diff --git a/changelog b/changelog index a3cb399..f6e1eb0 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100615 tpd src/axiom-website/patches.html 20100615.01.tpd.patch +20100615 tpd src/input/Makefile rule-based hyper integration +20100615 tpd src/input/richhyper400-499.input rule-based hyper integration 20100614 tpd src/axiom-website/patches.html 20100614.02.tpd.patch 20100614 tpd src/input/Makefile rule-based hyper integration 20100614 tpd src/input/richhyper300-399.input rule-based hyper integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 3df61f8..e72e233 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2896,6 +2896,8 @@ src/input/richhyper100-199.input rule-based hyper integration
src/input/richhyper200-299.input rule-based hyper integration
20100614.02.tpd.patch src/input/richhyper300-399.input rule-based hyper integration
+20100615.01.tpd.patch +src/input/richhyper400-499.input rule-based hyper integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 6c2cf17..606d076 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -379,6 +379,7 @@ REGRES= ackermann.regress \ richhyper100-199.regress \ richhyper200-299.regress \ richhyper300-399.regress \ + richhyper400-499.regress \ richrational.regress \ richtrig000-099.regress \ richtrig100-199.regress \ @@ -712,6 +713,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richhyper100-199.input \ ${OUT}/richhyper200-299.input \ ${OUT}/richhyper300-399.input \ + ${OUT}/richhyper400-499.input \ ${OUT}/richrational.input \ ${OUT}/richtrig000-099.input \ ${OUT}/richtrig100-199.input \ @@ -1074,6 +1076,7 @@ DOCFILES= \ ${DOC}/richhyper100-199.input.dvi \ ${DOC}/richhyper200-299.input.dvi \ ${DOC}/richhyper300-399.input.dvi \ + ${DOC}/richhyper400-499.input.dvi \ ${DOC}/richrational.input.dvi \ ${DOC}/richtrig000-099.input.dvi \ ${DOC}/richtrig100-199.input.dvi \ diff --git a/src/input/richhyper400-499.input.pamphlet b/src/input/richhyper400-499.input.pamphlet new file mode 100644 index 0000000..3d04ba8 --- /dev/null +++ b/src/input/richhyper400-499.input.pamphlet @@ -0,0 +1,38935 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richhyper400-499.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper400-499.output +)spool richhyper400-499.output +)set message auto off +)clear all + +--S 1 of 526 +t0400:= 1/(a+b*sech(x)) +--R +--R +--R 1 +--R (1) ------------- +--R b sech(x) + a +--R Type: Expression Integer +--E 1 + +--S 2 of 526 +r0400:= x/a-2*b*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(1/2) +--R +--R +--R x +--R (b - a)tanh(-) +---------+ +--R 2 | 2 2 +--R 2b atan(--------------) + x\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) --------------------------------------- +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R Type: Expression Integer +--E 2 + +--S 3 of 526 +a0400:= integrate(t0400,x) +--R +--R +--R (3) +--R [ +--R 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 +-------+ +--R | 2 2 +--R x\|b - a +--R / +--R +-------+ +--R | 2 2 +--R a\|b - a +--R , +--R +---------+ +--R | 2 2 +---------+ +--R (a sinh(x) + a cosh(x) + b)\|- b + a | 2 2 +--R 2b atan(---------------------------------------) + x\|- b + a +--R 2 2 +--R b - a +--R ----------------------------------------------------------------] +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R Type: Union(List Expression Integer,...) +--E 3 + +--S 4 of 526 +m0400a:= a0400.1-r0400 +--R +--R +--R (4) +--R +---------+ +--R | 2 2 +--R b\|- 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 +--R - 2b\|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R a\|- b + a \|b - a +--R Type: Expression Integer +--E 4 + +--S 5 of 526 +d0400a:= D(m0400a,x) +--R +--R +--R (5) +--R 2 2 +--R (b sinh(x) + (2b cosh(x) + 2b)sinh(x) + b cosh(x) + 2b cosh(x) + b) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 +--R - b sinh(x) + (- 2b cosh(x) + 2b)sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 2 2 2 2 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) + 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (a b - a )cosh(x) + (2b - 2a b)cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 +--R (- a b - a )sinh(x) + ((- 2a b - 2a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (- a b - a )cosh(x) + (- 2b - 2a b)cosh(x) - a b - a +--R Type: Expression Integer +--E 5 + +--S 6 of 526 +m0400b:= a0400.2-r0400 +--R +--R +--R (6) +--R +---------+ x +--R | 2 2 (b - a)tanh(-) +--R (a sinh(x) + a cosh(x) + b)\|- b + a 2 +--R 2b atan(---------------------------------------) - 2b atan(--------------) +--R 2 2 +---------+ +--R b - a | 2 2 +--R \|- b + a +--R -------------------------------------------------------------------------- +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R Type: Expression Integer +--E 6 + +--S 7 of 526 +d0400b:= D(m0400b,x) +--R +--R +--R (7) +--R 2 2 +--R (b sinh(x) + (2b cosh(x) + 2b)sinh(x) + b cosh(x) + 2b cosh(x) + b) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 +--R - b sinh(x) + (- 2b cosh(x) + 2b)sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 2 2 2 2 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) + 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (a b - a )cosh(x) + (2b - 2a b)cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 +--R (- a b - a )sinh(x) + ((- 2a b - 2a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (- a b - a )cosh(x) + (- 2b - 2a b)cosh(x) - a b - a +--R Type: Expression Integer +--E 7 + +--S 8 of 526 +t0401:= 1/(a+b*sech(x))^2 +--R +--R +--R 1 +--R (8) ------------------------------ +--R 2 2 2 +--R b sech(x) + 2a b sech(x) + a +--R Type: Expression Integer +--E 8 + +--S 9 of 526 +r0401:= x/a^2-2*b^3*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(3/2)-4*b*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)+b^2*sinh(x)/a/(a^2-b^2)/(b+a*cosh(x)) +--R +--R +--R (9) +--R x +--R (b - a)tanh(-) +--R 3 3 4 2 2 2 +--R ((2a b - 4a b)cosh(x) + 2b - 4a b )atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 3 3 2 | 2 2 +--R (- a b sinh(x) + (a b - a )x cosh(x) + (b - a b)x)\|- b + a +--R / +--R +---------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )cosh(x) + a b - a b)\|- b + a +--R Type: Expression Integer +--E 9 + +--S 10 of 526 +a0401:= integrate(t0401,x) +--R +--R +--R (10) +--R [ +--R 3 3 2 +--R (a b - 2a b)sinh(x) +--R + +--R 3 3 4 2 2 +--R ((2a b - 4a b)cosh(x) + 2b - 4a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (a b - 2a b)cosh(x) + (2b - 4a b )cosh(x) + a b - 2a 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 3 2 +--R (a b - a )x sinh(x) +--R + +--R 2 3 3 2 3 +--R ((2a b - 2a )x cosh(x) + (2b - 2a b)x + 2b )sinh(x) +--R + +--R 2 3 2 3 2 3 2 3 +--R (a b - a )x cosh(x) + ((2b - 2a b)x + 2b )cosh(x) + (a b - a )x +--R + +--R 2 +--R 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 3 2 5 2 3 2 5 2 3 4 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) + 2a b - 2a b)sinh(x) +--R + +--R 3 2 5 2 2 3 4 3 2 5 +--R (a b - a )cosh(x) + (2a b - 2a b)cosh(x) + a b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 3 2 +--R (2a b - 4a b)sinh(x) +--R + +--R 3 3 4 2 2 +--R ((4a b - 8a b)cosh(x) + 4b - 8a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (2a b - 4a b)cosh(x) + (4b - 8a b )cosh(x) + 2a b - 4a b +--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 3 2 +--R (a b - a )x sinh(x) +--R + +--R 2 3 3 2 3 +--R ((2a b - 2a )x cosh(x) + (2b - 2a b)x + 2b )sinh(x) +--R + +--R 2 3 2 3 2 3 2 3 +--R (a b - a )x cosh(x) + ((2b - 2a b)x + 2b )cosh(x) + (a b - a )x +--R + +--R 2 +--R 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 2 5 2 3 2 5 2 3 4 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) + 2a b - 2a b)sinh(x) +--R + +--R 3 2 5 2 2 3 4 3 2 5 +--R (a b - a )cosh(x) + (2a b - 2a b)cosh(x) + a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 10 + +--S 11 of 526 +m0401a:= a0401.1-r0401 +--R +--R +--R (11) +--R 2 3 4 4 3 2 2 +--R ((a b - 2a b)cosh(x) + a b - 2a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 2 3 +--R ((2a b - 4a b)cosh(x) + (4a b - 8a b )cosh(x) + 2b - 4a b ) +--R * +--R sinh(x) +--R + +--R 2 3 4 3 4 3 2 2 +--R (a b - 2a b)cosh(x) + (3a b - 6a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (2b - 3a b - 2a b)cosh(x) + a b - 2a 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 2 3 4 4 3 2 2 +--R ((- 2a b + 4a b)cosh(x) - 2a b + 4a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 +--R (- 4a b + 8a b)cosh(x) + (- 8a b + 16a b )cosh(x) - 4b +--R + +--R 2 3 +--R 8a b +--R * +--R sinh(x) +--R + +--R 2 3 4 3 4 3 2 2 +--R (- 2a b + 4a b)cosh(x) + (- 6a b + 12a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (- 4b + 6a b + 4a b)cosh(x) - 2a b + 4a b +--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 3 2 2 3 2 +--R a b sinh(x) + (2a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 2 3 4 2 2 3 2 +--R (a b cosh(x) + 4a b cosh(x) + 2b + a b )sinh(x) + 2a b cosh(x) +--R + +--R 4 2 2 3 +--R (2b + 2a b )cosh(x) + 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 6 3 3 5 2 +--R ((a b - a )cosh(x) + a b - a b)sinh(x) +--R + +--R 4 2 6 2 3 3 5 2 4 4 2 +--R ((2a b - 2a )cosh(x) + (4a b - 4a b)cosh(x) + 2a b - 2a b )sinh(x) +--R + +--R 4 2 6 3 3 3 5 2 +--R (a b - a )cosh(x) + (3a b - 3a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (2a b - a b - a )cosh(x) + a b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 11 + +--S 12 of 526 +d0401a:= D(m0401a,x) +--R +--R +--R (12) +--R 3 3 4 2 6 +--R (- a b + a b )sinh(x) +--R + +--R 3 3 4 2 2 4 3 3 5 +--R ((- 4a b + 4a b )cosh(x) - 4a b + 4a b )sinh(x) +--R + +--R 3 3 4 2 5 2 +--R (- 4a b + 5a b - 2a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 3 3 4 2 +--R (- 9a b + 11a b - 4a b )cosh(x) - 3a b + 4a b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 3 3 4 2 5 2 +--R (4a b - 8a b)cosh(x) + (4a b + 8a b - 20a b - 4a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 +--R (12a b - 20a b - 4a b )cosh(x) + 4a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 5 4 +--R (11a b - 5a b - 12a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (26a b - 2a b - 36a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (18a b + 16a b - 38a b - 28a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 5 +--R (4b + 16a b - 18a b - 18a b - 8a b )cosh(x) + 4b - 2a b +--R + +--R 2 4 3 3 4 2 +--R - 4a b - 5a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 2 5 5 +--R (8a b - 4a b - 8a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (24a b - 4a b - 28a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (24a b + 12a b - 32a b - 36a b - 8a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (8b + 20a b - 12a b - 32a b - 20a b - 4a b)cosh(x) +--R + +--R 6 2 4 3 3 4 2 5 2 4 3 3 +--R (8b - 4a b - 16a b - 8a b )cosh(x) + 4a b - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 5 +--R (2a b - a b - 2a b)cosh(x) + (7a b - a b - 8a b - 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (9a b + 4a b - 10a b - 14a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (4b + 8a b - 2a b - 14a b - 12a b - 4a b)cosh(x) +--R + +--R 6 5 3 3 4 2 5 2 +--R (4b + 2a b - 10a b - 9a b - 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 3 +--R (4a b - a b - 5a b - 4a b )cosh(x) + a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 3 4 2 6 3 3 4 2 2 4 3 3 5 +--R (a b + a b )sinh(x) + ((4a b + 4a b )cosh(x) + 4a b + 4a b )sinh(x) +--R + +--R 3 3 4 2 5 2 2 4 3 3 4 2 +--R (4a b + 5a b + 2a b)cosh(x) + (9a b + 11a b + 4a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R 3a b + 4a b + 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 3 3 4 2 5 2 +--R (- 4a b + 8a b)cosh(x) + (- 4a b + 8a b + 20a b - 4a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 +--R (12a b + 20a b - 4a b )cosh(x) + 4a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 5 4 +--R (- 11a b - 5a b + 12a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 26a b - 2a b + 36a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 18a b + 16a b + 38a b - 28a b + 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 5 +--R (- 4b + 16a b + 18a b - 18a b + 8a b )cosh(x) + 4b + 2a b +--R + +--R 2 4 3 3 4 2 +--R - 4a b + 5a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 2 5 5 +--R (- 8a b - 4a b + 8a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 24a b - 4a b + 28a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (- 24a b + 12a b + 32a b - 36a b + 8a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 8b + 20a b + 12a b - 32a b + 20a b - 4a b)cosh(x) +--R + +--R 6 2 4 3 3 4 2 5 2 4 3 3 +--R (8b - 4a b + 16a b - 8a b )cosh(x) + 4a b + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 5 +--R (- 2a b - a b + 2a b)cosh(x) + (- 7a b - a b + 8a b - 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 9a b + 4a b + 10a b - 14a b + 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (- 4b + 8a b + 2a b - 14a b + 12a b - 4a b)cosh(x) +--R + +--R 6 5 3 3 4 2 5 2 +--R (4b - 2a b + 10a b - 9a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 3 +--R (4a b + a b - 5a b + 4a b )cosh(x) - a b + 2a b +--R / +--R 5 3 6 2 7 8 2 +--R (a b - a b - a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 5 4 4 5 3 6 2 +--R (2a b - 2a b - 2a b + 2a b)cosh(x) + a b - a b - a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 3 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 +--R (12a b - 12a b - 12a b + 12a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 6 3 5 +--R (12a b - 12a b - 12a b + 12a b )cosh(x) + 4a b - 4a b +--R + +--R 4 4 5 3 +--R - 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 4 +--R (6a b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (24a b - 24a b - 24a b + 24a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 2 +--R (34a b - 34a b - 32a b + 32a b - 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 7 +--R (20a b - 20a b - 16a b + 16a b - 4a b + 4a b)cosh(x) + 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 4a b - 2a b + 2a b - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 5 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (20a b - 20a b - 20a b + 20a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (36a b - 36a b - 32a b + 32a b - 4a b + 4a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (28a b - 28a b - 16a b + 16a b - 12a b + 12a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 6 +--R (8a b - 8a b + 4a b - 4a b - 12a b + 12a b )cosh(x) + 4a b +--R + +--R 3 5 4 4 5 3 +--R - 4a b - 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 3 6 2 7 8 6 +--R (a b - a b - a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (6a b - 6a b - 6a b + 6a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 4 +--R (13a b - 13a b - 11a b + 11a b - 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 +--R (12a b - 12a b - 4a b + 4a b - 8a b + 8a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (4a b - 4a b + 6a b - 6a b - 9a b + 9a b - a b + a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 5 4 4 +--R (4a b - 4a b - 2a b + 2a b - 2a b + 2a b)cosh(x) + a b - a b +--R + +--R 5 3 6 2 +--R - a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 3 6 2 7 8 2 +--R (- a b - a b + a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 5 4 4 5 3 6 2 +--R (- 2a b - 2a b + 2a b + 2a b)cosh(x) - a b - a b + a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 3 +--R (- 4a b - 4a b + 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 +--R (- 12a b - 12a b + 12a b + 12a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 6 3 5 4 4 +--R (- 12a b - 12a b + 12a b + 12a b )cosh(x) - 4a b - 4a b + 4a b +--R + +--R 5 3 +--R 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 4 +--R (- 6a b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (- 24a b - 24a b + 24a b + 24a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 2 +--R (- 34a b - 34a b + 32a b + 32a b + 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 7 +--R (- 20a b - 20a b + 16a b + 16a b + 4a b + 4a b)cosh(x) - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 4a b + 2a b + 2a b + 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 5 +--R (- 4a b - 4a b + 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (- 20a b - 20a b + 20a b + 20a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (- 36a b - 36a b + 32a b + 32a b + 4a b + 4a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (- 28a b - 28a b + 16a b + 16a b + 12a b + 12a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 6 +--R (- 8a b - 8a b - 4a b - 4a b + 12a b + 12a b )cosh(x) - 4a b +--R + +--R 3 5 4 4 5 3 +--R - 4a b + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 3 6 2 7 8 6 +--R (- a b - a b + a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (- 6a b - 6a b + 6a b + 6a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 4 +--R (- 13a b - 13a b + 11a b + 11a b + 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 +--R (- 12a b - 12a b + 4a b + 4a b + 8a b + 8a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (- 4a b - 4a b - 6a b - 6a b + 9a b + 9a b + a b + a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 5 4 4 +--R (- 4a b - 4a b + 2a b + 2a b + 2a b + 2a b)cosh(x) - a b - a b +--R + +--R 5 3 6 2 +--R a b + a b +--R Type: Expression Integer +--E 12 + +--S 13 of 526 +m0401b:= a0401.2-r0401 +--R +--R +--R (13) +--R 2 3 4 4 3 2 2 +--R ((2a b - 4a b)cosh(x) + 2a b - 4a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 2 3 +--R ((4a b - 8a b)cosh(x) + (8a b - 16a b )cosh(x) + 4b - 8a b ) +--R * +--R sinh(x) +--R + +--R 2 3 4 3 4 3 2 2 +--R (2a b - 4a b)cosh(x) + (6a b - 12a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (4b - 6a b - 4a b)cosh(x) + 2a b - 4a b +--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 3 4 4 3 2 2 +--R ((- 2a b + 4a b)cosh(x) - 2a b + 4a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 +--R (- 4a b + 8a b)cosh(x) + (- 8a b + 16a b )cosh(x) - 4b +--R + +--R 2 3 +--R 8a b +--R * +--R sinh(x) +--R + +--R 2 3 4 3 4 3 2 2 +--R (- 2a b + 4a b)cosh(x) + (- 6a b + 12a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (- 4b + 6a b + 4a b)cosh(x) - 2a b + 4a b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 2 2 3 2 +--R a b sinh(x) + (2a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 2 3 4 2 2 3 2 +--R (a b cosh(x) + 4a b cosh(x) + 2b + a b )sinh(x) + 2a b cosh(x) +--R + +--R 4 2 2 3 +--R (2b + 2a b )cosh(x) + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 6 3 3 5 2 +--R ((a b - a )cosh(x) + a b - a b)sinh(x) +--R + +--R 4 2 6 2 3 3 5 2 4 4 2 +--R ((2a b - 2a )cosh(x) + (4a b - 4a b)cosh(x) + 2a b - 2a b )sinh(x) +--R + +--R 4 2 6 3 3 3 5 2 +--R (a b - a )cosh(x) + (3a b - 3a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (2a b - a b - a )cosh(x) + a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 13 + +--S 14 of 526 +d0401b:= D(m0401b,x) +--R +--R +--R (14) +--R 3 3 4 2 6 +--R (- a b + a b )sinh(x) +--R + +--R 3 3 4 2 2 4 3 3 5 +--R ((- 4a b + 4a b )cosh(x) - 4a b + 4a b )sinh(x) +--R + +--R 3 3 4 2 5 2 +--R (- 4a b + 5a b - 2a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 3 3 4 2 +--R (- 9a b + 11a b - 4a b )cosh(x) - 3a b + 4a b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 3 3 4 2 5 2 +--R (4a b - 8a b)cosh(x) + (4a b + 8a b - 20a b - 4a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 +--R (12a b - 20a b - 4a b )cosh(x) + 4a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 5 4 +--R (11a b - 5a b - 12a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (26a b - 2a b - 36a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (18a b + 16a b - 38a b - 28a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 5 +--R (4b + 16a b - 18a b - 18a b - 8a b )cosh(x) + 4b - 2a b +--R + +--R 2 4 3 3 4 2 +--R - 4a b - 5a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 2 5 5 +--R (8a b - 4a b - 8a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (24a b - 4a b - 28a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (24a b + 12a b - 32a b - 36a b - 8a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (8b + 20a b - 12a b - 32a b - 20a b - 4a b)cosh(x) +--R + +--R 6 2 4 3 3 4 2 5 2 4 3 3 +--R (8b - 4a b - 16a b - 8a b )cosh(x) + 4a b - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 5 +--R (2a b - a b - 2a b)cosh(x) + (7a b - a b - 8a b - 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (9a b + 4a b - 10a b - 14a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (4b + 8a b - 2a b - 14a b - 12a b - 4a b)cosh(x) +--R + +--R 6 5 3 3 4 2 5 2 +--R (4b + 2a b - 10a b - 9a b - 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 3 +--R (4a b - a b - 5a b - 4a b )cosh(x) + a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 3 4 2 6 3 3 4 2 2 4 3 3 5 +--R (a b + a b )sinh(x) + ((4a b + 4a b )cosh(x) + 4a b + 4a b )sinh(x) +--R + +--R 3 3 4 2 5 2 2 4 3 3 4 2 +--R (4a b + 5a b + 2a b)cosh(x) + (9a b + 11a b + 4a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R 3a b + 4a b + 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 3 3 4 2 5 2 +--R (- 4a b + 8a b)cosh(x) + (- 4a b + 8a b + 20a b - 4a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 +--R (12a b + 20a b - 4a b )cosh(x) + 4a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 5 4 +--R (- 11a b - 5a b + 12a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 26a b - 2a b + 36a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 18a b + 16a b + 38a b - 28a b + 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 5 +--R (- 4b + 16a b + 18a b - 18a b + 8a b )cosh(x) + 4b + 2a b +--R + +--R 2 4 3 3 4 2 +--R - 4a b + 5a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 2 5 5 +--R (- 8a b - 4a b + 8a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 24a b - 4a b + 28a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (- 