 515 of 526 +m0697:= a0697-r0697 +--R +--R +--R (512) +--R 3 6 3 5 +--R 3a b sinh(x) + 18a b cosh(x)sinh(x) +--R + +--R 3 2 3 4 +--R (45a b cosh(x) + 9a b)sinh(x) +--R + +--R 3 3 3 3 +--R (60a b cosh(x) + 36a b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (45a b cosh(x) + 54a b cosh(x) + 9a b)sinh(x) +--R + +--R 3 5 3 3 3 +--R (18a b cosh(x) + 36a b cosh(x) + 18a b cosh(x))sinh(x) +--R + +--R 3 6 3 4 3 2 3 +--R 3a b cosh(x) + 9a b cosh(x) + 9a b cosh(x) + 3a b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 3 6 3 5 +--R 6a b sinh(x) + 36a b cosh(x)sinh(x) +--R + +--R 3 2 3 4 +--R (90a b cosh(x) + 18a b)sinh(x) +--R + +--R 3 3 3 3 +--R (120a b cosh(x) + 72a b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (90a b cosh(x) + 108a b cosh(x) + 18a b)sinh(x) +--R + +--R 3 5 3 3 3 +--R (36a b cosh(x) + 72a b cosh(x) + 36a b cosh(x))sinh(x) +--R + +--R 3 6 3 4 3 2 3 +--R 6a b cosh(x) + 18a b cosh(x) + 18a b cosh(x) + 6a b +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 6 2 3 5 +--R (a b + a )sinh(x) + (6a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((15a b + 15a )cosh(x) + 3a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((20a b + 20a )cosh(x) + (12a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (15a b + 15a )cosh(x) + (18a b + 18a )cosh(x) + 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (6a b + 6a )cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 3 +--R (6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (a b + a )cosh(x) + (3a b + 3a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (3a b + 3a )cosh(x) + a b + a +--R * +--R 3 +--R tanh(x) +--R + +--R 3 6 3 5 +--R - 3a sinh(x) - 18a cosh(x)sinh(x) +--R + +--R 3 2 3 4 +--R (- 45a cosh(x) - 9a )sinh(x) +--R + +--R 3 3 3 3 +--R (- 60a cosh(x) - 36a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (- 45a cosh(x) - 54a cosh(x) - 9a )sinh(x) +--R + +--R 3 5 3 3 3 +--R (- 18a cosh(x) - 36a cosh(x) - 18a cosh(x))sinh(x) +--R + +--R 3 6 3 4 3 2 3 +--R - 3a cosh(x) - 9a cosh(x) - 9a cosh(x) - 3a +--R * +--R tanh(x) +--R + +--R 3 2 3 2 6 +--R ((b + a b)sech(x) + 3a b sech(x))sinh(x) +--R + +--R 3 2 3 2 2 5 +--R ((6b + 6a b)cosh(x)sech(x) + 18a b cosh(x)sech(x) - 6a b)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R ((15b + 15a b)cosh(x) + 3b + 3a b)sech(x) +--R + +--R 2 2 2 2 2 +--R (45a b cosh(x) + 9a b)sech(x) - 30a b cosh(x) + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((20b + 20a b)cosh(x) + (12b + 12a b)cosh(x))sech(x) +--R + +--R 2 3 2 2 2 +--R (60a b cosh(x) + 36a b cosh(x))sech(x) - 60a b cosh(x) +--R + +--R 2 3 2 +--R 24a b cosh(x) - 8b - 20a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((15b + 15a b)cosh(x) + (18b + 18a b)cosh(x) + 3b + 3a b) +--R * +--R 3 +--R sech(x) +--R + +--R 