24a b + 12a b + 32a b - 36a b + 8a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 8b + 20a b + 12a b - 32a b + 20a b - 4a b)cosh(x) +--R + +--R 6 2 4 3 3 4 2 5 2 4 3 3 +--R (8b - 4a b + 16a b - 8a b )cosh(x) + 4a b + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 5 +--R (- 2a b - a b + 2a b)cosh(x) + (- 7a b - a b + 8a b - 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 9a b + 4a b + 10a b - 14a b + 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (- 4b + 8a b + 2a b - 14a b + 12a b - 4a b)cosh(x) +--R + +--R 6 5 3 3 4 2 5 2 +--R (4b - 2a b + 10a b - 9a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 3 +--R (4a b + a b - 5a b + 4a b )cosh(x) - a b + 2a b +--R / +--R 5 3 6 2 7 8 2 +--R (a b - a b - a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 5 4 4 5 3 6 2 +--R (2a b - 2a b - 2a b + 2a b)cosh(x) + a b - a b - a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 3 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 +--R (12a b - 12a b - 12a b + 12a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 6 3 5 +--R (12a b - 12a b - 12a b + 12a b )cosh(x) + 4a b - 4a b +--R + +--R 4 4 5 3 +--R - 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 4 +--R (6a b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (24a b - 24a b - 24a b + 24a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 2 +--R (34a b - 34a b - 32a b + 32a b - 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 7 +--R (20a b - 20a b - 16a b + 16a b - 4a b + 4a b)cosh(x) + 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 4a b - 2a b + 2a b - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 5 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (20a b - 20a b - 20a b + 20a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (36a b - 36a b - 32a b + 32a b - 4a b + 4a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (28a b - 28a b - 16a b + 16a b - 12a b + 12a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 6 +--R (8a b - 8a b + 4a b - 4a b - 12a b + 12a b )cosh(x) + 4a b +--R + +--R 3 5 4 4 5 3 +--R - 4a b - 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 3 6 2 7 8 6 +--R (a b - a b - a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (6a b - 6a b - 6a b + 6a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 4 +--R (13a b - 13a b - 11a b + 11a b - 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 +--R (12a b - 12a b - 4a b + 4a b - 8a b + 8a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (4a b - 4a b + 6a b - 6a b - 9a b + 9a b - a b + a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 5 4 4 +--R (4a b - 4a b - 2a b + 2a b - 2a b + 2a b)cosh(x) + a b - a b +--R + +--R 5 3 6 2 +--R - a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 3 6 2 7 8 2 +--R (- a b - a b + a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 5 4 4 5 3 6 2 +--R (- 2a b - 2a b + 2a b + 2a b)cosh(x) - a b - a b + a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 3 +--R (- 4a b - 4a b + 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 +--R (- 12a b - 12a b + 12a b + 12a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 6 3 5 4 4 +--R (- 12a b - 12a b + 12a b + 12a b )cosh(x) - 4a b - 4a b + 4a b +--R + +--R 5 3 +--R 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 4 +--R (- 6a b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (- 24a b - 24a b + 24a b + 24a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 2 +--R (- 34a b - 34a b + 32a b + 32a b + 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 7 +--R (- 20a b - 20a b + 16a b + 16a b + 4a b + 4a b)cosh(x) - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 4a b + 2a b + 2a b + 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 5 +--R (- 4a b - 4a b + 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (- 20a b - 20a b + 20a b + 20a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (- 36a b - 36a b + 32a b + 32a b + 4a b + 4a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (- 28a b - 28a b + 16a b + 16a b + 12a b + 12a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 6 +--R (- 8a b - 8a b - 4a b - 4a b + 12a b + 12a b )cosh(x) - 4a b +--R + +--R 3 5 4 4 5 3 +--R - 4a b + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 3 6 2 7 8 6 +--R (- a b - a b + a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (- 6a b - 6a b + 6a b + 6a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 4 +--R (- 13a b - 13a b + 11a b + 11a b + 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 +--R (- 12a b - 12a b + 4a b + 4a b + 8a b + 8a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (- 4a b - 4a b - 6a b - 6a b + 9a b + 9a b + a b + a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 5 4 4 +--R (- 4a b - 4a b + 2a b + 2a b + 2a b + 2a b)cosh(x) - a b - a b +--R + +--R 5 3 6 2 +--R a b + a b +--R Type: Expression Integer +--E 14 + +--S 15 of 526 +t0402:= 1/(a+b*sech(x))^3 +--R +--R +--R 1 +--R (15) ---------------------------------------------- +--R 3 3 2 2 2 3 +--R b sech(x) + 3a b sech(x) + 3a b sech(x) + a +--R Type: Expression Integer +--E 15 + +--S 16 of 526 +r0402:= x/a^3-6*b^3*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)/a^3-6*b*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)-b^3*(a^2+2*b^2)*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)/a^3-1/2*b^3*sinh(x)/a^2/(a^2-b^2)/(b+a*cosh(x))^2+3/2*b^4*sinh(x)/a^2/(a^2-b^2)^2/(b+a*cosh(x))+3*b^2*sinh(x)/a^2/(a^2-b^2)/(b+a*cosh(x)) +--R +--R +--R (16) +--R 2 5 4 3 6 2 6 3 4 5 2 +--R (4a b - 10a b + 12a b)cosh(x) + (8a b - 20a b + 24a b )cosh(x) +--R + +--R 7 2 5 4 3 +--R 4b - 10a b + 12a b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 5 3 3 +--R ((- 3a b + 6a b )cosh(x) - 2a b + 5a b )sinh(x) +--R + +--R 2 4 4 2 6 2 5 3 3 5 +--R (2a b - 4a b + 2a )x cosh(x) + (4a b - 8a b + 4a b)x cosh(x) +--R + +--R 6 2 4 4 2 +--R (2b - 4a b + 2a b )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 7 2 9 2 4 5 6 3 8 3 6 +--R (2a b - 4a b + 2a )cosh(x) + (4a b - 8a b + 4a b)cosh(x) + 2a b +--R + +--R 5 4 7 2 +--R - 4a b + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 16 + +--S 17 of 526 +a0402:= integrate(t0402,x) +--R +--R +--R (17) +--R [ +--R 2 5 4 3 6 4 +--R (2a b - 5a b + 6a b)sinh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 3 +--R ((8a b - 20a b + 24a b)cosh(x) + 8a b - 20a b + 24a b )sinh(x) +--R + +--R 2 5 4 3 6 2 +--R (12a b - 30a b + 36a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 5 4 3 6 +--R (24a b - 60a b + 72a b )cosh(x) + 8b - 16a b + 14a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 3 6 3 +--R (8a b - 20a b + 24a b)cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (24a b - 60a b + 72a b )cosh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 +--R (16b - 32a b + 28a b + 24a b)cosh(x) + 8a b - 20a b + 24a b +--R * +--R sinh(x) +--R + +--R 2 5 4 3 6 4 6 3 4 5 2 3 +--R (2a b - 5a b + 6a b)cosh(x) + (8a b - 20a b + 24a b )cosh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (8b - 16a b + 14a b + 12a b)cosh(x) +--R + +--R 6 3 4 5 2 2 5 4 3 6 +--R (8a b - 20a b + 24a b )cosh(x) + 2a b - 5a b + 6a 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 4 4 2 6 4 +--R (2a b - 4a b + 2a )x sinh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (8a b - 16a b + 8a )x cosh(x) + (8a b - 16a b + 8a b)x +--R + +--R 5 3 3 +--R 8a b - 14a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 2 6 2 +--R (12a b - 24a b + 12a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((24a b - 48a b + 24a b)x + 24a b - 42a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R (8b - 12a b + 4a )x + 12b - 18a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 +--R (8a b - 16a b + 8a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 2 +--R ((24a b - 48a b + 24a b)x + 24a b - 42a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R ((16b - 24a b + 8a )x + 24b - 36a b - 24a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R (8a b - 16a b + 8a b)x + 16a b - 34a b +--R * +--R sinh(x) +--R + +--R 2 4 4 2 6 4 +--R (2a b - 4a b + 2a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 3 +--R ((8a b - 16a b + 8a b)x + 8a b - 14a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 2 +--R ((8b - 12a b + 4a )x + 12b - 18a b - 12a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((8a b - 16a b + 8a b)x + 16a b - 34a b )cosh(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (2a b - 4a b + 2a )x + 6a b - 12a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 5 4 7 2 9 4 +--R (2a b - 4a b + 2a )sinh(x) +--R + +--R 5 4 7 2 9 4 5 6 3 8 3 +--R ((8a b - 16a b + 8a )cosh(x) + 8a b - 16a b + 8a b)sinh(x) +--R + +--R 5 4 7 2 9 2 +--R (12a b - 24a b + 12a )cosh(x) +--R + +--R 4 5 6 3 8 3 6 5 4 9 +--R (24a b - 48a b + 24a b)cosh(x) + 8a b - 12a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 7 2 9 3 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 4 5 6 3 8 2 +--R (24a b - 48a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 9 4 5 6 3 8 +--R (16a b - 24a b + 8a )cosh(x) + 8a b - 16a b + 8a b +--R * +--R sinh(x) +--R + +--R 5 4 7 2 9 4 4 5 6 3 8 3 +--R (2a b - 4a b + 2a )cosh(x) + (8a b - 16a b + 8a b)cosh(x) +--R + +--R 3 6 5 4 9 2 4 5 6 3 8 +--R (8a b - 12a b + 4a )cosh(x) + (8a b - 16a b + 8a b)cosh(x) +--R + +--R 5 4 7 2 9 +--R 2a b - 4a b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 2 5 4 3 6 4 +--R (2a b - 5a b + 6a b)sinh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 3 +--R ((8a b - 20a b + 24a b)cosh(x) + 8a b - 20a b + 24a b )sinh(x) +--R + +--R 2 5 4 3 6 2 +--R (12a b - 30a b + 36a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 5 4 3 6 +--R (24a b - 60a b + 72a b )cosh(x) + 8b - 16a b + 14a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 3 6 3 +--R (8a b - 20a b + 24a b)cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (24a b - 60a b + 72a b )cosh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 +--R (16b - 32a b + 28a b + 24a b)cosh(x) + 8a b - 20a b + 24a b +--R * +--R sinh(x) +--R + +--R 2 5 4 3 6 4 6 3 4 5 2 3 +--R (2a b - 5a b + 6a b)cosh(x) + (8a b - 20a b + 24a b )cosh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (8b - 16a b + 14a b + 12a b)cosh(x) +--R + +--R 6 3 4 5 2 2 5 4 3 6 +--R (8a b - 20a b + 24a b )cosh(x) + 2a b - 5a b + 6a b +--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 4 2 6 4 +--R (a b - 2a b + a )x sinh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (4a b - 8a b + 4a )x cosh(x) + (4a b - 8a b + 4a b)x +--R + +--R 5 3 3 +--R 4a b - 7a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 2 6 2 +--R (6a b - 12a b + 6a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((12a b - 24a b + 12a b)x + 12a b - 21a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R (4b - 6a b + 2a )x + 6b - 9a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 +--R (4a b - 8a b + 4a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 2 +--R ((12a b - 24a b + 12a b)x + 12a b - 21a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R ((8b - 12a b + 4a )x + 12b - 18a b - 12a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R (4a b - 8a b + 4a b)x + 8a b - 17a b +--R * +--R sinh(x) +--R + +--R 2 4 4 2 6 4 +--R (a b - 2a b + a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 3 +--R ((4a b - 8a b + 4a b)x + 4a b - 7a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 2 +--R ((4b - 6a b + 2a )x + 6b - 9a b - 6a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((4a b - 8a b + 4a b)x + 8a b - 17a b )cosh(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (a b - 2a b + a )x + 3a b - 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 7 2 9 4 +--R (a b - 2a b + a )sinh(x) +--R + +--R 5 4 7 2 9 4 5 6 3 8 3 +--R ((4a b - 8a b + 4a )cosh(x) + 4a b - 8a b + 4a b)sinh(x) +--R + +--R 5 4 7 2 9 2 4 5 6 3 8 +--R (6a b - 12a b + 6a )cosh(x) + (12a b - 24a b + 12a b)cosh(x) +--R + +--R 3 6 5 4 9 +--R 4a b - 6a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 7 2 9 3 4 5 6 3 8 2 +--R (4a b - 8a b + 4a )cosh(x) + (12a b - 24a b + 12a b)cosh(x) +--R + +--R 3 6 5 4 9 4 5 6 3 8 +--R (8a b - 12a b + 4a )cosh(x) + 4a b - 8a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 4 7 2 9 4 4 5 6 3 8 3 +--R (a b - 2a b + a )cosh(x) + (4a b - 8a b + 4a b)cosh(x) +--R + +--R 3 6 5 4 9 2 4 5 6 3 8 5 4 +--R (4a b - 6a b + 2a )cosh(x) + (4a b - 8a b + 4a b)cosh(x) + a b +--R + +--R 7 2 9 +--R - 2a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 17 + +--S 18 of 526 +m0402a:= a0402.1-r0402 +--R +--R +--R (18) +--R 4 5 6 3 8 2 3 6 5 4 7 2 +--R (2a b - 5a b + 6a b)cosh(x) + (4a b - 10a b + 12a b )cosh(x) +--R + +--R 2 7 4 5 6 3 +--R 2a b - 5a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (8a b - 20a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (24a b - 60a b + 72a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (24a b - 60a b + 72a b )cosh(x) + 8a b - 20a b + 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (12a b - 30a b + 36a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (48a b - 120a b + 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (68a b - 166a b + 194a b + 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 2 7 +--R (40a b - 92a b + 100a b + 24a b )cosh(x) + 8b - 16a b +--R + +--R 4 5 6 3 +--R 14a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 6 3 8 5 +--R (8a b - 20a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (40a b - 100a b + 120a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (72a b - 172a b + 196a b + 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (56a b - 116a b + 108a b + 72a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 5 4 +--R (16b - 16a b - 12a b + 72a b )cosh(x) + 8a b - 20a b + 24a b +--R * +--R sinh(x) +--R + +--R 4 5 6 3 8 6 3 6 5 4 7 2 5 +--R (2a b - 5a b + 6a b)cosh(x) + (12a b - 30a b + 36a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (26a b - 61a b + 68a b + 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (24a b - 44a b + 32a b + 48a b )cosh(x) +--R + +--R 9 4 5 6 3 8 2 +--R (8b - 24a b + 55a b + 6a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 +--R (8a b - 16a b + 14a b + 12a b )cosh(x) + 2a b - 5a b + 6a 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 4 5 6 3 8 2 +--R (- 4a b + 10a b - 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 +--R (- 8a b + 20a b - 24a b )cosh(x) - 4a b + 10a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (- 16a b + 40a b - 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 48a b + 120a b - 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (- 48a b + 120a b - 144a b )cosh(x) - 16a b + 40a b - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (- 24a b + 60a b - 72a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 96a b + 240a b - 288a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 136a b + 332a b - 388a b - 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 2 7 +--R (- 80a b + 184a b - 200a b - 48a b )cosh(x) - 16b + 32a b +--R + +--R 4 5 6 3 +--R - 28a b - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 6 3 8 5 +--R (- 16a b + 40a b - 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- 80a b + 200a b - 240a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 144a b + 344a b - 392a b - 48a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 112a b + 232a b - 216a b - 144a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 +--R (- 32b + 32a b + 24a b - 144a b )cosh(x) - 16a b + 40a b +--R + +--R 5 4 +--R - 48a b +--R * +--R sinh(x) +--R + +--R 4 5 6 3 8 6 +--R (- 4a b + 10a b - 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- 24a b + 60a b - 72a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 52a b + 122a b - 136a b - 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 48a b + 88a b - 64a b - 96a b )cosh(x) +--R + +--R 9 4 5 6 3 8 2 +--R (- 16b + 48a b - 110a b - 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 +--R (- 16a b + 32a b - 28a b - 24a b )cosh(x) - 4a b + 10a b - 12a b +--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 4 6 2 3 5 5 3 5 +--R ((3a b - 6a b )cosh(x) + 2a b - 5a b )sinh(x) +--R + +--R 4 4 6 2 2 3 5 5 3 2 6 +--R (12a b - 24a b )cosh(x) + (20a b - 44a b )cosh(x) + 8a b +--R + +--R 4 4 +--R - 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 4 6 2 3 3 5 5 3 2 +--R (18a b - 36a b )cosh(x) + (56a b - 116a b )cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 +--R (52a b - 106a b - 12a b )cosh(x) + 16a b - 30a b - 10a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (12a b - 24a b )cosh(x) + (68a b - 134a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (108a b - 198a b - 36a b )cosh(x) +--R + +--R 7 3 5 5 3 8 2 6 4 4 +--R (64a b - 98a b - 68a b )cosh(x) + 12b - 10a b - 32a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 5 3 5 5 3 4 +--R (3a b - 6a b )cosh(x) + (38a b - 71a b )cosh(x) +--R + +--R 2 6 4 4 6 2 3 +--R (92a b - 158a b - 36a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (80a b - 102a b - 116a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 7 3 5 5 3 +--R (24b + 4a b - 109a b - 6a b )cosh(x) + 16a b - 32a b - 5a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 5 2 6 4 4 6 2 4 +--R (8a b - 14a b )cosh(x) + (28a b - 46a b - 12a b )cosh(x) +--R + +--R 7 3 5 5 3 3 +--R (32a b - 34a b - 58a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (12b + 14a b - 74a b - 12a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 +--R (16a b - 22a b - 24a b )cosh(x) + 6a b - 12a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 7 4 9 2 11 2 6 5 8 3 10 +--R (2a b - 4a b + 2a )cosh(x) + (4a b - 8a b + 4a b)cosh(x) +--R + +--R 5 6 7 4 9 2 +--R 2a b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 4 9 2 11 3 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 6 5 8 3 10 2 +--R (24a b - 48a b + 24a b)cosh(x) +--R + +--R 5 6 7 4 9 2 4 7 6 5 8 3 +--R (24a b - 48a b + 24a b )cosh(x) + 8a b - 16a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 4 9 2 11 4 +--R (12a b - 24a b + 12a )cosh(x) +--R + +--R 6 5 8 3 10 3 +--R (48a b - 96a b + 48a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 2 +--R (68a b - 132a b + 60a b + 4a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 3 8 5 6 9 2 +--R (40a b - 72a b + 24a b + 8a b)cosh(x) + 8a b - 12a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 4 9 2 11 5 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 6 5 8 3 10 4 +--R (40a b - 80a b + 40a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 3 +--R (72a b - 136a b + 56a b + 8a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (56a b - 88a b + 8a b + 24a b)cosh(x) +--R + +--R 3 8 5 6 7 4 9 2 4 7 6 5 8 3 +--R (16a b - 8a b - 32a b + 24a b )cosh(x) + 8a b - 16a b + 8a b +--R * +--R sinh(x) +--R + +--R 7 4 9 2 11 6 6 5 8 3 10 5 +--R (2a b - 4a b + 2a )cosh(x) + (12a b - 24a b + 12a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 4 +--R (26a b - 48a b + 18a b + 4a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (24a b - 32a b - 8a b + 16a b)cosh(x) +--R + +--R 3 8 5 6 7 4 9 2 11 2 +--R (8a b + 4a b - 30a b + 16a b + 2a )cosh(x) +--R + +--R 4 7 6 5 10 5 6 7 4 9 2 +--R (8a b - 12a b + 4a b)cosh(x) + 2a b - 4a b + 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 18 + +--S 19 of 526 +d0402a:= D(m0402a,x) +--R +--R +--R (19) +--R 5 5 6 4 7 3 8 2 4 6 5 5 6 4 +--R (- 3a b + 3a b + 6a b - 6a b )cosh(x) - a b + a b + 4a b +--R + +--R 7 3 +--R - 4a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 2 +--R (- 18a b + 18a b + 36a b - 36a b )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 3 7 4 6 +--R (- 24a b + 24a b + 60a b - 60a b )cosh(x) - 6a b + 6a b +--R + +--R 5 5 6 4 +--R 24a b - 24a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 3 +--R (- 40a b + 42a b + 79a b - 84a b + 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 2 +--R (- 94a b + 100a b + 214a b - 229a b + 18a b )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 58a b + 64a b + 163a b - 178a b + 36a b - 18a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 10a b + 12a b + 40a b - 45a b + 18a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 4 +--R (- 30a b + 42a b + 54a b - 84a b + 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R (- 116a b + 164a b + 242a b - 362a b + 132a b + 12a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 126a b + 198a b + 288a b - 468a b + 252a b - 36a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R (- 48a b + 96a b + 114a b - 234a b + 228a b - 84a b )cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 8a b + 20a b + 14a b - 44a b + 72a b - 36a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (30a b - 75a b + 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 4 +--R (60a b + 90a b - 180a b - 195a b + 390a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 30a b + 264a b - 171a b - 558a b + 753a b + 114a b +--R + +--R 9 +--R 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 6a b + 276a b - 144a b - 543a b + 804a b - 3a b +--R + +--R 8 2 +--R 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 132a b - 78a b - 234a b + 411a b - 60a b + 72a b +--R + +--R 8 2 +--R - 18a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b - 18a b - 36a b + 78a b - 21a b + 30a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 6 +--R (82a b - 42a b - 184a b + 84a b + 120a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 5 +--R (304a b - 64a b - 736a b + 136a b + 600a b + 120a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 430a b + 146a b - 1144a b - 272a b + 1212a b + 456a b +--R + +--R 9 +--R 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 304a b + 400a b - 924a b - 740a b + 1316a b + 556a b +--R + +--R 8 2 9 +--R 264a b + 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 112a b + 344a b - 412a b - 584a b + 774a b + 234a b +--R + +--R 7 3 8 2 +--R 396a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b + 128a b - 88a b - 176a b + 204a b - 12a b +--R + +--R 6 4 7 3 +--R 276a b + 12a b +--R * +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b - 8a b - 8a b + 14a b - 26a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 7 +--R (72a b - 42a b - 159a b + 84a b + 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R (326a b - 116a b - 770a b + 245a b + 510a b + 120a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 3 7 5 5 6 4 7 3 8 2 9 +--R (594a b - 1467a b + 18a b + 1098a b + 594a b + 108a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 546a b + 324a b - 1368a b - 627a b + 1134a b + 1026a b +--R + +--R 8 2 9 +--R 468a b + 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 256a b + 440a b - 628a b - 764a b + 570a b + 654a b +--R + +--R 7 3 8 2 9 +--R 789a b + 240a b + 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 240a b - 108a b - 288a b + 90a b - 18a b +--R + +--R 6 4 7 3 8 2 +--R 654a b + 273a b + 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 3 7 4 6 5 5 6 4 +--R 48b + 24a b - 18a b - 180a b + 249a b + 138a b +--R + +--R 7 3 8 2 +--R 60a b - 6a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b - 6a b - 48a b + 32a b + 25a b + 22a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 8 +--R (30a b - 18a b - 66a b + 36a b + 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 7 +--R (156a b - 60a b - 366a b + 126a b + 228a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 342a b - 30a b - 816a b + 60a b + 528a b + 348a b +--R + +--R 9 +--R 72a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 384a b + 144a b - 870a b - 306a b + 504a b + 720a b +--R + +--R 8 2 9 +--R 360a b + 72a b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 216a b + 276a b - 402a b - 492a b + 102a b + 546a b +--R + +--R 7 3 8 2 9 +--R 678a b + 300a b + 36a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 192a b - 24a b - 192a b - 120a b - 72a b +--R + +--R 6 4 7 3 8 2 9 +--R 594a b + 438a b + 132a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 24a b + 72a b - 54a b - 270a b + 228a b +--R + +--R 6 4 7 3 8 2 +--R 240a b + 180a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 4 6 5 5 6 4 7 3 +--R (48a b - 72a b + 18a b + 6a b + 108a b + 36a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 12a b - 6a b - 24a b + 24a b + 12a b +--R * +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 9 +--R (5a b - 3a b - 11a b + 6a b + 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 8 +--R (29a b - 11a b - 68a b + 23a b + 42a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (74a b - 8a b - 173a b + 14a b + 105a b + 78a b + 18a b) +--R * +--R 7 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 98a b + 28a b - 208a b - 65a b + 92a b + 181a b + 102a b +--R + +--R 9 +--R 24a b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 64a b + 68a b - 94a b - 122a b - 33a b + 150a b + 213a b +--R + +--R 8 2 9 +--R 114a b + 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b + 56a b + 14a b - 44a b - 84a b - 45a b + 186a b +--R + +--R 7 3 8 2 9 +--R 189a b + 78a b + 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b + 16a b + 40a b - 22a b - 116a b + 53a b + 102a b +--R + +--R 7 3 8 2 9 +--R 115a b + 42a b + 6a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 6a b - 24a b - 4a b - 23a b + 64a b + 47a b +--R + +--R 8 2 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 2 8 +--R (12a b + 2a b - 26a b + 4a b + 17a b + 18a b )cosh(x) + 2a b +--R + +--R 4 6 6 4 +--R - 5a b + 6a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 5 6 4 7 3 8 2 4 6 5 5 6 4 7 3 +--R ((3a b + 3a b - 6a b - 6a b )cosh(x) + a b + a b - 4a b - 4a b ) +--R * +--R 8 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 2 +--R (18a b + 18a b - 36a b - 36a b )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 3 7 4 6 5 5 +--R (24a b + 24a b - 60a b - 60a b )cosh(x) + 6a b + 6a b - 24a b +--R + +--R 6 4 +--R - 24a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 3 +--R (40a b + 42a b - 79a b - 84a b - 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 2 +--R (94a b + 100a b - 214a b - 229a b - 18a b )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (58a b + 64a b - 163a b - 178a b - 36a b - 18a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 10a b + 12a b - 40a b - 45a b - 18a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 4 +--R (30a b + 42a b - 54a b - 84a b - 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 3 +--R (116a b + 164a b - 242a b - 362a b - 132a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 2 +--R (126a b + 198a b - 288a b - 468a b - 252a b - 36a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R (48a b + 96a b - 114a b - 234a b - 228a b - 84a b )cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 8a b + 20a b - 14a b - 44a b - 72a b - 36a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (- 30a b + 75a b - 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 4 +--R (- 60a b + 90a b + 180a b - 195a b - 390a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 30a b + 264a b + 171a b - 558a b - 753a b + 114a b +--R + +--R 9 +--R - 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 6a b + 276a b + 144a b - 543a b - 804a b - 3a b - 54a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (132a b + 78a b - 234a b - 411a b - 60a b - 72a b - 18a b ) +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 18a b - 36a b - 78a b - 21a b - 30a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 6 +--R (- 82a b - 42a b + 184a b + 84a b - 120a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 5 +--R (- 304a b - 64a b + 736a b + 136a b - 600a b + 120a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 430a b + 146a b + 1144a b - 272a b - 1212a b + 456a b +--R + +--R 9 +--R - 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 304a b + 400a b + 924a b - 740a b - 1316a b + 556a b +--R + +--R 8 2 9 +--R - 264a b + 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 112a b + 344a b + 412a b - 584a b - 774a b + 234a b +--R + +--R 7 3 8 2 +--R - 396a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 16b + 128a b + 88a b - 176a b - 204a b - 12a b - 276a b +--R + +--R 7 3 +--R 12a b +--R * +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b + 8a b - 8a b - 14a b - 26a b - 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 7 +--R (- 72a b - 42a b + 159a b + 84a b - 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 6 +--R (- 326a b - 116a b + 770a b + 245a b - 510a b + 120a b)cosh(x) +--R + +--R 3 7 5 5 6 4 7 3 8 2 9 5 +--R (- 594a b + 1467a b + 18a b - 1098a b + 594a b - 108a b)cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 546a b + 324a b + 1368a b - 627a b - 1134a b + 1026a b +--R + +--R 8 2 9 +--R - 468a b + 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 256a b + 440a b + 628a b - 764a b - 570a b + 654a b +--R + +--R 7 3 8 2 9 +--R - 789a b + 240a b - 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 48b + 240a b + 108a b - 288a b - 90a b - 18a b - 654a b +--R + +--R 7 3 8 2 +--R 273a b - 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 3 7 4 6 5 5 6 4 7 3 +--R 48b + 24a b + 18a b - 180a b - 249a b + 138a b - 60a b +--R + +--R 8 2 +--R - 6a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 6a b - 48a b - 32a b + 25a b - 22a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 8 +--R (- 30a b - 18a b + 66a b + 36a b - 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 7 +--R (- 156a b - 60a b + 366a b + 126a b - 228a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (- 342a b - 30a b + 816a b + 60a b - 528a b + 348a b - 72a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 384a b + 144a b + 870a b - 306a b - 504a b + 720a b +--R + +--R 8 2 9 +--R - 360a b + 72a b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 216a b + 276a b + 402a b - 492a b - 102a b + 546a b +--R + +--R 7 3 8 2 9 +--R - 678a b + 300a b - 36a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 48b + 192a b + 24a b - 192a b + 120a b - 72a b - 594a b +--R + +--R 7 3 8 2 9 +--R 438a b - 132a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 48b - 24a b + 72a b + 54a b - 270a b - 228a b + 240a b +--R + +--R 7 3 8 2 +--R - 180a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 4 6 5 5 6 4 7 3 2 8 +--R (48a b - 72a b - 18a b + 6a b - 108a b + 36a b )cosh(x) + 12a b +--R + +--R 3 7 4 6 5 5 6 4 +--R 6a b - 24a b - 24a b + 12a b +--R * +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 9 +--R (- 5a b - 3a b + 11a b + 6a b - 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 8 +--R (- 29a b - 11a b + 68a b + 23a b - 42a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 7 +--R (- 74a b - 8a b + 173a b + 14a b - 105a b + 78a b - 18a b)cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 98a b + 28a b + 208a b - 65a b - 92a b + 181a b - 102a b +--R + +--R 9 +--R 24a b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 64a b + 68a b + 94a b - 122a b + 33a b + 150a b - 213a b +--R + +--R 8 2 9 +--R 114a b - 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 16b + 56a b - 14a b - 44a b + 84a b - 45a b - 186a b +--R + +--R 7 3 8 2 9 +--R 189a b - 78a b + 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b - 16a b + 40a b + 22a b - 116a b - 53a b + 102a b +--R + +--R 7 3 8 2 9 +--R - 115a b + 42a b - 6a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (24a b - 6a b - 24a b + 4a b - 23a b - 64a b + 47a b - 18a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 2 8 +--R (12a b - 2a b - 26a b - 4a b + 17a b - 18a b )cosh(x) - 2a b +--R + +--R 4 6 6 4 +--R 5a b - 6a b +--R / +--R 8 5 9 4 10 3 11 2 12 13 3 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 2 +--R (6a b - 6a b - 12a b + 12a b + 6a b - 6a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R (6a b - 6a b - 12a b + 12a b + 6a b - 6a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 2a b - 2a b - 4a b + 4a b + 2a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 4 +--R (12a b - 12a b - 24a b + 24a b + 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 3 +--R (48a b - 48a b - 96a b + 96a b + 48a b - 48a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 2 +--R (72a b - 72a b - 144a b + 144a b + 72a b - 72a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R (48a b - 48a b - 96a b + 96a b + 48a b - 48a b )cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 12a b - 12a b - 24a b + 24a b + 12a b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 5 +--R (30a b - 30a b - 60a b + 60a b + 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (150a b - 150a b - 300a b + 300a b + 150a b - 150a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 294a b - 294a b - 582a b + 582a b + 282a b - 282a b +--R + +--R 12 13 +--R 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 282a b - 282a b - 546a b + 546a b + 246a b - 246a b +--R + +--R 11 2 12 +--R 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 132a b - 132a b - 246a b + 246a b + 96a b - 96a b +--R + +--R 10 3 11 2 +--R 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 42a b + 42a b + 12a b - 12a b + 6a b +--R + +--R 10 3 +--R - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 6 +--R (40a b - 40a b - 80a b + 80a b + 40a b - 40a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (240a b - 240a b - 480a b + 480a b + 240a b - 240a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 576a b - 576a b - 1128a b + 1128a b + 528a b - 528a b +--R + +--R 12 13 +--R 24a b - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 704a b - 704a b - 1312a b + 1312a b + 512a b - 512a b +--R + +--R 11 2 12 +--R 96a b - 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 456a b - 456a b - 768a b + 768a b + 168a b - 168a b +--R + +--R 10 3 11 2 +--R 144a b - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 144a b - 144a b - 192a b + 192a b - 48a b + 48a b +--R + +--R 9 4 10 3 +--R 96a b - 96a b +--R * +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R 16a b - 16a b - 8a b + 8a b - 32a b + 32a b + 24a b +--R + +--R 9 4 +--R - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 7 +--R (30a b - 30a b - 60a b + 60a b + 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (210a b - 210a b - 420a b + 420a b + 210a b - 210a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 594a b - 594a b - 1152a b + 1152a b + 522a b - 522a b +--R + +--R 12 13 +--R 36a b - 36a +--R * +--R 5 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 870a b - 870a b - 1560a b + 1560a b + 510a b - 510a b +--R + +--R 11 2 12 +--R 180a b - 180a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 696a b - 696a b - 1044a b + 1044a b + 6a b - 6a b +--R + +--R 10 3 11 2 12 13 +--R 336a b - 336a b + 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 288a b - 288a b - 252a b + 252a b - 342a b + 342a b +--R + +--R 9 4 10 3 11 2 12 +--R 288a b - 288a b + 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R 48a b - 48a b + 48a b - 48a b - 222a b + 222a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 108a b - 108a b + 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 42a b + 42a b + 12a b - 12a b + 6a b +--R + +--R 10 3 +--R - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 8 +--R (12a b - 12a b - 24a b + 24a b + 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 7 +--R (96a b - 96a b - 192a b + 192a b + 96a b - 96a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 312a b - 312a b - 600a b + 600a b + 264a b - 264a b +--R + +--R 12 13 +--R 24a b - 24a +--R * +--R 6 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 528a b - 528a b - 912a b + 912a b + 240a b - 240a b +--R + +--R 11 2 12 +--R 144a b - 144a b +--R * +--R 5 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 492a b - 492a b - 648a b + 648a b - 168a b + 168a b +--R + +--R 10 3 11 2 12 13 +--R 312a b - 312a b + 12a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 240a b - 240a b - 96a b + 96a b - 480a b + 480a b +--R + +--R 9 4 10 3 11 2 12 +--R 288a b - 288a b + 48a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R 48a b - 48a b + 120a b - 120a b - 312a b + 312a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 72a b - 72a b + 72a b - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 48a b - 48a b - 48a b + 48a b - 48a b + 48a b + 48a b +--R + +--R 10 3 +--R - 48a b +--R * +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 12a b - 12a b - 24a b + 24a b + 12a b - 12a b +--R * +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 9 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 8 +--R (18a b - 18a b - 36a b + 36a b + 18a b - 18a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 12 +--R 66a b - 66a b - 126a b + 126a b + 54a b - 54a b + 6a b +--R + +--R 13 +--R - 6a +--R * +--R 7 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 126a b - 126a b - 210a b + 210a b + 42a b - 42a b +--R + +--R 11 2 12 +--R 42a b - 42a b +--R * +--R 6 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 132a b - 132a b - 150a b + 150a b - 90a b + 90a b +--R + +--R 10 3 11 2 12 13 +--R 102a b - 102a b + 6a b - 6a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 72a b - 72a b + 6a b - 6a b - 198a b + 198a b + 90a b +--R + +--R 10 3 11 2 12 +--R - 90a b + 30a b - 30a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R 16a b - 16a b + 64a b - 64a b - 122a b + 122a b - 10a b +--R + +--R 9 4 10 3 11 2 12 13 +--R 10a b + 50a b - 50a b + 2a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 6a b + 6a b - 54a b + 54a b + 30a b +--R + +--R 10 3 11 2 12 +--R - 30a b + 6a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 10 3 11 2 5 8 +--R (12a b - 12a b - 18a b + 18a b + 6a b - 6a b )cosh(x) + 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b - 4a b + 4a b + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 8 5 9 4 10 3 11 2 12 13 3 +--R (- 2a b - 2a b + 4a b + 4a b - 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 2 +--R (- 6a b - 6a b + 12a b + 12a b - 6a b - 6a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 5 8 +--R (- 6a b - 6a b + 12a b + 12a b - 6a b - 6a b )cosh(x) - 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b + 4a b + 4a b - 2a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 4 +--R (- 12a b - 12a b + 24a b + 24a b - 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 3 +--R (- 48a b - 48a b + 96a b + 96a b - 48a b - 48a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 2 +--R (- 72a b - 72a b + 144a b + 144a b - 72a b - 72a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R (- 48a b - 48a b + 96a b + 96a b - 48a b - 48a b )cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 12a b - 12a b + 24a b + 24a b - 12a b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 5 +--R (- 30a b - 30a b + 60a b + 60a b - 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 150a b - 150a b + 300a b + 300a b - 150a b - 150a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 294a b - 294a b + 582a b + 582a b - 282a b - 282a b +--R + +--R 12 13 +--R - 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 282a b - 282a b + 546a b + 546a b - 246a b - 246a b +--R + +--R 11 2 12 +--R - 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 132a b - 132a b + 246a b + 246a b - 96a b - 96a b +--R + +--R 10 3 11 2 +--R - 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 24a b - 24a b + 42a b + 42a b - 12a b - 12a b - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 6 +--R (- 40a b - 40a b + 80a b + 80a b - 40a b - 40a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 240a b - 240a b + 480a b + 480a b - 240a b - 240a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 576a b - 576a b + 1128a b + 1128a b - 528a b - 528a b +--R + +--R 12 13 +--R - 24a b - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 704a b - 704a b + 1312a b + 1312a b - 512a b - 512a b +--R + +--R 11 2 12 +--R - 96a b - 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 456a b - 456a b + 768a b + 768a b - 168a b - 168a b +--R + +--R 10 3 11 2 +--R - 144a b - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 144a b - 144a b + 192a b + 192a b + 48a b + 48a b +--R + +--R 9 4 10 3 +--R - 96a b - 96a b +--R * +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 16a b - 16a b + 8a b + 8a b + 32a b + 32a b - 24a b - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 7 +--R (- 30a b - 30a b + 60a b + 60a b - 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 210a b - 210a b + 420a b + 420a b - 210a b - 210a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 594a b - 594a b + 1152a b + 1152a b - 522a b - 522a b +--R + +--R 12 13 +--R - 36a b - 36a +--R * +--R 5 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 870a b - 870a b + 1560a b + 1560a b - 510a b - 510a b +--R + +--R 11 2 12 +--R - 180a b - 180a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 696a b - 696a b + 1044a b + 1044a b - 6a b - 6a b +--R + +--R 10 3 11 2 12 13 +--R - 336a b - 336a b - 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 288a b - 288a b + 252a b + 252a b + 342a b + 342a b +--R + +--R 9 4 10 3 11 2 12 +--R - 288a b - 288a b - 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 48a b - 48a b - 48a b + 222a b + 222a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 108a b - 108a b - 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 24a b - 24a b + 42a b + 42a b - 12a b - 12a b - 6a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 8 +--R (- 12a b - 12a b + 24a b + 24a b - 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 7 +--R (- 96a b - 96a b + 192a b + 192a b - 96a b - 96a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 312a b - 312a b + 600a b + 600a b - 264a b - 264a b +--R + +--R 12 13 +--R - 24a b - 24a +--R * +--R 6 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 528a b - 528a b + 912a b + 912a b - 240a b - 240a b +--R + +--R 11 2 12 +--R - 144a b - 144a b +--R * +--R 5 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 492a b - 492a b + 648a b + 648a b + 168a b + 168a b +--R + +--R 10 3 11 2 12 13 +--R - 312a b - 312a b - 12a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 240a b - 240a b + 96a b + 96a b + 480a b + 480a b +--R + +--R 9 4 10 3 11 2 12 +--R - 288a b - 288a b - 48a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 48a b - 120a b - 120a b + 312a b + 312a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 72a b - 72a b - 72a b - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 48a b - 48a b + 48a b + 48a b + 48a b + 48a b - 48a b +--R + +--R 10 3 +--R - 48a b +--R * +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 12a b - 12a b + 24a b + 24a b - 12a b - 12a b +--R * +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 9 +--R (- 2a b - 2a b + 4a b + 4a b - 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 8 +--R (- 18a b - 18a b + 36a b + 36a b - 18a b - 18a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 12 +--R - 66a b - 66a b + 126a b + 126a b - 54a b - 54a b - 6a b +--R + +--R 13 +--R - 6a +--R * +--R 7 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 126a b - 126a b + 210a b + 210a b - 42a b - 42a b - 42a b +--R + +--R 12 +--R - 42a b +--R * +--R 6 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 132a b - 132a b + 150a b + 150a b + 90a b + 90a b - 102a b +--R + +--R 11 2 12 13 +--R - 102a b - 6a b - 6a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 72a b - 72a b - 6a b - 6a b + 198a b + 198a b - 90a b +--R + +--R 10 3 11 2 12 +--R - 90a b - 30a b - 30a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 16a b - 16a b - 64a b - 64a b + 122a b + 122a b + 10a b +--R + +--R 9 4 10 3 11 2 12 13 +--R 10a b - 50a b - 50a b - 2a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 