2 4 2 2 2 2 3 +--R (45a b cosh(x) + 54a b cosh(x) + 9a b)sech(x) - 60a b cosh(x) +--R + +--R 2 2 3 2 3 +--R 36a b cosh(x) + (- 24b - 60a b)cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (6b + 6a b)cosh(x) + (12b + 12a b)cosh(x) +--R + +--R 3 2 +--R (6b + 6a b)cosh(x) +--R * +--R 3 +--R sech(x) +--R + +--R 2 5 2 3 2 +--R (18a b cosh(x) + 36a b cosh(x) + 18a b cosh(x))sech(x) +--R + +--R 2 4 2 3 3 2 2 +--R - 30a b cosh(x) + 24a b cosh(x) + (- 24b - 60a b)cosh(x) +--R + +--R 3 2 +--R - 24a cosh(x) - 6a b +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R (b + a b)cosh(x) + (3b + 3a b)cosh(x) + (3b + 3a b)cosh(x) +--R + +--R 3 2 +--R b + a b +--R * +--R 3 +--R sech(x) +--R + +--R 2 6 2 4 2 2 2 +--R (3a b cosh(x) + 9a b cosh(x) + 9a b cosh(x) + 3a b)sech(x) +--R + +--R 2 5 2 4 3 2 3 +--R - 6a b cosh(x) + 6a b cosh(x) + (- 8b - 20a b)cosh(x) +--R + +--R 3 2 2 2 3 +--R - 12a cosh(x) - 6a b cosh(x) + 2a b - 4a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 2 2 4 6 4 2 2 4 5 +--R (3b + 6a b + 3a )sinh(x) + (18b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 4 +--R ((45b + 90a b + 45a )cosh(x) + 9b + 18a b + 9a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((60b + 120a b + 60a )cosh(x) + (36b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (45b + 90a b + 45a )cosh(x) + (54b + 108a b + 54a )cosh(x) +--R + +--R 4 2 2 4 +--R 9b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (18b + 36a b + 18a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 +--R (18b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (3b + 6a b + 3a )cosh(x) + (9b + 18a b + 9a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (9b + 18a b + 9a )cosh(x) + 3b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression Integer +--E 515 + +--S 516 of 526 +--d0697:= D(m0697,x) +--E 516 + +--S 517 of 526 +t0698:= sech(x)/(%i+csch(x)) +--R +--R +--R sech(x) +--R (513) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 517 + +--S 518 of 526 +r0698:= -1/2*%i*atan(sinh(x))-%i/(2*%i-2*sinh(x)) +--R +--R +--R 1 1 1 +--R (- - %i sinh(x) - -)atan(sinh(x)) + - %i +--R 2 2 2 +--R (514) ---------------------------------------- +--R sinh(x) - %i +--R Type: Expression Complex Fraction Integer +--E 518 + +--S 519 of 526 +a0698:= integrate(t0698,x) +--R +--R +--R (515) +--R 2 2 +--R (sinh(x) + (2cosh(x) - 2%i)sinh(x) + cosh(x) - 2%i cosh(x) - 1) +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 2 2 +--R (- sinh(x) + (- 2cosh(x) + 2%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1) +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 2%i sinh(x) + 2%i cosh(x) +--R / +--R 2 2 +--R 2sinh(x) + (4cosh(x) - 4%i)sinh(x) + 2cosh(x) - 4%i cosh(x) - 2 +--R Type: Union(Expression Complex Integer,...) +--E 519 + +--S 520 of 