24a b - 24a b + 6a b + 6a b + 54a b + 54a b - 30a b +--R + +--R 10 3 11 2 12 +--R - 30a b - 6a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 10 3 11 2 5 8 +--R (- 12a b - 12a b + 18a b + 18a b - 6a b - 6a b )cosh(x) - 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b + 4a b + 4a b - 2a b - 2a b +--R Type: Expression Integer +--E 19 + +--S 20 of 526 +m0402b:= a0402.2-r0402 +--R +--R +--R (20) +--R 4 5 6 3 8 2 +--R (4a b - 10a b + 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 +--R (8a b - 20a b + 24a b )cosh(x) + 4a b - 10a b + 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (16a b - 40a b + 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (48a b - 120a b + 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (48a b - 120a b + 144a b )cosh(x) + 16a b - 40a b + 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (24a b - 60a b + 72a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (96a b - 240a b + 288a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (136a b - 332a b + 388a b + 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 2 7 +--R (80a b - 184a b + 200a b + 48a b )cosh(x) + 16b - 32a b +--R + +--R 4 5 6 3 +--R 28a b + 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 6 3 8 5 +--R (16a b - 40a b + 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (80a b - 200a b + 240a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (144a b - 344a b + 392a b + 48a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (112a b - 232a b + 216a b + 144a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 +--R (32b - 32a b - 24a b + 144a b )cosh(x) + 16a b - 40a b +--R + +--R 5 4 +--R 48a b +--R * +--R sinh(x) +--R + +--R 4 5 6 3 8 6 3 6 5 4 7 2 5 +--R (4a b - 10a b + 12a b)cosh(x) + (24a b - 60a b + 72a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (52a b - 122a b + 136a b + 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (48a b - 88a b + 64a b + 96a b )cosh(x) +--R + +--R 9 4 5 6 3 8 2 +--R (16b - 48a b + 110a b + 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 +--R (16a b - 32a b + 28a b + 24a b )cosh(x) + 4a b - 10a b + 12a b +--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 5 6 3 8 2 +--R (- 4a b + 10a b - 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 +--R (- 8a b + 20a b - 24a b )cosh(x) - 4a b + 10a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (- 16a b + 40a b - 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 48a b + 120a b - 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (- 48a b + 120a b - 144a b )cosh(x) - 16a b + 40a b - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (- 24a b + 60a b - 72a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 96a b + 240a b - 288a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 136a b + 332a b - 388a b - 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 2 7 +--R (- 80a b + 184a b - 200a b - 48a b )cosh(x) - 16b + 32a b +--R + +--R 4 5 6 3 +--R - 28a b - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 6 3 8 5 +--R (- 16a b + 40a b - 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- 80a b + 200a b - 240a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 144a b + 344a b - 392a b - 48a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 112a b + 232a b - 216a b - 144a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 +--R (- 32b + 32a b + 24a b - 144a b )cosh(x) - 16a b + 40a b +--R + +--R 5 4 +--R - 48a b +--R * +--R sinh(x) +--R + +--R 4 5 6 3 8 6 +--R (- 4a b + 10a b - 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- 24a b + 60a b - 72a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 52a b + 122a b - 136a b - 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 48a b + 88a b - 64a b - 96a b )cosh(x) +--R + +--R 9 4 5 6 3 8 2 +--R (- 16b + 48a b - 110a b - 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 +--R (- 16a b + 32a b - 28a b - 24a b )cosh(x) - 4a b + 10a b - 12a b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 4 6 2 3 5 5 3 5 +--R ((3a b - 6a b )cosh(x) + 2a b - 5a b )sinh(x) +--R + +--R 4 4 6 2 2 3 5 5 3 2 6 +--R (12a b - 24a b )cosh(x) + (20a b - 44a b )cosh(x) + 8a b +--R + +--R 4 4 +--R - 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 4 6 2 3 3 5 5 3 2 +--R (18a b - 36a b )cosh(x) + (56a b - 116a b )cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 +--R (52a b - 106a b - 12a b )cosh(x) + 16a b - 30a b - 10a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (12a b - 24a b )cosh(x) + (68a b - 134a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (108a b - 198a b - 36a b )cosh(x) +--R + +--R 7 3 5 5 3 8 2 6 4 4 +--R (64a b - 98a b - 68a b )cosh(x) + 12b - 10a b - 32a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 5 3 5 5 3 4 +--R (3a b - 6a b )cosh(x) + (38a b - 71a b )cosh(x) +--R + +--R 2 6 4 4 6 2 3 +--R (92a b - 158a b - 36a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (80a b - 102a b - 116a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 7 3 5 5 3 +--R (24b + 4a b - 109a b - 6a b )cosh(x) + 16a b - 32a b - 5a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 5 2 6 4 4 6 2 4 +--R (8a b - 14a b )cosh(x) + (28a b - 46a b - 12a b )cosh(x) +--R + +--R 7 3 5 5 3 3 +--R (32a b - 34a b - 58a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (12b + 14a b - 74a b - 12a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 +--R (16a b - 22a b - 24a b )cosh(x) + 6a b - 12a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 7 4 9 2 11 2 6 5 8 3 10 +--R (2a b - 4a b + 2a )cosh(x) + (4a b - 8a b + 4a b)cosh(x) +--R + +--R 5 6 7 4 9 2 +--R 2a b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 4 9 2 11 3 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 6 5 8 3 10 2 +--R (24a b - 48a b + 24a b)cosh(x) +--R + +--R 5 6 7 4 9 2 4 7 6 5 8 3 +--R (24a b - 48a b + 24a b )cosh(x) + 8a b - 16a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 4 9 2 11 4 +--R (12a b - 24a b + 12a )cosh(x) +--R + +--R 6 5 8 3 10 3 +--R (48a b - 96a b + 48a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 2 +--R (68a b - 132a b + 60a b + 4a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 3 8 5 6 9 2 +--R (40a b - 72a b + 24a b + 8a b)cosh(x) + 8a b - 12a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 4 9 2 11 5 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 6 5 8 3 10 4 +--R (40a b - 80a b + 40a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 3 +--R (72a b - 136a b + 56a b + 8a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (56a b - 88a b + 8a b + 24a b)cosh(x) +--R + +--R 3 8 5 6 7 4 9 2 4 7 6 5 8 3 +--R (16a b - 8a b - 32a b + 24a b )cosh(x) + 8a b - 16a b + 8a b +--R * +--R sinh(x) +--R + +--R 7 4 9 2 11 6 6 5 8 3 10 5 +--R (2a b - 4a b + 2a )cosh(x) + (12a b - 24a b + 12a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 4 +--R (26a b - 48a b + 18a b + 4a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (24a b - 32a b - 8a b + 16a b)cosh(x) +--R + +--R 3 8 5 6 7 4 9 2 11 2 +--R (8a b + 4a b - 30a b + 16a b + 2a )cosh(x) +--R + +--R 4 7 6 5 10 5 6 7 4 9 2 +--R (8a b - 12a b + 4a b)cosh(x) + 2a b - 4a b + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 20 + +--S 21 of 526 +d0402b:= D(m0402b,x) +--R +--R +--R (21) +--R 5 5 6 4 7 3 8 2 4 6 5 5 6 4 +--R (- 3a b + 3a b + 6a b - 6a b )cosh(x) - a b + a b + 4a b +--R + +--R 7 3 +--R - 4a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 2 +--R (- 18a b + 18a b + 36a b - 36a b )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 3 7 4 6 +--R (- 24a b + 24a b + 60a b - 60a b )cosh(x) - 6a b + 6a b +--R + +--R 5 5 6 4 +--R 24a b - 24a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 3 +--R (- 40a b + 42a b + 79a b - 84a b + 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 2 +--R (- 94a b + 100a b + 214a b - 229a b + 18a b )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 58a b + 64a b + 163a b - 178a b + 36a b - 18a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 10a b + 12a b + 40a b - 45a b + 18a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 4 +--R (- 30a b + 42a b + 54a b - 84a b + 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R (- 116a b + 164a b + 242a b - 362a b + 132a b + 12a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 126a b + 198a b + 288a b - 468a b + 252a b - 36a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R (- 48a b + 96a b + 114a b - 234a b + 228a b - 84a b )cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 8a b + 20a b + 14a b - 44a b + 72a b - 36a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (30a b - 75a b + 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 4 +--R (60a b + 90a b - 180a b - 195a b + 390a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 30a b + 264a b - 171a b - 558a b + 753a b + 114a b +--R + +--R 9 +--R 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 6a b + 276a b - 144a b - 543a b + 804a b - 3a b +--R + +--R 8 2 +--R 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 132a b - 78a b - 234a b + 411a b - 60a b + 72a b +--R + +--R 8 2 +--R - 18a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b - 18a b - 36a b + 78a b - 21a b + 30a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 6 +--R (82a b - 42a b - 184a b + 84a b + 120a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 5 +--R (304a b - 64a b - 736a b + 136a b + 600a b + 120a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 430a b + 146a b - 1144a b - 272a b + 1212a b + 456a b +--R + +--R 9 +--R 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 304a b + 400a b - 924a b - 740a b + 1316a b + 556a b +--R + +--R 8 2 9 +--R 264a b + 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 112a b + 344a b - 412a b - 584a b + 774a b + 234a b +--R + +--R 7 3 8 2 +--R 396a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b + 128a b - 88a b - 176a b + 204a b - 12a b +--R + +--R 6 4 7 3 +--R 276a b + 12a b +--R * +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b - 8a b - 8a b + 14a b - 26a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 7 +--R (72a b - 42a b - 159a b + 84a b + 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R (326a b - 116a b - 770a b + 245a b + 510a b + 120a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 3 7 5 5 6 4 7 3 8 2 9 +--R (594a b - 1467a b + 18a b + 1098a b + 594a b + 108a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 546a b + 324a b - 1368a b - 627a b + 1134a b + 1026a b +--R + +--R 8 2 9 +--R 468a b + 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 256a b + 440a b - 628a b - 764a b + 570a b + 654a b +--R + +--R 7 3 8 2 9 +--R 789a b + 240a b + 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 240a b - 108a b - 288a b + 90a b - 18a b +--R + +--R 6 4 7 3 8 2 +--R 654a b + 273a b + 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 3 7 4 6 5 5 6 4 +--R 48b + 24a b - 18a b - 180a b + 249a b + 138a b +--R + +--R 7 3 8 2 +--R 60a b - 6a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b - 6a b - 48a b + 32a b + 25a b + 22a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 8 +--R (30a b - 18a b - 66a b + 36a b + 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 7 +--R (156a b - 60a b - 366a b + 126a b + 228a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 342a b - 30a b - 816a b + 60a b + 528a b + 348a b +--R + +--R 9 +--R 72a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 384a b + 144a b - 870a b - 306a b + 504a b + 720a b +--R + +--R 8 2 9 +--R 360a b + 72a b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 216a b + 276a b - 402a b - 492a b + 102a b + 546a b +--R + +--R 7 3 8 2 9 +--R 678a b + 300a b + 36a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 192a b - 24a b - 192a b - 120a b - 72a b +--R + +--R 6 4 7 3 8 2 9 +--R 594a b + 438a b + 132a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 24a b + 72a b - 54a b - 270a b + 228a b +--R + +--R 6 4 7 3 8 2 +--R 240a b + 180a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 4 6 5 5 6 4 7 3 +--R (48a b - 72a b + 18a b + 6a b + 108a b + 36a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 12a b - 6a b - 24a b + 24a b + 12a b +--R * +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 9 +--R (5a b - 3a b - 11a b + 6a b + 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 8 +--R (29a b - 11a b - 68a b + 23a b + 42a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (74a b - 8a b - 173a b + 14a b + 105a b + 78a b + 18a b) +--R * +--R 7 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 98a b + 28a b - 208a b - 65a b + 92a b + 181a b + 102a b +--R + +--R 9 +--R 24a b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 64a b + 68a b - 94a b - 122a b - 33a b + 150a b + 213a b +--R + +--R 8 2 9 +--R 114a b + 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b + 56a b + 14a b - 44a b - 84a b - 45a b + 186a b +--R + +--R 7 3 8 2 9 +--R 189a b + 78a b + 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b + 16a b + 40a b - 22a b - 116a b + 53a b + 102a b +--R + +--R 7 3 8 2 9 +--R 115a b + 42a b + 6a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 6a b - 24a b - 4a b - 23a b + 64a b + 47a b +--R + +--R 8 2 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 2 8 +--R (12a b + 2a b - 26a b + 4a b + 17a b + 18a b )cosh(x) + 2a b +--R + +--R 4 6 6 4 +--R - 5a b + 6a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 5 6 4 7 3 8 2 4 6 5 5 6 4 7 3 +--R ((3a b + 3a b - 6a b - 6a b )cosh(x) + a b + a b - 4a b - 4a b ) +--R * +--R 8 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 2 +--R (18a b + 18a b - 36a b - 36a b )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 3 7 4 6 5 5 +--R (24a b + 24a b - 60a b - 60a b )cosh(x) + 6a b + 6a b - 24a b +--R + +--R 6 4 +--R - 24a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 3 +--R (40a b + 42a b - 79a b - 84a b - 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 2 +--R (94a b + 100a b - 214a b - 229a b - 18a b )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (58a b + 64a b - 163a b - 178a b - 36a b - 18a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 10a b + 12a b - 40a b - 45a b - 18a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 4 +--R (30a b + 42a b - 54a b - 84a b - 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 3 +--R (116a b + 164a b - 242a b - 362a b - 132a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 2 +--R (126a b + 198a b - 288a b - 468a b - 252a b - 36a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R (48a b + 96a b - 114a b - 234a b - 228a b - 84a b )cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 8a b + 20a b - 14a b - 44a b - 72a b - 36a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (- 30a b + 75a b - 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 4 +--R (- 60a b + 90a b + 180a b - 195a b - 390a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 30a b + 264a b + 171a b - 558a b - 753a b + 114a b +--R + +--R 9 +--R - 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 6a b + 276a b + 144a b - 543a b - 804a b - 3a b - 54a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (132a b + 78a b - 234a b - 411a b - 60a b - 72a b - 18a b ) +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 18a b - 36a b - 78a b - 21a b - 30a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 6 +--R (- 82a b - 42a b + 184a b + 84a b - 120a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 5 +--R (- 304a b - 64a b + 736a b + 136a b - 600a b + 120a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 430a b + 146a b + 1144a b - 272a b - 1212a b + 456a b +--R + +--R 9 +--R - 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 304a b + 400a b + 924a b - 740a b - 1316a b + 556a b +--R + +--R 8 2 9 +--R - 264a b + 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 112a b + 344a b + 412a b - 584a b - 774a b + 234a b +--R + +--R 7 3 8 2 +--R - 396a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 16b + 128a b + 88a b - 176a b - 204a b - 12a b - 276a b +--R + +--R 7 3 +--R 12a b +--R * +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b + 8a b - 8a b - 14a b - 26a b - 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 7 +--R (- 72a b - 42a b + 159a b + 84a b - 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 6 +--R (- 326a b - 116a b + 770a b + 245a b - 510a b + 120a b)cosh(x) +--R + +--R 3 7 5 5 6 4 7 3 8 2 9 5 +--R (- 594a b + 1467a b + 18a b - 1098a b + 594a b - 108a b)cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 546a b + 324a b + 1368a b - 627a b - 1134a b + 1026a b +--R + +--R 8 2 9 +--R - 468a b + 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 256a b + 440a b + 628a b - 764a b - 570a b + 654a b +--R + +--R 7 3 8 2 9 +--R - 789a b + 240a b - 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 48b + 240a b + 108a b - 288a b - 90a b - 18a b - 654a b +--R + +--R 7 3 8 2 +--R 273a b - 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 3 7 4 6 5 5 6 4 7 3 +--R 48b + 24a b + 18a b - 180a b - 249a b + 138a b - 60a b +--R + +--R 8 2 +--R - 6a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 6a b - 48a b - 32a b + 25a b - 22a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 8 +--R (- 30a b - 18a b + 66a b + 36a b - 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 7 +--R (- 156a b - 60a b + 366a b + 126a b - 228a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (- 342a b - 30a b + 816a b + 60a b - 528a b + 348a b - 72a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 384a b + 144a b + 870a b - 306a b - 504a b + 720a b +--R + +--R 8 2 9 +--R - 360a b + 72a b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 216a b + 276a b + 402a b - 492a b - 102a b + 546a b +--R + +--R 7 3 8 2 9 +--R - 678a b + 300a b - 36a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 48b + 192a b + 24a b - 192a b + 120a b - 72a b - 594a b +--R + +--R 7 3 8 2 9 +--R 438a b - 132a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 48b - 24a b + 72a b + 54a b - 270a b - 228a b + 240a b +--R + +--R 7 3 8 2 +--R - 180a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 4 6 5 5 6 4 7 3 2 8 +--R (48a b - 72a b - 18a b + 6a b - 108a b + 36a b )cosh(x) + 12a b +--R + +--R 3 7 4 6 5 5 6 4 +--R 6a b - 24a b - 24a b + 12a b +--R * +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 9 +--R (- 5a b - 3a b + 11a b + 6a b - 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 8 +--R (- 29a b - 11a b + 68a b + 23a b - 42a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 7 +--R (- 74a b - 8a b + 173a b + 14a b - 105a b + 78a b - 18a b)cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 98a b + 28a b + 208a b - 65a b - 92a b + 181a b - 102a b +--R + +--R 9 +--R 24a b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 64a b + 68a b + 94a b - 122a b + 33a b + 150a b - 213a b +--R + +--R 8 2 9 +--R 114a b - 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 16b + 56a b - 14a b - 44a b + 84a b - 45a b - 186a b +--R + +--R 7 3 8 2 9 +--R 189a b - 78a b + 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b - 16a b + 40a b + 22a b - 116a b - 53a b + 102a b +--R + +--R 7 3 8 2 9 +--R - 115a b + 42a b - 6a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (24a b - 6a b - 24a b + 4a b - 23a b - 64a b + 47a b - 18a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 2 8 +--R (12a b - 2a b - 26a b - 4a b + 17a b - 18a b )cosh(x) - 2a b +--R + +--R 4 6 6 4 +--R 5a b - 6a b +--R / +--R 8 5 9 4 10 3 11 2 12 13 3 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 2 +--R (6a b - 6a b - 12a b + 12a b + 6a b - 6a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R (6a b - 6a b - 12a b + 12a b + 6a b - 6a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 2a b - 2a b - 4a b + 4a b + 2a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 4 +--R (12a b - 12a b - 24a b + 24a b + 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 3 +--R (48a b - 48a b - 96a b + 96a b + 48a b - 48a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 2 +--R (72a b - 72a b - 144a b + 144a b + 72a b - 72a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R (48a b - 48a b - 96a b + 96a b + 48a b - 48a b )cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 12a b - 12a b - 24a b + 24a b + 12a b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 5 +--R (30a b - 30a b - 60a b + 60a b + 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (150a b - 150a b - 300a b + 300a b + 150a b - 150a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 294a b - 294a b - 582a b + 582a b + 282a b - 282a b +--R + +--R 12 13 +--R 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 282a b - 282a b - 546a b + 546a b + 246a b - 246a b +--R + +--R 11 2 12 +--R 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 132a b - 132a b - 246a b + 246a b + 96a b - 96a b +--R + +--R 10 3 11 2 +--R 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 42a b + 42a b + 12a b - 12a b + 6a b +--R + +--R 10 3 +--R - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 6 +--R (40a b - 40a b - 80a b + 80a b + 40a b - 40a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (240a b - 240a b - 480a b + 480a b + 240a b - 240a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 576a b - 576a b - 1128a b + 1128a b + 528a b - 528a b +--R + +--R 12 13 +--R 24a b - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 704a b - 704a b - 1312a b + 1312a b + 512a b - 512a b +--R + +--R 11 2 12 +--R 96a b - 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 456a b - 456a b - 768a b + 768a b + 168a b - 168a b +--R + +--R 10 3 11 2 +--R 144a b - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 144a b - 144a b - 192a b + 192a b - 48a b + 48a b +--R + +--R 9 4 10 3 +--R 96a b - 96a b +--R * +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R 16a b - 16a b - 8a b + 8a b - 32a b + 32a b + 24a b +--R + +--R 9 4 +--R - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 7 +--R (30a b - 30a b - 60a b + 60a b + 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (210a b - 210a b - 420a b + 420a b + 210a b - 210a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 594a b - 594a b - 1152a b + 1152a b + 522a b - 522a b +--R + +--R 12 13 +--R 36a b - 36a +--R * +--R 5 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 870a b - 870a b - 1560a b + 1560a b + 510a b - 510a b +--R + +--R 11 2 12 +--R 180a b - 180a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 696a b - 696a b - 1044a b + 1044a b + 6a b - 6a b +--R + +--R 10 3 11 2 12 13 +--R 336a b - 336a b + 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 288a b - 288a b - 252a b + 252a b - 342a b + 342a b +--R + +--R 9 4 10 3 11 2 12 +--R 288a b - 288a b + 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R 48a b - 48a b + 48a b - 48a b - 222a b + 222a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 108a b - 108a b + 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 42a b + 42a b + 12a b - 12a b + 6a b +--R + +--R 10 3 +--R - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 8 +--R (12a b - 12a b - 24a b + 24a b + 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 7 +--R (96a b - 96a b - 192a b + 192a b + 96a b - 96a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 312a b - 312a b - 600a b + 600a b + 264a b - 264a b +--R + +--R 12 13 +--R 24a b - 24a +--R * +--R 6 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 528a b - 528a b - 912a b + 912a b + 240a b - 240a b +--R + +--R 11 2 12 +--R 144a b - 144a b +--R * +--R 5 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 492a b - 492a b - 648a b + 648a b - 168a b + 168a b +--R + +--R 10 3 11 2 12 13 +--R 312a b - 312a b + 12a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 240a b - 240a b - 96a b + 96a b - 480a b + 480a b +--R + +--R 9 4 10 3 11 2 12 +--R 288a b - 288a b + 48a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R 48a b - 48a b + 120a b - 120a b - 312a b + 312a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 72a b - 72a b + 72a b - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 48a b - 48a b - 48a b + 48a b - 48a b + 48a b + 48a b +--R + +--R 10 3 +--R - 48a b +--R * +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 12a b - 12a b - 24a b + 24a b + 12a b - 12a b +--R * +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 9 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 8 +--R (18a b - 18a b - 36a b + 36a b + 18a b - 18a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 12 +--R 66a b - 66a b - 126a b + 126a b + 54a b - 54a b + 6a b +--R + +--R 13 +--R - 6a +--R * +--R 7 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 126a b - 126a b - 210a b + 210a b + 42a b - 42a b +--R + +--R 11 2 12 +--R 42a b - 42a b +--R * +--R 6 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 132a b - 132a b - 150a b + 150a b - 90a b + 90a b +--R + +--R 10 3 11 2 12 13 +--R 102a b - 102a b + 6a b - 6a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 72a b - 72a b + 6a b - 6a b - 198a b + 198a b + 90a b +--R + +--R 10 3 11 2 12 +--R - 90a b + 30a b - 30a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R 16a b - 16a b + 64a b - 64a b - 122a b + 122a b - 10a b +--R + +--R 9 4 10 3 11 2 12 13 +--R 10a b + 50a b - 50a b + 2a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 6a b + 6a b - 54a b + 54a b + 30a b +--R + +--R 10 3 11 2 12 +--R - 30a b + 6a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 10 3 11 2 5 8 +--R (12a b - 12a b - 18a b + 18a b + 6a b - 6a b )cosh(x) + 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b - 4a b + 4a b + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 8 5 9 4 10 3 11 2 12 13 3 +--R (- 2a b - 2a b + 4a b + 4a b - 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 2 +--R (- 6a b - 6a b + 12a b + 12a b - 6a b - 6a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 5 8 +--R (- 6a b - 6a b + 12a b + 12a b - 6a b - 6a b )cosh(x) - 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b + 4a b + 4a b - 2a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 4 +--R (- 12a b - 12a b + 24a b + 24a b - 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 3 +--R (- 48a b - 48a b + 96a b + 96a b - 48a b - 48a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 2 +--R (- 72a b - 72a b + 144a b + 144a b - 72a b - 72a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R (- 48a b - 48a b + 96a b + 96a b - 48a b - 48a b )cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 12a b - 12a b + 24a b + 24a b - 12a b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 5 +--R (- 30a b - 30a b + 60a b + 60a b - 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 150a b - 150a b + 300a b + 300a b - 150a b - 150a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 294a b - 294a b + 582a b + 582a b - 282a b - 282a b +--R + +--R 12 13 +--R - 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 282a b - 282a b + 546a b + 546a b - 246a b - 246a b +--R + +--R 11 2 12 +--R - 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 132a b - 132a b + 246a b + 246a b - 96a b - 96a b +--R + +--R 10 3 11 2 +--R - 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 24a b - 24a b + 42a b + 42a b - 12a b - 12a b - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 6 +--R (- 40a b - 40a b + 80a b + 80a b - 40a b - 40a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 240a b - 240a b + 480a b + 480a b - 240a b - 240a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 576a b - 576a b + 1128a b + 1128a b - 528a b - 528a b +--R + +--R 12 13 +--R - 24a b - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 704a b - 704a b + 1312a b + 1312a b - 512a b - 512a b +--R + +--R 11 2 12 +--R - 96a b - 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 456a b - 456a b + 768a b + 768a b - 168a b - 168a b +--R + +--R 10 3 11 2 +--R - 144a b - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 144a b - 144a b + 192a b + 192a b + 48a b + 48a b +--R + +--R 9 4 10 3 +--R - 96a b - 96a b +--R * +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 16a b - 16a b + 8a b + 8a b + 32a b + 32a b - 24a b - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 7 +--R (- 30a b - 30a b + 60a b + 60a b - 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 210a b - 210a b + 420a b + 420a b - 210a b - 210a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 594a b - 594a b + 1152a b + 1152a b - 522a b - 522a b +--R + +--R 12 13 +--R - 36a b - 36a +--R * +--R 5 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 870a b - 870a b + 1560a b + 1560a b - 510a b - 510a b +--R + +--R 11 2 12 +--R - 180a b - 180a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 696a b - 696a b + 1044a b + 1044a b - 6a b - 6a b +--R + +--R 10 3 11 2 12 13 +--R - 336a b - 336a b - 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 288a b - 288a b + 252a b + 252a b + 342a b + 342a b +--R + +--R 9 4 10 3 11 2 12 +--R - 288a b - 288a b - 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 48a b - 48a b - 48a b + 222a b + 222a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 108a b - 108a b - 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 24a b - 24a b + 42a b + 42a b - 12a b - 12a b - 6a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 8 +--R (- 12a b - 12a b + 24a b + 24a b - 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 7 +--R (- 96a b - 96a b + 192a b + 192a b - 96a b - 96a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 312a b - 312a b + 600a b + 600a b - 264a b - 264a b +--R + +--R 12 13 +--R - 24a b - 24a +--R * +--R 6 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 528a b - 528a b + 912a b + 912a b - 240a b - 240a b +--R + +--R 11 2 12 +--R - 144a b - 144a b +--R * +--R 5 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 492a b - 492a b + 648a b + 648a b + 168a b + 168a b +--R + +--R 10 3 11 2 12 13 +--R - 312a b - 312a b - 12a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 240a b - 240a b + 96a b + 96a b + 480a b + 480a b +--R + +--R 9 4 10 3 11 2 12 +--R - 288a b - 288a b - 48a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 48a b - 120a b - 120a b + 312a b + 312a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 72a b - 72a b - 72a b - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 48a b - 48a b + 48a b + 48a b + 48a b + 48a b - 48a b +--R + +--R 10 3 +--R - 48a b +--R * +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 12a b - 12a b + 24a b + 24a b - 12a b - 12a b +--R * +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 9 +--R (- 2a b - 2a b + 4a b + 4a b - 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 8 +--R (- 18a b - 18a b + 36a b + 36a b - 18a b - 18a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 12 +--R - 66a b - 66a b + 126a b + 126a b - 54a b - 54a b - 6a b +--R + +--R 13 +--R - 6a +--R * +--R 7 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 126a b - 126a b + 210a b + 210a b - 42a b - 42a b - 42a b +--R + +--R 12 +--R - 42a b +--R * +--R 6 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 132a b - 132a b + 150a b + 150a b + 90a b + 90a b - 102a b +--R + +--R 11 2 12 13 +--R - 102a b - 6a b - 6a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 72a b - 72a b - 6a b - 6a b + 198a b + 198a b - 90a b +--R + +--R 10 3 11 2 12 +--R - 90a b - 30a b - 30a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 16a b - 16a b - 64a b - 64a b + 122a b + 122a b + 10a b +--R + +--R 9 4 10 3 11 2 12 13 +--R 10a b - 50a b - 50a b - 2a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 24a b - 24a b + 6a b + 6a b + 54a b + 54a b - 30a b +--R + +--R 10 3 11 2 12 +--R - 30a b - 6a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 10 3 11 2 5 8 +--R (- 12a b - 12a b + 18a b + 18a b - 6a b - 6a b )cosh(x) - 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b + 4a b + 4a b - 2a b - 2a b +--R Type: Expression Integer +--E 21 + +--S 22 of 526 +t0403:= 1/(a+b*sech(x)^2) +--R +--R +--R 1 +--R (22) -------------- +--R 2 +--R b sech(x) + a +--R Type: Expression Integer +--E 22 + +--S 23 of 526 +r0403:= x/a-b^(1/2)*atanh(b^(1/2)*tanh(x)/(a+b)^(1/2))/a/(a+b)^(1/2) +--R +--R +--R +-+ +--R +-+ tanh(x)\|b +-----+ +--R - \|b atanh(-----------) + x\|b + a +--R +-----+ +--R \|b + a +--R (23) ------------------------------------ +--R +-----+ +--R a\|b + a +--R Type: Expression Integer +--E 23 + +--S 24 of 526 +a0403:= integrate(t0403,x) +--R +--R +--R (24) +--R [ +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4a b + 4a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b + 4a )cosh(x) + 8b + 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b + 2a )cosh(x) + 8b + 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b + 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b + 2a)cosh(x) + a +--R + +--R 2x +--R / +--R 2a +--R , +--R +-------+ +--R | b +--R +-------+ (2b + 2a) |- ----- +--R | b \| b + a +--R - |- ----- atan(----------------------------------------------------) + x +--R \| b + a 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b + a +--R --------------------------------------------------------------------------] +--R a +--R Type: Union(List Expression Integer,...) +--E 24 + +--S 25 of 526 +m0403a:= a0403.1-r0403 +--R +--R +--R (25) +--R +-----+ +--R | b +-----+ +--R |----- \|b + a +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4a b + 4a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b + 4a )cosh(x) + 8b + 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b + 2a )cosh(x) + 8b + 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b + 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b + 2a)cosh(x) + a +--R + +--R +-+ +--R +-+ tanh(x)\|b +--R 2\|b atanh(-----------) +--R +-----+ +--R \|b + a +--R / +--R +-----+ +--R 2a\|b + a +--R Type: Expression Integer +--E 25 + +--S 26 of 526 +d0403a:= D(m0403a,x) +--R +--R +--R (26) +--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 2 +--R tanh(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 / +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (8b + 4a b)cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (4b + 2a b)cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (- a b - a )sinh(x) + (- 4a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6a b - 6a )cosh(x) - 4b - 6a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4a b - 4a )cosh(x) + (- 8b - 12a b - 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- a b - a )cosh(x) + (- 4b - 6a b - 2a )cosh(x) - a b - a +--R Type: Expression Integer +--E 26 + +--S 27 of 526 +m0403b:= a0403.2-r0403 +--R +--R +--R (27) +--R +-+ +--R +-+ tanh(x)\|b +--R \|b atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R - +--R +-------+ +--R | b +-----+ +--R |- ----- \|b + a +--R \| b + a +--R * +--R +-------+ +--R | b +--R (2b + 2a) |- ----- +--R \| b + a +--R atan(----------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b + a +--R / +--R +-----+ +--R a\|b + a +--R Type: Expression Integer +--E 27 + +--S 28 of 526 +d0403b:= D(m0403b,x) +--R +--R +--R (28) +--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 2 +--R tanh(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 / +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (8b + 4a b)cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (4b + 2a b)cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (- a b - a )sinh(x) + (- 4a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6a b - 6a )cosh(x) - 4b - 6a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4a b - 4a )cosh(x) + (- 8b - 12a b - 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- a b - a )cosh(x) + (- 4b - 6a b - 2a )cosh(x) - a b - a +--R Type: Expression Integer +--E 28 + +--S 29 of 526 +t0404:= 1/(a+b*sech(x)^2)^2 +--R +--R +--R 1 +--R (29) ------------------------------- +--R 2 4 2 2 +--R b sech(x) + 2a b sech(x) + a +--R Type: Expression Integer +--E 29 + +--S 30 of 526 +r0404:= x/a^2-2*b^(1/2)*atanh(b^(1/2)*tanh(x)/(a+b)^(1/2))/a^2/(a+b)^(1/2)+1/2*b^(1/2)*(a+2*b)*atanh(b^(1/2)*tanh(x)/(a+b)^(1/2))/a^2/(a+b)^(3/2)-b*tanh(x)/a^2/(a+b*sech(x)^2)+1/2*b*(a+2*b)*tanh(x)/a^2/(a+b)/(a+b*sech(x)^2) +--R +--R +--R (30) +--R +-+ +--R 2 2 2 +-+ tanh(x)\|b +--R ((- 2b - 3a b)sech(x) - 2a b - 3a )\|b atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 2 2 +-----+ +--R (- a b tanh(x) + (2b + 2a b)x sech(x) + (2a b + 2a )x)\|b + a +--R / +--R 2 2 3 2 3 4 +-----+ +--R ((2a b + 2a b)sech(x) + 2a b + 2a )\|b + a +--R Type: Expression Integer +--E 30 + +--S 31 of 526 +a0404:= integrate(t0404,x) +--R +--R +--R (31) +--R [ +--R 2 4 2 3 +--R (2a b + 3a )sinh(x) + (8a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((12a b + 18a )cosh(x) + 8b + 16a b + 6a )sinh(x) +--R + +--R 2 3 2 2 +--R ((8a b + 12a )cosh(x) + (16b + 32a b + 12a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (2a b + 3a )cosh(x) + (8b + 16a b + 6a )cosh(x) + 2a b + 3a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4a b + 4a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b + 4a )cosh(x) + 8b + 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b + 2a )cosh(x) + 8b + 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b + 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b + 2a)cosh(x) + a +--R + +--R 2 4 2 3 +--R (4a b + 4a )x sinh(x) + (16a b + 16a )x cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24a b + 24a )x cosh(x) + (16b + 24a b + 8a )x + 8b + 4a b)sinh(x) +--R + +--R 2 3 +--R (16a b + 16a )x cosh(x) +--R + +--R 2 2 2 +--R ((32b + 48a b + 16a )x + 16b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (4a b + 4a )x cosh(x) + ((16b + 24a b + 8a )x + 8b + 4a b)cosh(x) +--R + +--R 2 +--R (4a b + 4a )x + 4a b +--R / +--R 3 4 4 3 4 3 +--R (4a b + 4a )sinh(x) + (16a b + 16a )cosh(x)sinh(x) +--R + +--R 3 4 2 2 2 3 4 2 +--R ((24a b + 24a )cosh(x) + 16a b + 24a b + 8a )sinh(x) +--R + +--R 3 4 3 2 2 3 4 +--R ((16a b + 16a )cosh(x) + (32a b + 48a b + 16a )cosh(x))sinh(x) +--R + +--R 3 4 4 2 2 3 4 2 3 4 +--R (4a b + 4a )cosh(x) + (16a b + 24a b + 8a )cosh(x) + 4a b + 4a +--R , +--R +--R 2 4 2 3 +--R (- 2a b - 3a )sinh(x) + (- 8a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 12a b - 18a )cosh(x) - 8b - 16a b - 6a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 8a b - 12a )cosh(x) + (- 16b - 32a b - 12a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 2a b - 3a )cosh(x) + (- 8b - 16a b - 6a )cosh(x) - 2a b - 3a +--R * +--R +-------+ +--R | b +--R +-------+ (2b + 2a) |- ----- +--R | b \| b + a +--R |- ----- atan(----------------------------------------------------) +--R \| b + a 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b + a +--R + +--R 2 4 2 3 +--R (2a b + 2a )x sinh(x) + (8a b + 8a )x cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12a b + 12a )x cosh(x) + (8b + 12a b + 4a )x + 4b + 2a b)sinh(x) +--R + +--R 2 3 +--R (8a b + 8a )x cosh(x) +--R + +--R 2 2 2 +--R ((16b + 24a b + 8a )x + 8b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (2a b + 2a )x cosh(x) + ((8b + 12a b + 4a )x + 4b + 2a b)cosh(x) +--R + +--R 2 +--R (2a b + 2a )x + 2a b +--R / +--R 3 4 4 3 4 3 +--R (2a b + 2a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 3 4 2 2 2 3 4 2 +--R ((12a b + 12a )cosh(x) + 8a b + 12a b + 4a )sinh(x) +--R + +--R 3 4 3 2 2 3 4 +--R ((8a b + 8a )cosh(x) + (16a b + 24a b + 8a )cosh(x))sinh(x) +--R + +--R 3 4 4 2 2 3 4 2 3 4 +--R (2a b + 2a )cosh(x) + (8a b + 12a b + 4a )cosh(x) + 2a b + 2a +--R ] +--R Type: Union(List Expression Integer,...) +--E 31 + +--S 32 of 526 +m0404a:= a0404.1-r0404 +--R +--R +--R (32) +--R 2 2 2 2 3 4 +--R ((2a b + 3a b)sech(x) + 2a b + 3a )sinh(x) +--R + +--R 2 2 2 2 3 3 +--R ((8a b + 12a b)cosh(x)sech(x) + (8a b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((12a b + 18a b)cosh(x) + 8b + 16a b + 6a b)sech(x) +--R + +--R 2 3 2 2 2 3 +--R (12a b + 18a )cosh(x) + 8a b + 16a b + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((8a b + 12a b)cosh(x) + (16b + 32a b + 12a b)cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 3 2 2 3 +--R (8a b + 12a )cosh(x) + (16a b + 32a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 2 +--R (2a b + 3a b)cosh(x) + (8b + 16a b + 6a b)cosh(x) + 2a b +--R + +--R 2 +--R 3a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 4 2 2 3 2 2 3 +--R (2a b + 3a )cosh(x) + (8a b + 16a b + 6a )cosh(x) + 2a b + 3a +--R * +--R +-----+ +--R | b +-----+ +--R |----- \|b + a +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4a b + 4a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b + 4a )cosh(x) + 8b + 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b + 2a )cosh(x) + 8b + 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b + 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b + 2a)cosh(x) + a +--R + +--R 2 2 2 2 3 4 +--R ((4a b + 6a b)sech(x) + 4a b + 6a )sinh(x) +--R + +--R 2 2 2 2 3 3 +--R ((16a b + 24a b)cosh(x)sech(x) + (16a b + 24a )cosh(x))sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((24a b + 36a b)cosh(x) + 16b + 32a b + 12a b)sech(x) +--R + +--R 2 3 2 2 2 3 +--R (24a b + 36a )cosh(x) + 16a b + 32a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((16a b + 24a b)cosh(x) + (32b + 64a b + 24a b)cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 3 2 2 3 +--R (16a b + 24a )cosh(x) + (32a b + 64a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 2 +--R (4a b + 6a b)cosh(x) + (16b + 32a b + 12a b)cosh(x) + 4a b +--R + +--R 2 +--R 6a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 4 2 2 3 2 2 3 +--R (4a b + 6a )cosh(x) + (16a b + 32a b + 12a )cosh(x) + 4a b + 6a +--R * +--R +-+ +--R +-+ tanh(x)\|b +--R \|b atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 4 2 3 +--R 2a b sinh(x) + 8a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (12a b cosh(x) + 8a b + 4a b)sinh(x) +--R + +--R 2 3 2 2 2 4 +--R (8a b cosh(x) + (16a b + 8a b)cosh(x))sinh(x) + 2a b cosh(x) +--R + +--R 2 2 2 2 +--R (8a b + 4a b)cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 3 2 2 2 2 2 +--R ((8b + 4a b )sech(x) + 8a b + 4a b)sinh(x) +--R + +--R 3 2 2 2 2 +--R ((16b + 8a b )cosh(x)sech(x) + (16a b + 8a b)cosh(x))sinh(x) +--R + +--R 3 2 2 2 2 2 2 2 2 +--R ((8b + 4a b )cosh(x) + 4a b )sech(x) + (8a b + 4a b)cosh(x) + 4a b +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 2 4 2 4 5 4 +--R ((4a b + 4a b)sech(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 +--R ((16a b + 16a b)cosh(x)sech(x) + (16a b + 16a )cosh(x))sinh(x) +--R + +--R 3 2 4 2 2 3 3 2 4 2 +--R ((24a b + 24a b)cosh(x) + 16a b + 24a b + 8a b)sech(x) +--R + +--R 4 5 2 3 2 4 5 +--R (24a b + 24a )cosh(x) + 16a b + 24a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 3 2 4 +--R ((16a b + 16a b)cosh(x) + (32a b + 48a b + 16a b)cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 4 5 3 3 2 4 5 +--R (16a b + 16a )cosh(x) + (32a b + 48a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 4 4 2 3 3 2 4 2 3 2 +--R (4a b + 4a b)cosh(x) + (16a b + 24a b + 8a b)cosh(x) + 4a b +--R + +--R 4 +--R 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 5 4 3 2 4 5 2 4 5 +--R (4a b + 4a )cosh(x) + (16a b + 24a b + 8a )cosh(x) + 4a b + 4a +--R * +--R +-----+ +--R \|b + a +--R Type: Expression Integer +--E 32 + +--S 33 of 526 +d0404a:= D(m0404a,x) +--R +--R +--R (33) +--R 2 3 2 3 2 8 +--R (a b sech(x) - a b )sinh(x) +--R + +--R 2 3 2 3 2 7 +--R (8a b cosh(x)sech(x) - 8a b cosh(x))sinh(x) +--R + +--R 2 3 2 4 2 3 2 3 2 2 2 3 +--R (28a b cosh(x) + 8a b + 4a b )sech(x) - 28a b cosh(x) - 8a b +--R + +--R 3 2 +--R - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 