526 +m0698:= a0698-r0698 +--R +--R +--R (516) +--R 1 3 3 2 +--R - sinh(x) + (cosh(x) - - %i)sinh(x) +--R 2 2 +--R + +--R 1 2 3 1 2 1 +--R (- cosh(x) - 2%i cosh(x) - -)sinh(x) - - %i cosh(x) - cosh(x) + - %i +--R 2 2 2 2 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 1 3 3 2 +--R - - sinh(x) + (- cosh(x) + - %i)sinh(x) +--R 2 2 +--R + +--R 1 2 3 1 2 +--R (- - cosh(x) + 2%i cosh(x) + -)sinh(x) + - %i cosh(x) + cosh(x) +--R 2 2 2 +--R + +--R 1 +--R - - %i +--R 2 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 1 3 3 2 +--R - %i sinh(x) + (%i cosh(x) + -)sinh(x) +--R 2 2 +--R + +--R 1 2 3 1 2 1 +--R (- %i cosh(x) + 2cosh(x) - - %i)sinh(x) + - cosh(x) - %i cosh(x) - - +--R 2 2 2 2 +--R * +--R atan(sinh(x)) +--R + +--R 1 2 1 2 1 +--R - %i sinh(x) - - %i cosh(x) + - %i +--R 2 2 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) - 3%i)sinh(x) + (cosh(x) - 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R - %i cosh(x) - 2cosh(x) + %i +--R Type: Expression Complex Fraction Integer +--E 520 + +--S 521 of 526 +d0698:= D(m0698,x) +--R +--R +--R (517) +--R 6 5 +--R - 2%i sinh(x) + (- 5%i cosh(x) - 2)sinh(x) +--R + +--R 2 4 +--R (- 2%i cosh(x) - 4cosh(x))sinh(x) +--R + +--R 3 3 +--R (4%i cosh(x) - 4%i cosh(x))sinh(x) +--R + +--R 4 3 2 2 +--R (4%i cosh(x) + 4cosh(x) - 6%i cosh(x) - 2cosh(x) + 2%i)sinh(x) +--R + +--R 5 4 3 2 +--R (%i cosh(x) + 2cosh(x) - 2%i cosh(x) - 4cosh(x) + %i cosh(x) + 2) +--R * +--R sinh(x) +--R + +--R 3 +--R - 2cosh(x) + 2cosh(x) +--R / +--R 7 6 +--R sinh(x) + (4cosh(x) - 3%i)sinh(x) +--R + +--R 2 5 +--R (6cosh(x) - 10%i cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 12%i cosh(x) - 2cosh(x) - 5%i)sinh(x) +--R + +--R 4 3 3 +--R (cosh(x) - 6%i cosh(x) - 12%i cosh(x) - 5)sinh(x) +--R + +--R 4 3 2 2 +--R (- %i cosh(x) + 2cosh(x) - 12%i cosh(x) - 8cosh(x) - %i)sinh(x) +--R + +--R 4 3 2 +--R (cosh(x) - 6%i cosh(x) - 6cosh(x) - 2%i cosh(x) - 3)sinh(x) +--R + +--R 4 3 +--R - %i cosh(x) - 2cosh(x) - 2cosh(x) + %i +--R Type: Expression Complex Fraction Integer +--E 521 + +--S 522 of 526 +t0699:= sech(x)^2/(%i+csch(x)) +--R +--R +--R 2 +--R sech(x) +--R (518) ------------ +--R csch(x) + %i +--R Type: Expression Complex Integer +--E 522 + +--S 523 of 526 +r0699:= -1/3/cosh(x)^3*(%i*sinh(x)*cosh(x)^2-%i*sinh(x)+1) +--R +--R +--R 2 +--R (- %i cosh(x) + %i)sinh(x) - 1 +--R (519) ------------------------------- +--R 3 +--R 3cosh(x) +--R Type: Expression Complex Integer +--E 523 + +--S 524 of 526 +a0699:= integrate(t0699,x) +--R +--R +--R (520) +--R 8%i sinh(x) + 4%i cosh(x) + 4 +--R / +--R 3 2 +--R 3sinh(x) + (9cosh(x) - 6%i)sinh(x) +--R + +--R 2 3 2 +--R (9cosh(x) - 12%i cosh(x) + 3)sinh(x) + 3cosh(x) - 6%i cosh(x) +--R + +--R - 3cosh(x) - 6%i +--R Type: Union(Expression Complex