4 2 3 2 +--R (56a b cosh(x) + (48a b + 24a b )cosh(x))sech(x) +--R + +--R 3 2 3 2 3 3 2 +--R - 56a b cosh(x) + (- 48a b - 24a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 4 4 2 3 2 5 4 +--R 70a b cosh(x) + (120a b + 60a b )cosh(x) + 16b + 16a b +--R + +--R 2 3 +--R 6a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 2 3 3 2 2 4 2 3 +--R - 70a b cosh(x) + (- 120a b - 60a b )cosh(x) - 16a b - 16a b +--R + +--R 3 2 +--R - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 4 2 3 3 +--R 56a b cosh(x) + (160a b + 80a b )cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 64a b + 24a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 5 2 3 3 2 3 +--R - 56a b cosh(x) + (- 160a b - 80a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 64a b - 64a b - 24a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 6 4 2 3 4 +--R 28a b cosh(x) + (120a b + 60a b )cosh(x) +--R + +--R 5 4 2 3 2 4 2 3 +--R (96b + 96a b + 36a b )cosh(x) + 8a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 6 2 3 3 2 4 +--R - 28a b cosh(x) + (- 120a b - 60a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (- 96a b - 96a b - 36a b )cosh(x) - 8a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 7 4 2 3 5 +--R 8a b cosh(x) + (48a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 4 2 3 +--R (64b + 64a b + 24a b )cosh(x) + (16a b + 8a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 7 2 3 3 2 5 +--R - 8a b cosh(x) + (- 48a b - 24a b )cosh(x) +--R + +--R 4 2 3 3 2 3 2 3 3 2 +--R (- 64a b - 64a b - 24a b )cosh(x) + (- 16a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 8 4 2 3 6 +--R a b cosh(x) + (8a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 4 4 2 3 2 2 3 +--R (16b + 16a b + 6a b )cosh(x) + (8a b + 4a b )cosh(x) + a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 8 2 3 3 2 6 +--R - a b cosh(x) + (- 8a b - 4a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 2 3 2 +--R (- 16a b - 16a b - 6a b )cosh(x) + (- 8a b - 4a b )cosh(x) - a b +--R * +--R 4 +--R tanh(x) +--R + +--R 4 2 3 4 2 3 3 2 2 3 2 4 +--R ((2a b + 3a b )sech(x) + (4a b + 5a b )sech(x) + 4a b + 4a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 3 4 +--R (16a b + 24a b )cosh(x)sech(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (32a b + 40a b )cosh(x)sech(x) + (32a b + 32a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 2 4 2 3 4 +--R ((56a b + 84a b )cosh(x) + 16a b + 12a b )sech(x) +--R + +--R 2 3 3 2 2 2 3 3 2 2 +--R ((112a b + 140a b )cosh(x) + 24a b + 20a b )sech(x) +--R + +--R 3 2 4 2 2 3 3 2 4 +--R (112a b + 112a b)cosh(x) + 16a b + 32a b + 16a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 4 2 3 4 +--R ((112a b + 168a b )cosh(x) + (96a b + 72a b )cosh(x))sech(x) +--R + +--R 2 3 3 2 3 2 3 3 2 +--R ((224a b + 280a b )cosh(x) + (144a b + 120a b )cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 3 3 2 4 +--R (224a b + 224a b)cosh(x) + (96a b + 192a b + 96a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 4 4 2 3 2 +--R (140a b + 210a b )cosh(x) + (240a b + 180a b )cosh(x) +--R + +--R 5 4 2 3 +--R 16b + 28a b + 18a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 4 2 3 3 2 2 +--R (280a b + 350a b )cosh(x) + (360a b + 300a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R 16a b + 40a b + 30a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 4 2 3 3 2 4 2 +--R (280a b + 280a b)cosh(x) + (240a b + 480a b + 240a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R 32a b + 64a b + 56a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 5 4 2 3 3 +--R (112a b + 168a b )cosh(x) + (320a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 112a b + 72a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 5 2 3 3 2 3 +--R (224a b + 280a b )cosh(x) + (480a b + 400a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (64a b + 160a b + 120a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 5 2 3 3 2 4 3 +--R (224a b + 224a b)cosh(x) + (320a b + 640a b + 320a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (128a b + 256a b + 224a b + 96a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 6 4 2 3 4 +--R (56a b + 84a b )cosh(x) + (240a b + 180a b )cosh(x) +--R + +--R 5 4 2 3 2 4 2 3 +--R (96b + 168a b + 108a b )cosh(x) + 16a b + 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 6 2 3 3 2 4 +--R (112a b + 140a b )cosh(x) + (360a b + 300a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (96a b + 240a b + 180a b )cosh(x) + 24a b + 20a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 6 2 3 3 2 4 4 +--R (112a b + 112a b)cosh(x) + (240a b + 480a b + 240a b)cosh(x) +--R + +--R 4 2 3 3 2 4 2 2 3 3 2 +--R (192a b + 384a b + 336a b + 144a b)cosh(x) + 16a b + 32a b +--R + +--R 4 +--R 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 7 4 2 3 5 +--R (16a b + 24a b )cosh(x) + (96a b + 72a b )cosh(x) +--R + +--R 5 4 2 3 3 4 2 3 +--R (64b + 112a b + 72a b )cosh(x) + (32a b + 24a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 7 2 3 3 2 5 +--R (32a b + 40a b )cosh(x) + (144a b + 120a b )cosh(x) +--R + +--R 4 2 3 3 2 3 2 3 3 2 +--R (64a b + 160a b + 120a b )cosh(x) + (48a b + 40a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 +--R (32a b + 32a b)cosh(x) + (96a b + 192a b + 96a b)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (128a b + 256a b + 224a b + 96a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (32a b + 64a b + 32a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 8 4 2 3 6 +--R (2a b + 3a b )cosh(x) + (16a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 4 4 2 3 2 +--R (16b + 28a b + 18a b )cosh(x) + (16a b + 12a b )cosh(x) +--R + +--R 4 2 3 +--R 2a b + 3a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 8 2 3 3 2 6 +--R (4a b + 5a b )cosh(x) + (24a b + 20a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 2 +--R (16a b + 40a b + 30a b )cosh(x) + (24a b + 20a b )cosh(x) +--R + +--R 2 3 3 2 +--R 4a b + 5a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 8 2 3 3 2 4 6 +--R (4a b + 4a b)cosh(x) + (16a b + 32a b + 16a b)cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (32a b + 64a b + 56a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 4 2 3 2 4 +--R (16a b + 32a b + 16a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 2 3 4 2 3 3 2 2 3 2 4 +--R ((- 2a b - 3a b )sech(x) + (- 5a b - 7a b )sech(x) - 3a b - 4a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 3 4 +--R (- 16a b - 24a b )cosh(x)sech(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 40a b - 56a b )cosh(x)sech(x) + (- 24a b - 32a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 2 2 3 4 +--R ((- 56a b - 84a b )cosh(x) + 4a b )sech(x) +--R + +--R 2 3 3 2 2 4 2 3 3 2 2 +--R ((- 140a b - 196a b )cosh(x) - 8a b - 12a b + 4a b )sech(x) +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 84a b - 112a b)cosh(x) - 8a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 2 3 4 +--R ((- 112a b - 168a b )cosh(x) + 24a b cosh(x))sech(x) +--R + +--R 2 3 3 2 3 +--R (- 280a b - 392a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 48a b - 72a b + 24a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 3 3 2 +--R (- 168a b - 224a b)cosh(x) + (- 48a b - 72a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 4 2 3 2 5 4 +--R (- 140a b - 210a b )cosh(x) + 60a b cosh(x) + 16b + 36a b +--R + +--R 2 3 +--R 14a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 4 +--R (- 350a b - 490a b )cosh(x) +--R + +--R 4 2 3 3 2 2 5 2 3 3 2 +--R (- 120a b - 180a b + 60a b )cosh(x) - 16b + 50a b + 22a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 4 2 3 3 2 2 4 +--R (- 210a b - 280a b)cosh(x) + (- 120a b - 180a b )cosh(x) - 16a b +--R + +--R 2 3 3 2 4 +--R - 16a b + 14a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 5 2 3 3 +--R (- 112a b - 168a b )cosh(x) + 80a b cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 144a b + 56a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 5 +--R (- 280a b - 392a b )cosh(x) +--R + +--R 4 2 3 3 2 3 +--R (- 160a b - 240a b + 80a b )cosh(x) +--R + +--R 5 2 3 3 2 +--R (- 64b + 200a b + 88a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 5 2 3 3 2 3 +--R (- 168a b - 224a b)cosh(x) + (- 160a b - 240a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 64a b - 64a b + 56a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 6 2 3 4 +--R (- 56a b - 84a b )cosh(x) + 60a b cosh(x) +--R + +--R 5 4 2 3 2 2 3 +--R (96b + 216a b + 84a b )cosh(x) + 4a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 6 +--R (- 140a b - 196a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 120a b - 180a b + 60a b )cosh(x) +--R + +--R 5 2 3 3 2 2 4 2 3 3 2 +--R (- 96b + 300a b + 132a b )cosh(x) - 8a b - 12a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 6 2 3 3 2 4 +--R (- 84a b - 112a b)cosh(x) + (- 120a b - 180a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 2 3 3 2 +--R (- 96a b - 96a b + 84a b + 48a b)cosh(x) - 8a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 7 2 3 5 +--R (- 16a b - 24a b )cosh(x) + 24a b cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (64b + 144a b + 56a b )cosh(x) + 8a b cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 7 +--R (- 40a b - 56a b )cosh(x) +--R + +--R 4 2 3 3 2 5 +--R (- 48a b - 72a b + 24a b )cosh(x) +--R + +--R 5 2 3 3 2 3 +--R (- 64b + 200a b + 88a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 16a b - 24a b + 8a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 7 2 3 3 2 5 +--R (- 24a b - 32a b)cosh(x) + (- 48a b - 72a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 64a b - 64a b + 56a b + 32a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 16a b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 8 2 3 6 +--R (- 2a b - 3a b )cosh(x) + 4a b cosh(x) +--R + +--R 5 4 2 3 4 2 3 2 4 2 3 +--R (16b + 36a b + 14a b )cosh(x) + 4a b cosh(x) - 2a b - 3a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 8 4 2 3 3 2 6 +--R (- 5a b - 7a b )cosh(x) + (- 8a b - 12a b + 4a b )cosh(x) +--R + +--R 5 2 3 3 2 4 +--R (- 16b + 50a b + 22a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (- 8a b - 12a b + 4a b )cosh(x) - 5a b - 7a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 8 2 3 3 2 6 +--R (- 3a b - 4a b)cosh(x) + (- 8a b - 12a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 2 +--R (- 16a b - 16a b + 14a b + 8a b)cosh(x) + (- 8a b - 12a b )cosh(x) +--R + +--R 3 2 4 +--R - 3a b - 4a b +--R / +--R 3 4 4 3 4 4 3 5 2 2 5 2 6 +--R ((2a b + 2a b )sech(x) + (4a b + 4a b )sech(x) + 2a b + 2a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 4 3 4 +--R (16a b + 16a b )cosh(x)sech(x) +--R + +--R 4 3 5 2 2 5 2 6 +--R (32a b + 32a b )cosh(x)sech(x) + (16a b + 16a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 2 2 5 3 4 4 3 4 +--R ((56a b + 56a b )cosh(x) + 16a b + 24a b + 8a b )sech(x) +--R + +--R 4 3 5 2 2 3 4 4 3 5 2 2 +--R ((112a b + 112a b )cosh(x) + 32a b + 48a b + 16a b )sech(x) +--R + +--R 5 2 6 2 4 3 5 2 6 +--R (56a b + 56a b)cosh(x) + 16a b + 24a b + 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 4 3 3 +--R (112a b + 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 +--R (96a b + 144a b + 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 3 +--R (224a b + 224a b )cosh(x) +--R + +--R 3 4 4 3 5 2 +--R (192a b + 288a b + 96a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 3 4 3 5 2 6 +--R (112a b + 112a b)cosh(x) + (96a b + 144a b + 48a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 4 3 4 +--R (140a b + 140a b )cosh(x) +--R + +--R 2 5 3 4 4 3 2 6 2 5 +--R (240a b + 360a b + 120a b )cosh(x) + 32a b + 64a b +--R + +--R 3 4 4 3 +--R 44a b + 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 4 +--R (280a b + 280a b )cosh(x) +--R + +--R 3 4 4 3 5 2 2 2 5 3 4 +--R (480a b + 720a b + 240a b )cosh(x) + 64a b + 128a b +--R + +--R 4 3 5 2 +--R 88a b + 24a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 4 4 3 5 2 6 2 +--R (140a b + 140a b)cosh(x) + (240a b + 360a b + 120a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R 32a b + 64a b + 44a b + 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 +--R (112a b + 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 3 +--R (320a b + 480a b + 160a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 +--R (128a b + 256a b + 176a b + 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 5 +--R (224a b + 224a b )cosh(x) +--R + +--R 3 4 4 3 5 2 3 +--R (640a b + 960a b + 320a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (256a b + 512a b + 352a b + 96a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 5 4 3 5 2 6 3 +--R (112a b + 112a b)cosh(x) + (320a b + 480a b + 160a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (128a b + 256a b + 176a b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 6 +--R (56a b + 56a b )cosh(x) +--R + +--R 2 5 3 4 4 3 4 +--R (240a b + 360a b + 120a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 2 2 5 +--R (192a b + 384a b + 264a b + 72a b )cosh(x) + 16a b +--R + +--R 3 4 4 3 +--R 24a b + 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 +--R (112a b + 112a b )cosh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (480a b + 720a b + 240a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 3 4 +--R (384a b + 768a b + 528a b + 144a b )cosh(x) + 32a b +--R + +--R 4 3 5 2 +--R 48a b + 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 6 4 3 5 2 6 4 +--R (56a b + 56a b)cosh(x) + (240a b + 360a b + 120a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 4 3 5 2 +--R (192a b + 384a b + 264a b + 72a b)cosh(x) + 16a b + 24a b +--R + +--R 6 +--R 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 7 +--R (16a b + 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 +--R (96a b + 144a b + 48a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (128a b + 256a b + 176a b + 48a b )cosh(x) +--R + +--R 2 5 3 4 4 3 +--R (32a b + 48a b + 16a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 7 +--R (32a b + 32a b )cosh(x) +--R + +--R 3 4 4 3 5 2 5 +--R (192a b + 288a b + 96a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (256a b + 512a b + 352a b + 96a b )cosh(x) +--R + +--R 3 4 4 3 5 2 +--R (64a b + 96a b + 32a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 4 3 5 2 6 5 +--R (16a b + 16a b)cosh(x) + (96a b + 144a b + 48a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 3 +--R (128a b + 256a b + 176a b + 48a b)cosh(x) +--R + +--R 4 3 5 2 6 +--R (32a b + 48a b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 8 2 5 3 4 4 3 6 +--R (2a b + 2a b )cosh(x) + (16a b + 24a b + 8a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 4 +--R (32a b + 64a b + 44a b + 12a b )cosh(x) +--R + +--R 2 5 3 4 4 3 2 3 4 4 3 +--R (16a b + 24a b + 8a b )cosh(x) + 2a b + 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 8 3 4 4 3 5 2 6 +--R (4a b + 4a b )cosh(x) + (32a b + 48a b + 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 4 +--R (64a b + 128a b + 88a b + 24a b )cosh(x) +--R + +--R 3 4 4 3 5 2 2 4 3 5 2 +--R (32a b + 48a b + 16a b )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 8 4 3 5 2 6 6 +--R (2a b + 2a b)cosh(x) + (16a b + 24a b + 8a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (32a b + 64a b + 44a b + 12a b)cosh(x) +--R + +--R 4 3 5 2 6 2 5 2 6 +--R (16a b + 24a b + 8a b)cosh(x) + 2a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 +--R (- 2a b - 4a b - 2a b )sech(x) + (- 4a b - 8a b - 4a b)sech(x) +--R + +--R 5 2 6 7 +--R - 2a b - 4a b - 2a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (- 16a b - 32a b - 16a b )cosh(x)sech(x) +--R + +--R 4 3 5 2 6 2 +--R (- 32a b - 64a b - 32a b)cosh(x)sech(x) +--R + +--R 5 2 6 7 +--R (- 16a b - 32a b - 16a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 2 2 5 3 4 4 3 +--R (- 56a b - 112a b - 56a b )cosh(x) - 16a b - 40a b - 32a b +--R + +--R 5 2 +--R - 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 2 3 4 4 3 5 2 +--R (- 112a b - 224a b - 112a b)cosh(x) - 32a b - 80a b - 64a b +--R + +--R 6 +--R - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 2 4 3 5 2 6 7 +--R (- 56a b - 112a b - 56a )cosh(x) - 16a b - 40a b - 32a b - 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 3 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- 96a b - 240a b - 192a b - 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 3 +--R (- 224a b - 448a b - 224a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 192a b - 480a b - 384a b - 96a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 3 +--R (- 112a b - 224a b - 112a )cosh(x) +--R + +--R 4 3 5 2 6 7 +--R (- 96a b - 240a b - 192a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (- 140a b - 280a b - 140a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 6 +--R (- 240a b - 600a b - 480a b - 120a b )cosh(x) - 32a b +--R + +--R 2 5 3 4 4 3 5 2 +--R - 96a b - 108a b - 56a b - 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 4 +--R (- 280a b - 560a b - 280a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 2 5 +--R (- 480a b - 1200a b - 960a b - 240a b)cosh(x) - 64a b +--R + +--R 3 4 4 3 5 2 6 +--R - 192a b - 216a b - 112a b - 24a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 4 +--R (- 140a b - 280a b - 140a )cosh(x) +--R + +--R 4 3 5 2 6 7 2 3 4 4 3 +--R (- 240a b - 600a b - 480a b - 120a )cosh(x) - 32a b - 96a b +--R + +--R 5 2 6 7 +--R - 108a b - 56a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 5 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (- 320a b - 800a b - 640a b - 160a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (- 128a b - 384a b - 432a b - 224a b - 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 5 +--R (- 224a b - 448a b - 224a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 3 +--R (- 640a b - 1600a b - 1280a b - 320a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 256a b - 768a b - 864a b - 448a b - 96a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 5 +--R (- 112a b - 224a b - 112a )cosh(x) +--R + +--R 4 3 5 2 6 7 3 +--R (- 320a b - 800a b - 640a b - 160a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R (- 128a b - 384a b - 432a b - 224a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 56a b - 112a b - 56a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 4 +--R (- 240a b - 600a b - 480a b - 120a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 +--R (- 192a b - 576a b - 648a b - 336a b - 72a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 16a b - 40a b - 32a b - 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 6 +--R (- 112a b - 224a b - 112a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 480a b - 1200a b - 960a b - 240a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 +--R (- 384a b - 1152a b - 1296a b - 672a b - 144a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R - 32a b - 80a b - 64a b - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 6 +--R (- 56a b - 112a b - 56a )cosh(x) +--R + +--R 4 3 5 2 6 7 4 +--R (- 240a b - 600a b - 480a b - 120a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 4 3 +--R (- 192a b - 576a b - 648a b - 336a b - 72a )cosh(x) - 16a b +--R + +--R 5 2 6 7 +--R - 40a b - 32a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 7 +--R (- 16a b - 32a b - 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 5 +--R (- 96a b - 240a b - 192a b - 48a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (- 128a b - 384a b - 432a b - 224a b - 48a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- 32a b - 80a b - 64a b - 16a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 7 +--R (- 32a b - 64a b - 32a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 5 +--R (- 192a b - 480a b - 384a b - 96a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (- 256a b - 768a b - 864a b - 448a b - 96a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 64a b - 160a b - 128a b - 32a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 7 +--R (- 16a b - 32a b - 16a )cosh(x) +--R + +--R 4 3 5 2 6 7 5 +--R (- 96a b - 240a b - 192a b - 48a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (- 128a b - 384a b - 432a b - 224a b - 48a )cosh(x) +--R + +--R 4 3 5 2 6 7 +--R (- 32a b - 80a b - 64a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 5 2 8 +--R (- 2a b - 4a b - 2a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 16a b - 40a b - 32a b - 8a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (- 32a b - 96a b - 108a b - 56a b - 12a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 3 4 4 3 5 2 +--R (- 16a b - 40a b - 32a b - 8a b )cosh(x) - 2a b - 4a b - 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 8 +--R (- 4a b - 8a b - 4a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (- 32a b - 80a b - 64a b - 16a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (- 64a b - 192a b - 216a b - 112a b - 24a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 4 3 5 2 6 +--R (- 32a b - 80a b - 64a b - 16a b)cosh(x) - 4a b - 8a b - 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 8 +--R (- 2a b - 4a b - 2a )cosh(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 16a b - 40a b - 32a b - 8a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- 32a b - 96a b - 108a b - 56a b - 12a )cosh(x) +--R + +--R 4 3 5 2 6 7 2 5 2 6 7 +--R (- 16a b - 40a b - 32a b - 8a )cosh(x) - 2a b - 4a b - 2a +--R Type: Expression Integer +--E 33 + +--S 34 of 526 +m0404b:= a0404.2-r0404 +--R +--R +--R (34) +--R 2 2 2 2 3 4 +--R ((2a b + 3a b)sech(x) + 2a b + 3a )sinh(x) +--R + +--R 2 2 2 2 3 3 +--R ((8a b + 12a b)cosh(x)sech(x) + (8a b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((12a b + 18a b)cosh(x) + 8b + 16a b + 6a b)sech(x) +--R + +--R 2 3 2 2 2 3 +--R (12a b + 18a )cosh(x) + 8a b + 16a b + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((8a b + 12a b)cosh(x) + (16b + 32a b + 12a b)cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 3 2 2 3 +--R (8a b + 12a )cosh(x) + (16a b + 32a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 2 +--R (2a b + 3a b)cosh(x) + (8b + 16a b + 6a b)cosh(x) + 2a b +--R + +--R 2 +--R 3a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 4 2 2 3 2 2 3 +--R (2a b + 3a )cosh(x) + (8a b + 16a b + 6a )cosh(x) + 2a b + 3a +--R * +--R +-+ +--R +-+ tanh(x)\|b +--R \|b atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 2 2 2 3 4 +--R ((- 2a b - 3a b)sech(x) - 2a b - 3a )sinh(x) +--R + +--R 2 2 2 2 3 3 +--R ((- 8a b - 12a b)cosh(x)sech(x) + (- 8a b - 12a )cosh(x))sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((- 12a b - 18a b)cosh(x) - 8b - 16a b - 6a b)sech(x) +--R + +--R 2 3 2 2 2 3 +--R (- 12a b - 18a )cosh(x) - 8a b - 16a b - 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((- 8a b - 12a b)cosh(x) + (- 16b - 32a b - 12a b)cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 3 2 2 3 +--R (- 8a b - 12a )cosh(x) + (- 16a b - 32a b - 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R (- 2a b - 3a b)cosh(x) + (- 8b - 16a b - 6a b)cosh(x) +--R + +--R 2 2 +--R - 2a b - 3a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 4 2 2 3 2 2 3 +--R (- 2a b - 3a )cosh(x) + (- 8a b - 16a b - 6a )cosh(x) - 2a b - 3a +--R * +--R +-------+ +--R | b +-----+ +--R |- ----- \|b + a +--R \| b + a +--R * +--R +-------+ +--R | b +--R (2b + 2a) |- ----- +--R \| b + a +--R atan(----------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b + a +--R + +--R 2 4 2 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a b cosh(x) + 4a b + 2a b)sinh(x) +--R + +--R 2 3 2 2 2 4 +--R (4a b cosh(x) + (8a b + 4a b)cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 2 2 +--R (4a b + 2a b)cosh(x) + a b +--R * +--R tanh(x) +--R + +--R 3 2 2 2 2 2 +--R ((4b + 2a b )sech(x) + 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 2 2 +--R ((8b + 4a b )cosh(x)sech(x) + (8a b + 4a b)cosh(x))sinh(x) +--R + +--R 3 2 2 2 2 2 2 2 2 +--R ((4b + 2a b )cosh(x) + 2a b )sech(x) + (4a b + 2a b)cosh(x) + 2a b +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 2 4 2 4 5 4 +--R ((2a b + 2a b)sech(x) + 2a b + 2a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 +--R ((8a b + 8a b)cosh(x)sech(x) + (8a b + 8a )cosh(x))sinh(x) +--R + +--R 3 2 4 2 2 3 3 2 4 2 +--R ((12a b + 12a b)cosh(x) + 8a b + 12a b + 4a b)sech(x) +--R + +--R 4 5 2 3 2 4 5 +--R (12a b + 12a )cosh(x) + 8a b + 12a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 3 2 4 2 +--R ((8a b + 8a b)cosh(x) + (16a b + 24a b + 8a b)cosh(x))sech(x) +--R + +--R 4 5 3 3 2 4 5 +--R (8a b + 8a )cosh(x) + (16a b + 24a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 4 4 2 3 3 2 4 2 3 2 +--R (2a b + 2a b)cosh(x) + (8a b + 12a b + 4a b)cosh(x) + 2a b +--R + +--R 4 +--R 2a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 5 4 3 2 4 5 2 4 5 +--R (2a b + 2a )cosh(x) + (8a b + 12a b + 4a )cosh(x) + 2a b + 2a +--R * +--R +-----+ +--R \|b + a +--R Type: Expression Integer +--E 34 + +--S 35 of 526 +d0404b:= D(m0404b,x) +--R +--R +--R (35) +--R 2 3 2 3 2 8 +--R (a b sech(x) - a b )sinh(x) +--R + +--R 2 3 2 3 2 7 +--R (8a b cosh(x)sech(x) - 8a b cosh(x))sinh(x) +--R + +--R 2 3 2 4 2 3 2 3 2 2 2 3 +--R (28a b cosh(x) + 8a b + 4a b )sech(x) - 28a b cosh(x) - 8a b +--R + +--R 3 2 +--R - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 4 2 3 2 +--R (56a b cosh(x) + (48a b + 24a b )cosh(x))sech(x) +--R + +--R 3 2 3 2 3 3 2 +--R - 56a b cosh(x) + (- 48a b - 24a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 4 4 2 3 2 5 4 +--R 70a b cosh(x) + (120a b + 60a b )cosh(x) + 16b + 16a b +--R + +--R 2 3 +--R 6a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 2 3 3 2 2 4 2 3 +--R - 70a b cosh(x) + (- 120a b - 60a b )cosh(x) - 16a b - 16a b +--R + +--R 3 2 +--R - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 4 2 3 3 +--R 56a b cosh(x) + (160a b + 80a b )cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 64a b + 24a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 5 2 3 3 2 3 +--R - 56a b cosh(x) + (- 160a b - 80a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 64a b - 64a b - 24a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 6 4 2 3 4 +--R 28a b cosh(x) + (120a b + 60a b )cosh(x) +--R + +--R 5 4 2 3 2 4 2 3 +--R (96b + 96a b + 36a b )cosh(x) + 8a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 6 2 3 3 2 4 +--R - 28a b cosh(x) + (- 120a b - 60a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (- 96a b - 96a b - 36a b )cosh(x) - 8a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 7 4 2 3 5 +--R 8a b cosh(x) + (48a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 4 2 3 +--R (64b + 64a b + 24a b )cosh(x) + (16a b + 8a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 7 2 3 3 2 5 +--R - 8a b cosh(x) + (- 48a b - 24a b )cosh(x) +--R + +--R 4 2 3 3 2 3 2 3 3 2 +--R (- 64a b - 64a b - 24a b )cosh(x) + (- 16a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 8 4 2 3 6 +--R a b cosh(x) + (8a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 4 4 2 3 2 2 3 +--R (16b + 16a b + 6a b )cosh(x) + (8a b + 4a b )cosh(x) + a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 8 2 3 3 2 6 +--R - a b cosh(x) + (- 8a b - 4a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 2 3 2 +--R (- 16a b - 16a b - 6a b )cosh(x) + (- 8a b - 4a b )cosh(x) - a b +--R * +--R 4 +--R tanh(x) +--R + +--R 4 2 3 4 2 3 3 2 2 3 2 4 +--R ((2a b + 3a b )sech(x) + (4a b + 5a b )sech(x) + 4a b + 4a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 3 4 +--R (16a b + 24a b )cosh(x)sech(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (32a b + 40a b )cosh(x)sech(x) + (32a b + 32a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 2 4 2 3 4 +--R ((56a b + 84a b )cosh(x) + 16a b + 12a b )sech(x) +--R + +--R 2 3 3 2 2 2 3 3 2 2 +--R ((112a b + 140a b )cosh(x) + 24a b + 20a b )sech(x) +--R + +--R 3 2 4 2 2 3 3 2 4 +--R (112a b + 112a b)cosh(x) + 16a b + 32a b + 16a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 4 2 3 4 +--R ((112a b + 168a b )cosh(x) + (96a b + 72a b )cosh(x))sech(x) +--R + +--R 2 3 3 2 3 2 3 3 2 +--R ((224a b + 280a b )cosh(x) + (144a b + 120a b )cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 3 3 2 4 +--R (224a b + 224a b)cosh(x) + (96a b + 192a b + 96a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 4 4 2 3 2 +--R (140a b + 210a b )cosh(x) + (240a b + 180a b )cosh(x) +--R + +--R 5 4 2 3 +--R 16b + 28a b + 18a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 4 2 3 3 2 2 +--R (280a b + 350a b )cosh(x) + (360a b + 300a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R 16a b + 40a b + 30a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 4 2 3 3 2 4 2 +--R (280a b + 280a b)cosh(x) + (240a b + 480a b + 240a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R 32a b + 64a b + 56a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 5 4 2 3 3 +--R (112a b + 168a b )cosh(x) + (320a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 112a b + 72a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 5 2 3 3 2 3 +--R (224a b + 280a b )cosh(x) + (480a b + 400a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (64a b + 160a b + 120a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 5 2 3 3 2 4 3 +--R (224a b + 224a b)cosh(x) + (320a b + 640a b + 320a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (128a b + 256a b + 224a b + 96a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 6 4 2 3 4 +--R (56a b + 84a b )cosh(x) + (240a b + 180a b )cosh(x) +--R + +--R 5 4 2 3 2 4 2 3 +--R (96b + 168a b + 108a b )cosh(x) + 16a b + 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 6 2 3 3 2 4 +--R (112a b + 140a b )cosh(x) + (360a b + 300a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (96a b + 240a b + 180a b )cosh(x) + 24a b + 20a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 6 2 3 3 2 4 4 +--R (112a b + 112a b)cosh(x) + (240a b + 480a b + 240a b)cosh(x) +--R + +--R 4 2 3 3 2 4 2 2 3 3 2 +--R (192a b + 384a b + 336a b + 144a b)cosh(x) + 16a b + 32a b +--R + +--R 4 +--R 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 7 4 2 3 5 +--R (16a b + 24a b )cosh(x) + (96a b + 72a b )cosh(x) +--R + +--R 5 4 2 3 3 4 2 3 +--R (64b + 112a b + 72a b )cosh(x) + (32a b + 24a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 7 2 3 3 2 5 +--R (32a b + 40a b )cosh(x) + (144a b + 120a b )cosh(x) +--R + +--R 4 2 3 3 2 3 2 3 3 2 +--R (64a b + 160a b + 120a b )cosh(x) + (48a b + 40a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 +--R (32a b + 32a b)cosh(x) + (96a b + 192a b + 96a b)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (128a b + 256a b + 224a b + 96a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (32a b + 64a b + 32a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 8 4 2 3 6 +--R (2a b + 3a b )cosh(x) + (16a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 4 4 2 3 2 +--R (16b + 28a b + 18a b )cosh(x) + (16a b + 12a b )cosh(x) +--R + +--R 4 2 3 +--R 2a b + 3a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 8 2 3 3 2 6 +--R (4a b + 5a b )cosh(x) + (24a b + 20a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 2 +--R (16a b + 40a b + 30a b )cosh(x) + (24a b + 20a b )cosh(x) +--R + +--R 2 3 3 2 +--R 4a b + 5a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 8 2 3 3 2 4 6 +--R (4a b + 4a b)cosh(x) + (16a b + 32a b + 16a b)cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (32a b + 64a b + 56a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 4 2 3 2 4 +--R (16a b + 32a b + 16a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 2 3 4 2 3 3 2 2 3 2 4 +--R ((- 2a b - 3a b )sech(x) + (- 5a b - 7a b )sech(x) - 3a b - 4a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 3 4 +--R (- 16a b - 24a b )cosh(x)sech(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 40a b - 56a b )cosh(x)sech(x) + (- 24a b - 32a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 2 2 3 4 +--R ((- 56a b - 84a b )cosh(x) + 4a b )sech(x) +--R + +--R 2 3 3 2 2 4 2 3 3 2 2 +--R ((- 140a b - 196a b )cosh(x) - 8a b - 12a b + 4a b )sech(x) +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 84a b - 112a b)cosh(x) - 8a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 2 3 4 +--R ((- 112a b - 168a b )cosh(x) + 24a b cosh(x))sech(x) +--R + +--R 2 3 3 2 3 +--R (- 280a b - 392a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 48a b - 72a b + 24a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 3 3 2 +--R (- 168a b - 224a b)cosh(x) + (- 48a b - 72a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 4 2 3 2 5 4 +--R (- 140a b - 210a b )cosh(x) + 60a b cosh(x) + 16b + 36a b +--R + +--R 2 3 +--R 14a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 4 +--R (- 350a b - 490a b )cosh(x) +--R + +--R 4 2 3 3 2 2 5 2 3 3 2 +--R (- 120a b - 180a b + 60a b )cosh(x) - 16b + 50a b + 22a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 4 2 3 3 2 2 4 +--R (- 210a b - 280a b)cosh(x) + (- 120a b - 180a b )cosh(x) - 16a b +--R + +--R 2 3 3 2 4 +--R - 16a b + 14a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 5 2 3 3 +--R (- 112a b - 168a b )cosh(x) + 80a b cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 144a b + 56a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 5 +--R (- 280a b - 392a b )cosh(x) +--R + +--R 4 2 3 3 2 3 +--R (- 160a b - 240a b + 80a b )cosh(x) +--R + +--R 5 2 3 3 2 +--R (- 64b + 200a b + 88a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 5 2 3 3 2 3 +--R (- 168a b - 224a b)cosh(x) + (- 160a b - 240a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 64a b - 64a b + 56a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 6 2 3 4 +--R (- 56a b - 84a b )cosh(x) + 60a b cosh(x) +--R + +--R 5 4 2 3 2 2 3 +--R (96b + 216a b + 84a b )cosh(x) + 4a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 6 +--R (- 140a b - 196a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 120a b - 180a b + 60a b )cosh(x) +--R + +--R 5 2 3 3 2 2 4 2 3 3 2 +--R (- 96b + 300a b + 132a b )cosh(x) - 8a b - 12a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 6 2 3 3 2 4 +--R (- 84a b - 112a b)cosh(x) + (- 120a b - 180a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 2 3 3 2 +--R (- 96a b - 96a b + 84a b + 48a b)cosh(x) - 8a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 7 2 3 5 +--R (- 16a b - 24a b )cosh(x) + 24a b cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (64b + 144a b + 56a b )cosh(x) + 8a b cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 7 +--R (- 40a b - 56a b )cosh(x) +--R + +--R 4 2 3 3 2 5 +--R (- 48a b - 72a b + 24a b )cosh(x) +--R + +--R 5 2 3 3 2 3 +--R (- 64b + 200a b + 88a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 16a b - 24a b + 8a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 7 2 3 3 2 5 +--R (- 24a b - 32a b)cosh(x) + (- 48a b - 72a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 64a b - 64a b + 56a b + 32a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 16a b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 8 2 3 6 +--R (- 2a b - 3a b )cosh(x) + 4a b cosh(x) +--R + +--R 5 4 2 3 4 2 3 2 4 2 3 +--R (16b + 36a b + 14a b )cosh(x) + 4a b cosh(x) - 2a b - 3a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 8 4 2 3 3 2 6 +--R (- 5a b - 7a b )cosh(x) + (- 8a b - 12a b + 4a b )cosh(x) +--R + +--R 5 2 3 3 2 4 +--R (- 16b + 50a b + 22a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (- 8a b - 12a b + 4a b )cosh(x) - 5a b - 7a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 8 2 3 3 2 6 +--R (- 3a b - 4a b)cosh(x) + (- 8a b - 12a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 2 +--R (- 16a b - 16a b + 14a b + 8a b)cosh(x) + (- 8a b - 12a b )cosh(x) +--R + +--R 3 2 4 +--R - 3a b - 4a b +--R / +--R 3 4 4 3 4 4 3 5 2 2 5 2 6 +--R ((2a b + 2a b )sech(x) + (4a b + 4a b )sech(x) + 2a b + 2a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 4 3 4 +--R (16a b + 16a b )cosh(x)sech(x) +--R + +--R 4 3 5 2 2 5 2 6 +--R (32a b + 32a b )cosh(x)sech(x) + (16a b + 16a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 2 2 5 3 4 4 3 4 +--R ((56a b + 56a b )cosh(x) + 16a b + 24a b + 8a b )sech(x) +--R + +--R 4 3 5 2 2 3 4 4 3 5 2 2 +--R ((112a b + 112a b )cosh(x) + 32a b + 48a b + 16a b )sech(x) +--R + +--R 5 2 6 2 4 3 5 2 6 +--R (56a b + 56a b)cosh(x) + 16a b + 24a b + 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 4 3 3 +--R (112a b + 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 +--R (96a b + 144a b + 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 3 +--R (224a b + 224a b )cosh(x) +--R + +--R 3 4 4 3 5 2 +--R (192a b + 288a b + 96a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 3 4 3 5 2 6 +--R (112a b + 112a b)cosh(x) + (96a b + 144a b + 48a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 4 3 4 +--R (140a b + 140a b )cosh(x) +--R + +--R 2 5 3 4 4 3 2 6 2 5 +--R (240a b + 360a b + 120a b )cosh(x) + 32a b + 64a b +--R + +--R 3 4 4 3 +--R 44a b + 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 4 +--R (280a b + 280a b )cosh(x) +--R + +--R 3 4 4 3 5 2 2 2 5 3 4 +--R (480a b + 720a b + 240a b )cosh(x) + 64a b + 128a b +--R + +--R 4 3 5 2 +--R 88a b + 24a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 4 4 3 5 2 6 2 +--R (140a b + 140a b)cosh(x) + (240a b + 360a b + 120a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R 32a b + 64a b + 44a b + 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 +--R (112a b + 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 3 +--R (320a b + 480a b + 160a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 +--R (128a b + 256a b + 176a b + 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 5 +--R (224a b + 224a b )cosh(x) +--R + +--R 3 4 4 3 5 2 3 +--R (640a b + 960a b + 320a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (256a b + 512a b + 352a b + 96a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 5 4 3 5 2 6 3 +--R (112a b + 112a b)cosh(x) + (320a b + 480a b + 160a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (128a b + 256a b + 176a b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 6 +--R (56a b + 56a b )cosh(x) +--R + +--R 2 5 3 4 4 3 4 +--R (240a b + 360a b + 120a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 2 2 5 +--R (192a b + 384a b + 264a b + 72a b )cosh(x) + 16a b +--R + +--R 3 4 4 3 +--R 24a b + 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 +--R (112a b + 112a b )cosh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (480a b + 720a b + 240a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 3 4 +--R (384a b + 768a b + 528a b + 144a b )cosh(x) + 32a b +--R + +--R 4 3 5 2 +--R 48a b + 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 6 4 3 5 2 6 4 +--R (56a b + 56a b)cosh(x) + (240a b + 360a b + 120a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 4 3 5 2 +--R (192a b + 384a b + 264a b + 72a b)cosh(x) + 16a b + 24a b +--R + +--R 6 +--R 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 7 +--R (16a b + 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 +--R (96a b + 144a b + 48a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (128a b + 256a b + 176a b + 48a b )cosh(x) +--R + +--R 2 5 3 4 4 3 +--R (32a b + 48a b + 16a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 7 +--R (32a b + 32a b )cosh(x) +--R + +--R 3 4 4 3 5 2 5 +--R (192a b + 288a b + 96a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (256a b + 512a b + 352a b + 96a b )cosh(x) +--R + +--R 3 4 4 3 5 2 +--R (64a b + 96a b + 32a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 4 3 5 2 6 5 +--R (16a b + 16a b)cosh(x) + (96a b + 144a b + 48a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 3 +--R (128a b + 256a b + 176a b + 48a b)cosh(x) +--R + +--R 4 3 5 2 6 +--R (32a b + 48a b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 8 2 5 3 4 4 3 6 +--R (2a b + 2a b )cosh(x) + (16a b + 24a b + 8a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 4 +--R (32a b + 64a b + 44a b + 12a b )cosh(x) +--R + +--R 2 5 3 4 4 3 2 3 4 4 3 +--R (16a b + 24a b + 8a b )cosh(x) + 2a b + 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 8 3 4 4 3 5 2 6 +--R (4a b + 4a b )cosh(x) + (32a b + 48a b + 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 4 +--R (64a b + 128a b + 88a b + 24a b )cosh(x) +--R + +--R 3 4 4 3 5 2 2 4 3 5 2 +--R (32a b + 48a b + 16a b )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 8 4 3 5 2 6 6 +--R (2a b + 2a b)cosh(x) + (16a b + 24a b + 8a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (32a b + 64a b + 44a b + 12a b)cosh(x) +--R + +--R 4 3 5 2 6 2 5 2 6 +--R (16a b + 24a b + 8a b)cosh(x) + 2a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 +--R (- 2a b - 4a b - 2a b )sech(x) + (- 4a b - 8a b - 4a b)sech(x) +--R + +--R 5 2 6 7 +--R - 2a b - 4a b - 2a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (- 16a b - 32a b - 16a b )cosh(x)sech(x) +--R + +--R 4 3 5 2 6 2 +--R (- 32a b - 64a b - 32a b)cosh(x)sech(x) +--R + +--R 5 2 6 7 +--R (- 16a b - 32a b - 16a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 2 2 5 3 4 4 3 +--R (- 56a b - 112a b - 56a b )cosh(x) - 16a b - 40a b - 32a b +--R + +--R 5 2 +--R - 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 2 3 4 4 3 5 2 +--R (- 112a b - 224a b - 112a b)cosh(x) - 32a b - 80a b - 64a b +--R + +--R 6 +--R - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 2 4 3 5 2 6 7 +--R (- 56a b - 112a b - 56a )cosh(x) - 16a b - 40a b - 32a b - 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 3 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- 96a b - 240a b - 192a b - 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 3 +--R (- 224a b - 448a b - 224a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 192a b - 480a b - 384a b - 96a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 3 +--R (- 112a b - 224a b - 112a )cosh(x) +--R + +--R 4 3 5 2 6 7 +--R (- 96a b - 240a b - 192a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (- 140a b - 280a b - 140a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 6 +--R (- 240a b - 600a b - 480a b - 120a b )cosh(x) - 32a b +--R + +--R 2 5 3 4 4 3 5 2 +--R - 96a b - 108a b - 56a b - 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 4 +--R (- 280a b - 560a b - 280a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 2 5 +--R (- 480a b - 1200a b - 960a b - 240a b)cosh(x) - 64a b +--R + +--R 3 4 4 3 5 2 6 +--R - 192a b - 216a b - 112a b - 24a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 4 +--R (- 140a b - 280a b - 140a )cosh(x) +--R + +--R 4 3 5 2 6 7 2 3 4 4 3 +--R (- 240a b - 600a b - 480a b - 120a )cosh(x) - 32a b - 96a b +--R + +--R 5 2 6 7 +--R - 108a b - 56a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 5 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (- 320a b - 800a b - 640a b - 160a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (- 128a b - 384a b - 432a b - 224a b - 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 5 +--R (- 224a b - 448a b - 224a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 3 +--R (- 640a b - 1600a b - 1280a b - 320a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 256a b - 768a b - 864a b - 448a b - 96a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 5 +--R (- 112a b - 224a b - 112a )cosh(x) +--R + +--R 4 3 5 2 6 7 3 +--R (- 320a b - 800a b - 640a b - 160a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R (- 128a b - 384a b - 432a b - 224a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 56a b - 112a b - 56a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 4 +--R (- 240a b - 600a b - 480a b - 120a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 +--R (- 192a b - 576a b - 648a b - 336a b - 72a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 