Integer,...) +--E 524 + +--S 525 of 526 +m0699:= a0699-r0699 +--R +--R +--R (521) +--R 2 4 +--R (%i cosh(x) - %i)sinh(x) +--R + +--R 3 2 3 +--R (3%i cosh(x) + 2cosh(x) - 3%i cosh(x) - 1)sinh(x) +--R + +--R 4 3 2 2 +--R (3%i cosh(x) + 4cosh(x) - 2%i cosh(x) - cosh(x) - 3%i)sinh(x) +--R + +--R 5 4 3 2 +--R (%i cosh(x) + 2cosh(x) + 6%i cosh(x) + 3cosh(x) - 3%i cosh(x) - 1) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R 4%i cosh(x) + 5cosh(x) - 2%i cosh(x) - cosh(x) - 2%i +--R / +--R 3 3 4 3 2 +--R 3cosh(x) sinh(x) + (9cosh(x) - 6%i cosh(x) )sinh(x) +--R + +--R 5 4 3 6 5 +--R (9cosh(x) - 12%i cosh(x) + 3cosh(x) )sinh(x) + 3cosh(x) - 6%i cosh(x) +--R + +--R 4 3 +--R - 3cosh(x) - 6%i cosh(x) +--R Type: Expression Complex Integer +--E 525 + +--S 526 of 526 +d0699:= D(m0699,x) +--R +--R +--R (522) +--R 2 8 +--R (- %i cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 7 +--R (- 6%i cosh(x) - 4cosh(x) + 18%i cosh(x) + 9)sinh(x) +--R + +--R 4 3 2 6 +--R (- 14%i cosh(x) - 20cosh(x) + 46%i cosh(x) + 42cosh(x) + 6%i)sinh(x) +--R + +--R 5 4 3 2 +--R - 14%i cosh(x) - 36cosh(x) + 66%i cosh(x) + 63cosh(x) +--R + +--R 24%i cosh(x) + 30 +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 20cosh(x) + 32%i cosh(x) + 24cosh(x) + 57%i cosh(x) + 84cosh(x) +--R + +--R 3%i +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 14%i cosh(x) + 20cosh(x) - 58%i cosh(x) - 61cosh(x) +--R + +--R 3 2 +--R 90%i cosh(x) + 84cosh(x) - 6%i cosh(x) + 33 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 14%i cosh(x) + 36cosh(x) - 102%i cosh(x) - 114cosh(x) +--R + +--R 4 3 2 +--R 94%i cosh(x) + 48cosh(x) + 14%i cosh(x) + 42cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 6%i cosh(x) + 20cosh(x) - 58%i cosh(x) - 75cosh(x) +--R + +--R 5 4 3 2 +--R 46%i cosh(x) + 26cosh(x) + 18%i cosh(x) + 17cosh(x) +--R + +--R - 12%i cosh(x) + 12 +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R %i cosh(x) + 4cosh(x) - 11%i cosh(x) - 16cosh(x) + 3%i cosh(x) +--R + +--R 5 4 3 2 +--R 8cosh(x) + 3%i cosh(x) + 4cosh(x) + 4%i cosh(x) +--R / +--R 4 6 5 4 5 +--R 3cosh(x) sinh(x) + (18cosh(x) - 12%i cosh(x) )sinh(x) +--R + +--R 6 5 4 4 +--R (45cosh(x) - 60%i cosh(x) - 6cosh(x) )sinh(x) +--R + +--R 7 6 5 4 3 +--R (60cosh(x) - 120%i cosh(x) - 36cosh(x) - 24%i cosh(x) )sinh(x) +--R + +--R 8 7 6 5 4 +--R (45cosh(x) - 120%i cosh(x) - 72cosh(x) - 48%i cosh(x) - 21cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R 18cosh(x) - 60%i cosh(x) - 60cosh(x) - 24%i cosh(x) - 54cosh(x) +--R + +--R 4 +--R - 12%i cosh(x) +--R * +--R sinh(x) +--R + +--R 10 9 8 6 5 +--R 3cosh(x) - 12%i cosh(x) - 18cosh(x) - 21cosh(x) + 12%i cosh(x) +--R + +--R 4 +--R - 12cosh(x) +--R Type: Expression Complex Integer +--E 526 + +)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}