16a b - 40a b - 32a b - 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 6 +--R (- 112a b - 224a b - 112a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 480a b - 1200a b - 960a b - 240a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 +--R (- 384a b - 1152a b - 1296a b - 672a b - 144a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R - 32a b - 80a b - 64a b - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 6 +--R (- 56a b - 112a b - 56a )cosh(x) +--R + +--R 4 3 5 2 6 7 4 +--R (- 240a b - 600a b - 480a b - 120a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 4 3 +--R (- 192a b - 576a b - 648a b - 336a b - 72a )cosh(x) - 16a b +--R + +--R 5 2 6 7 +--R - 40a b - 32a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 7 +--R (- 16a b - 32a b - 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 5 +--R (- 96a b - 240a b - 192a b - 48a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (- 128a b - 384a b - 432a b - 224a b - 48a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- 32a b - 80a b - 64a b - 16a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 7 +--R (- 32a b - 64a b - 32a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 5 +--R (- 192a b - 480a b - 384a b - 96a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (- 256a b - 768a b - 864a b - 448a b - 96a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 64a b - 160a b - 128a b - 32a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 7 +--R (- 16a b - 32a b - 16a )cosh(x) +--R + +--R 4 3 5 2 6 7 5 +--R (- 96a b - 240a b - 192a b - 48a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (- 128a b - 384a b - 432a b - 224a b - 48a )cosh(x) +--R + +--R 4 3 5 2 6 7 +--R (- 32a b - 80a b - 64a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 5 2 8 +--R (- 2a b - 4a b - 2a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 16a b - 40a b - 32a b - 8a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (- 32a b - 96a b - 108a b - 56a b - 12a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 3 4 4 3 5 2 +--R (- 16a b - 40a b - 32a b - 8a b )cosh(x) - 2a b - 4a b - 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 8 +--R (- 4a b - 8a b - 4a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (- 32a b - 80a b - 64a b - 16a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (- 64a b - 192a b - 216a b - 112a b - 24a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 4 3 5 2 6 +--R (- 32a b - 80a b - 64a b - 16a b)cosh(x) - 4a b - 8a b - 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 8 +--R (- 2a b - 4a b - 2a )cosh(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 16a b - 40a b - 32a b - 8a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- 32a b - 96a b - 108a b - 56a b - 12a )cosh(x) +--R + +--R 4 3 5 2 6 7 2 5 2 6 7 +--R (- 16a b - 40a b - 32a b - 8a )cosh(x) - 2a b - 4a b - 2a +--R Type: Expression Integer +--E 35 + +--S 36 of 526 +t0405:= (1+sech(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R (36) \|sech(x) + 1 +--R Type: Expression Integer +--E 36 + +--S 37 of 526 +r0405:= asin(1/2*2^(1/2)*tanh(x))+atanh(tanh(x)/(2-tanh(x)^2)^(1/2)) +--R +--R +--R +-+ +--R tanh(x) \|2 tanh(x) +--R (37) atanh(-----------------) + asin(-----------) +--R +--------------+ 2 +--R | 2 +--R \|- tanh(x) + 2 +--R Type: Expression Integer +--E 37 + +--S 38 of 526 +a0405:= integrate(t0405,x) +--R +--R +--R (38) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R 4 +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R / +--R 2 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 526 +m0405:= a0405-r0405 +--R +--R +--R (39) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R tanh(x) +--R - 2atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R + +--R 4 +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R / +--R 2 +--R + +--R +-+ +--R \|2 tanh(x) +--R - 2asin(-----------) +--R 2 +--R / +--R 2 +--R Type: Expression Integer +--E 39 + +--S 40 of 526 +d0405:= D(m0405,x) +--R +--R +--R (40) +--R 14 13 2 12 +--R - sinh(x) - 6cosh(x)sinh(x) + (- 11cosh(x) - 12)sinh(x) +--R + +--R 3 11 +--R (4cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (39cosh(x) - 24cosh(x) - 66)sinh(x) +--R + +--R 5 3 9 +--R (38cosh(x) + 144cosh(x) - 156cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 27cosh(x) + 204cosh(x) + 102cosh(x) - 140)sinh(x) +--R + +--R 7 5 3 7 +--R (- 72cosh(x) - 96cosh(x) + 432cosh(x) - 288cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 27cosh(x) - 336cosh(x) - 36cosh(x) - 16cosh(x) - 301) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 38cosh(x) - 96cosh(x) - 552cosh(x) + 288cosh(x) +--R + +--R - 430cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 39cosh(x) + 204cosh(x) - 36cosh(x) + 312cosh(x) +--R + +--R 2 +--R 285cosh(x) - 328 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 4cosh(x) + 144cosh(x) + 432cosh(x) + 288cosh(x) +--R + +--R 3 +--R 828cosh(x) - 48cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 11cosh(x) - 24cosh(x) + 102cosh(x) - 16cosh(x) +--R + +--R 4 2 +--R 285cosh(x) + 560cosh(x) - 48 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 6cosh(x) - 48cosh(x) - 156cosh(x) - 288cosh(x) +--R + +--R 5 3 +--R - 430cosh(x) - 48cosh(x) - 48cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - cosh(x) - 12cosh(x) - 66cosh(x) - 140cosh(x) +--R + +--R 6 4 2 +--R - 301cosh(x) - 328cosh(x) - 48cosh(x) +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R + +--R 14 13 2 12 +--R sinh(x) + 6cosh(x)sinh(x) + (11cosh(x) + 7)sinh(x) +--R + +--R 3 11 +--R (- 4cosh(x) + 28cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 39cosh(x) + 14cosh(x) + 30)sinh(x) +--R + +--R 5 3 9 +--R (- 38cosh(x) - 84cosh(x) + 84cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (27cosh(x) - 119cosh(x) + 6cosh(x) + 114)sinh(x) +--R + +--R 7 5 3 7 +--R (72cosh(x) + 56cosh(x) - 144cosh(x) + 240cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (27cosh(x) + 196cosh(x) - 36cosh(x) + 24cosh(x) + 205) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 38cosh(x) + 56cosh(x) + 120cosh(x) - 240cosh(x) +--R + +--R 270cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 39cosh(x) - 119cosh(x) - 36cosh(x) - 276cosh(x) +--R + +--R 2 +--R - 189cosh(x) + 163 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 4cosh(x) - 84cosh(x) - 144cosh(x) - 240cosh(x) +--R + +--R 3 +--R - 508cosh(x) + 52cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 11cosh(x) + 14cosh(x) + 6cosh(x) + 24cosh(x) +--R + +--R 4 2 +--R - 189cosh(x) - 222cosh(x) + 84 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 6cosh(x) + 28cosh(x) + 84cosh(x) + 240cosh(x) +--R + +--R 5 3 +--R 270cosh(x) + 52cosh(x) + 24cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R cosh(x) + 7cosh(x) + 30cosh(x) + 114cosh(x) + 205cosh(x) +--R + +--R 4 2 +--R 163cosh(x) + 84cosh(x) + 36 +--R * +--R 2 +--R tanh(x) +--R + +--R 14 13 2 12 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 22cosh(x) - 14)sinh(x) +--R + +--R 3 11 +--R (8cosh(x) - 56cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (78cosh(x) - 28cosh(x) - 60)sinh(x) +--R + +--R 5 3 9 +--R (76cosh(x) + 168cosh(x) - 168cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 54cosh(x) + 238cosh(x) - 12cosh(x) - 228)sinh(x) +--R + +--R 7 5 3 7 +--R (- 144cosh(x) - 112cosh(x) + 288cosh(x) - 480cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (- 54cosh(x) - 392cosh(x) + 72cosh(x) - 48cosh(x) - 410)sinh(x) +--R + +--R 9 7 5 3 +--R (76cosh(x) - 112cosh(x) - 240cosh(x) + 480cosh(x) - 540cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 78cosh(x) + 238cosh(x) + 72cosh(x) + 552cosh(x) +--R + +--R 2 +--R 378cosh(x) - 326 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 8cosh(x) + 168cosh(x) + 288cosh(x) + 480cosh(x) +--R + +--R 3 +--R 1016cosh(x) - 104cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 22cosh(x) - 28cosh(x) - 12cosh(x) - 48cosh(x) +--R + +--R 4 2 +--R 378cosh(x) + 444cosh(x) - 168 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 12cosh(x) - 56cosh(x) - 168cosh(x) - 480cosh(x) +--R + +--R 5 3 +--R - 540cosh(x) - 104cosh(x) - 48cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R - 2cosh(x) - 14cosh(x) - 60cosh(x) - 228cosh(x) - 410cosh(x) +--R + +--R 4 2 +--R - 326cosh(x) - 168cosh(x) - 72 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 12 11 2 10 +--R 8sinh(x) + 48cosh(x)sinh(x) + (112cosh(x) + 90)sinh(x) +--R + +--R 3 9 +--R (112cosh(x) + 420cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 8cosh(x) + 690cosh(x) + 412)sinh(x) +--R + +--R 5 3 7 +--R (- 160cosh(x) + 240cosh(x) + 1328cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 224cosh(x) - 780cosh(x) + 1072cosh(x) + 804)sinh(x) +--R + +--R 7 5 3 5 +--R (- 160cosh(x) - 1320cosh(x) - 1072cosh(x) + 1704cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 8cosh(x) - 780cosh(x) - 2456cosh(x) + 156cosh(x) + 616) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 112cosh(x) + 240cosh(x) - 1072cosh(x) - 1488cosh(x) +--R + +--R 1120cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 112cosh(x) + 690cosh(x) + 1072cosh(x) + 156cosh(x) +--R + +--R 2 +--R 1008cosh(x) + 450 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 48cosh(x) + 420cosh(x) + 1328cosh(x) + 1704cosh(x) +--R + +--R 3 +--R 1120cosh(x) + 756cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 8cosh(x) + 90cosh(x) + 412cosh(x) + 804cosh(x) + 616cosh(x) +--R + +--R 2 +--R 450cosh(x) + 180 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R + +--R 12 11 2 10 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 112cosh(x) - 68)sinh(x) +--R + +--R 3 9 +--R (- 112cosh(x) - 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (8cosh(x) - 532cosh(x) - 224)sinh(x) +--R + +--R 5 3 7 +--R (160cosh(x) - 192cosh(x) - 744cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (224cosh(x) + 600cosh(x) - 656cosh(x) - 432)sinh(x) +--R + +--R 7 5 3 5 +--R (160cosh(x) + 1024cosh(x) + 488cosh(x) - 920cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (8cosh(x) + 600cosh(x) + 1248cosh(x) - 496cosh(x) - 592)sinh(x) +--R + +--R 9 7 5 3 +--R - 112cosh(x) - 192cosh(x) + 488cosh(x) - 16cosh(x) +--R + +--R - 1064cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 112cosh(x) - 532cosh(x) - 656cosh(x) - 496cosh(x) +--R + +--R 2 +--R - 944cosh(x) - 396 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 48cosh(x) - 320cosh(x) - 744cosh(x) - 920cosh(x) +--R + +--R 3 +--R - 1064cosh(x) - 744cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 8cosh(x) - 68cosh(x) - 224cosh(x) - 432cosh(x) - 592cosh(x) +--R + +--R 2 +--R - 396cosh(x) - 72 +--R * +--R 2 +--R tanh(x) +--R + +--R 12 11 2 10 +--R 16sinh(x) + 96cosh(x)sinh(x) + (224cosh(x) + 136)sinh(x) +--R + +--R 3 9 +--R (224cosh(x) + 640cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 16cosh(x) + 1064cosh(x) + 448)sinh(x) +--R + +--R 5 3 7 +--R (- 320cosh(x) + 384cosh(x) + 1488cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 448cosh(x) - 1200cosh(x) + 1312cosh(x) + 864)sinh(x) +--R + +--R 7 5 3 5 +--R (- 320cosh(x) - 2048cosh(x) - 976cosh(x) + 1840cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (- 16cosh(x) - 1200cosh(x) - 2496cosh(x) + 992cosh(x) + 1184)sinh(x) +--R + +--R 9 7 5 3 +--R (224cosh(x) + 384cosh(x) - 976cosh(x) + 32cosh(x) + 2128cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 224cosh(x) + 1064cosh(x) + 1312cosh(x) + 992cosh(x) +--R + +--R 2 +--R 1888cosh(x) + 792 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 96cosh(x) + 640cosh(x) + 1488cosh(x) + 1840cosh(x) +--R + +--R 3 +--R 2128cosh(x) + 1488cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 16cosh(x) + 136cosh(x) + 448cosh(x) + 864cosh(x) + 1184cosh(x) +--R + +--R 2 +--R 792cosh(x) + 144 +--R / +--R 14 13 2 12 +--R sinh(x) + 6cosh(x)sinh(x) + (11cosh(x) + 7)sinh(x) +--R + +--R 3 11 +--R (- 4cosh(x) + 28cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 39cosh(x) + 14cosh(x) + 30)sinh(x) +--R + +--R 5 3 9 +--R (- 38cosh(x) - 84cosh(x) + 84cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (27cosh(x) - 119cosh(x) + 6cosh(x) + 114)sinh(x) +--R + +--R 7 5 3 7 +--R (72cosh(x) + 56cosh(x) - 144cosh(x) + 240cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (27cosh(x) + 196cosh(x) - 36cosh(x) + 24cosh(x) + 205)sinh(x) +--R + +--R 9 7 5 3 +--R - 38cosh(x) + 56cosh(x) + 120cosh(x) - 240cosh(x) +--R + +--R 270cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 39cosh(x) - 119cosh(x) - 36cosh(x) - 276cosh(x) +--R + +--R 2 +--R - 189cosh(x) + 163 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 4cosh(x) - 84cosh(x) - 144cosh(x) - 240cosh(x) +--R + +--R 3 +--R - 508cosh(x) + 52cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 11cosh(x) + 14cosh(x) + 6cosh(x) + 24cosh(x) - 189cosh(x) +--R + +--R 2 +--R - 222cosh(x) + 84 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R 6cosh(x) + 28cosh(x) + 84cosh(x) + 240cosh(x) + 270cosh(x) +--R + +--R 3 +--R 52cosh(x) + 24cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R cosh(x) + 7cosh(x) + 30cosh(x) + 114cosh(x) + 205cosh(x) +--R + +--R 4 2 +--R 163cosh(x) + 84cosh(x) + 36 +--R * +--R +-------------------------------------+ +--R +--------------+ | 2 2 +--R | 2 | 2sinh(x) + 2cosh(x) + 6 +--R \|- tanh(x) + 2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 12 11 2 10 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 112cosh(x) - 68)sinh(x) +--R + +--R 3 9 +--R (- 112cosh(x) - 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (8cosh(x) - 532cosh(x) - 224)sinh(x) +--R + +--R 5 3 7 +--R (160cosh(x) - 192cosh(x) - 744cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (224cosh(x) + 600cosh(x) - 656cosh(x) - 432)sinh(x) +--R + +--R 7 5 3 5 +--R (160cosh(x) + 1024cosh(x) + 488cosh(x) - 920cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (8cosh(x) + 600cosh(x) + 1248cosh(x) - 496cosh(x) - 592)sinh(x) +--R + +--R 9 7 5 3 +--R - 112cosh(x) - 192cosh(x) + 488cosh(x) - 16cosh(x) +--R + +--R - 1064cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 112cosh(x) - 532cosh(x) - 656cosh(x) - 496cosh(x) +--R + +--R 2 +--R - 944cosh(x) - 396 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 48cosh(x) - 320cosh(x) - 744cosh(x) - 920cosh(x) +--R + +--R 3 +--R - 1064cosh(x) - 744cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 8cosh(x) - 68cosh(x) - 224cosh(x) - 432cosh(x) - 592cosh(x) +--R + +--R 2 +--R - 396cosh(x) - 72 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R Type: Expression Integer +--E 40 + +--S 41 of 526 +t0406:= (1-sech(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (41) \|- sech(x) + 1 +--R Type: Expression Integer +--E 41 + +--S 42 of 526 +r0406:= coth(x)*log(cosh(x))*(tanh(x)^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R (42) coth(x)log(cosh(x))\|tanh(x) +--R Type: Expression Integer +--E 42 + +--S 43 of 526 +a0406:= integrate(t0406,x) +--R +--R +--R 2cosh(x) +--R (43) log(- -----------------) - x +--R sinh(x) - cosh(x) +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 526 +m0406:= a0406-r0406 +--R +--R +--R +--------+ +--R | 2 2cosh(x) +--R (44) - coth(x)log(cosh(x))\|tanh(x) + log(- -----------------) - x +--R sinh(x) - cosh(x) +--R Type: Expression Integer +--E 44 + +--S 45 of 526 +d0406:= D(m0406,x) +--R +--R +--R (45) +--R +--------+ +--R | 2 +--R sinh(x)\|tanh(x) +--R + +--R 3 2 2 +--R cosh(x)coth(x)tanh(x) + (cosh(x)coth(x) - cosh(x))tanh(x) +--R + +--R - cosh(x)coth(x)tanh(x) +--R * +--R log(cosh(x)) +--R + +--R 2 +--R - coth(x)sinh(x)tanh(x) +--R / +--R +--------+ +--R | 2 +--R cosh(x)\|tanh(x) +--R Type: Expression Integer +--E 45 + +--S 46 of 526 +t0407:= (-1+sech(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R (46) \|sech(x) - 1 +--R Type: Expression Integer +--E 46 + +--S 47 of 526 +r0407:= coth(x)*log(cosh(x))*(-tanh(x)^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (47) coth(x)log(cosh(x))\|- tanh(x) +--R Type: Expression Integer +--E 47 + +--S 48 of 526 +a0407:= integrate(t0407,x) +--R +--R +--R (48) 0 +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 526 +m0407:= a0407-r0407 +--R +--R +--R +----------+ +--R | 2 +--R (49) - coth(x)log(cosh(x))\|- tanh(x) +--R Type: Expression Integer +--E 49 + +--S 50 of 526 +d0407:= D(m0407,x) +--R +--R +--R (50) +--R 3 2 2 +--R - cosh(x)coth(x)tanh(x) + (- cosh(x)coth(x) + cosh(x))tanh(x) +--R + +--R cosh(x)coth(x)tanh(x) +--R * +--R log(cosh(x)) +--R + +--R 2 +--R coth(x)sinh(x)tanh(x) +--R / +--R +----------+ +--R | 2 +--R cosh(x)\|- tanh(x) +--R Type: Expression Integer +--E 50 + +--S 51 of 526 +t0408:= (-1-sech(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (51) \|- sech(x) - 1 +--R Type: Expression Integer +--E 51 + +--S 52 of 526 +r0408:= -atan(tanh(x)/(-2+tanh(x)^2)^(1/2))-atanh(coth(x)*(-2+tanh(x)^2)^(1/2)) +--R +--R +--R +------------+ +--R | 2 tanh(x) +--R (52) - atanh(coth(x)\|tanh(x) - 2 ) - atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R Type: Expression Integer +--E 52 + +--S 53 of 526 +a0408:= integrate(t0408,x) +--R +--R +--R (53) +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 + 2)(%e ) - \|- 1 +--R - 2log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R +---+ \|- (%e ) - 6(%e ) - 1 - \|- 1 (%e ) - \|- 1 +--R - \|- 1 log(-------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 - 2)(%e ) - \|- 1 +--R 2log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ +--R \|- 1 +--R * +--R log +--R +----------------------+ +--R +---+ x 2 +---+ | x 4 x 2 x 4 +--R (- 2\|- 1 (%e ) - 2\|- 1 )\|- (%e ) - 6(%e ) - 1 + 2(%e ) +--R + +--R x 2 +--R - 8(%e ) - 2 +--R / +--R x 4 +--R (%e ) +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 526 +m0408:= a0408-r0408 +--R +--R +--R (54) +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 + 2)(%e ) - \|- 1 +--R - 2log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R +---+ \|- (%e ) - 6(%e ) - 1 - \|- 1 (%e ) - \|- 1 +--R - \|- 1 log(-------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 - 2)(%e ) - \|- 1 +--R 2log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ +--R \|- 1 +--R * +--R log +--R +----------------------+ +--R +---+ x 2 +---+ | x 4 x 2 x 4 +--R (- 2\|- 1 (%e ) - 2\|- 1 )\|- (%e ) - 6(%e ) - 1 + 2(%e ) +--R + +--R x 2 +--R - 8(%e ) - 2 +--R / +--R x 4 +--R (%e ) +--R + +--R +------------+ +--R | 2 tanh(x) +--R 2atanh(coth(x)\|tanh(x) - 2 ) + 2atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R / +--R 2 +--R Type: Expression Integer +--E 54 + +--S 55 of 526 +d0408:= D(m0408,x) +--R +--R +--R (55) +--R +---+ 2 x 6 +---+ 2 x 4 +--R - 9\|- 1 coth(x) (%e ) - 21\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 2 +---+ 2 +--R - 9\|- 1 coth(x) (%e ) - \|- 1 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 6 +--R (18\|- 1 coth(x) + 9\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (42\|- 1 coth(x) + 21\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (18\|- 1 coth(x) + 9\|- 1 )(%e ) + 2\|- 1 coth(x) + \|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R 2 x 8 2 x 6 2 x 4 +--R - 7coth(x) (%e ) - 48coth(x) (%e ) - 44coth(x) (%e ) +--R + +--R 2 x 2 2 +--R - 12coth(x) (%e ) - coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 x 8 2 x 6 +--R (14coth(x) + 7)(%e ) + (96coth(x) + 48)(%e ) +--R + +--R 2 x 4 2 x 2 2 +--R (88coth(x) + 44)(%e ) + (24coth(x) + 12)(%e ) + 2coth(x) + 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R x 6 x 4 x 2 3 +--R (7coth(x)(%e ) + 13coth(x)(%e ) + 7coth(x)(%e ) + coth(x))tanh(x) +--R + +--R 2 x 6 2 x 4 +--R (14coth(x) - 7)(%e ) + (26coth(x) - 13)(%e ) +--R + +--R 2 x 2 2 +--R (14coth(x) - 7)(%e ) + 2coth(x) - 1 +--R * +--R 2 +--R tanh(x) +--R + +--R x 6 x 4 x 2 +--R (- 7coth(x)(%e ) - 13coth(x)(%e ) - 7coth(x)(%e ) - coth(x)) +--R * +--R tanh(x) +--R + +--R 2 x 6 2 x 4 +--R (- 28coth(x) + 7)(%e ) + (- 52coth(x) + 13)(%e ) +--R + +--R 2 x 2 2 +--R (- 28coth(x) + 7)(%e ) - 4coth(x) + 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +--R - 9\|- 1 coth(x)(%e ) - 30\|- 1 coth(x)(%e ) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R - 30\|- 1 coth(x)(%e ) - 10\|- 1 coth(x)(%e ) - \|- 1 coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 8 +--R (- 18\|- 1 coth(x) + 9\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (- 60\|- 1 coth(x) + 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (- 60\|- 1 coth(x) + 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 20\|- 1 coth(x) + 10\|- 1 )(%e ) - 2\|- 1 coth(x) + \|- 1 +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +--R 9\|- 1 coth(x)(%e ) + 30\|- 1 coth(x)(%e ) + 30\|- 1 coth(x)(%e ) +--R + +--R +---+ x 2 +---+ +--R 10\|- 1 coth(x)(%e ) + \|- 1 coth(x) +--R * +--R tanh(x) +--R + +--R +---+ 2 +---+ x 8 +---+ 2 +---+ x 6 +--R (36\|- 1 coth(x) - 9\|- 1 )(%e ) + (120\|- 1 coth(x) - 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (120\|- 1 coth(x) - 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (40\|- 1 coth(x) - 10\|- 1 )(%e ) + 4\|- 1 coth(x) - \|- 1 +--R / +--R 2 x 6 2 x 4 2 x 2 2 +--R (7coth(x) (%e ) + 13coth(x) (%e ) + 7coth(x) (%e ) + coth(x) ) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 x 6 2 x 4 +--R (- 14coth(x) - 7)(%e ) + (- 26coth(x) - 13)(%e ) +--R + +--R 2 x 2 2 +--R (- 14coth(x) - 7)(%e ) - 2coth(x) - 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ 2 x 8 +---+ 2 x 6 +--R - 9\|- 1 coth(x) (%e ) - 30\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 4 +---+ 2 x 2 +---+ 2 +--R - 30\|- 1 coth(x) (%e ) - 10\|- 1 coth(x) (%e ) - \|- 1 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 8 +--R (18\|- 1 coth(x) + 9\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (60\|- 1 coth(x) + 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (60\|- 1 coth(x) + 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (20\|- 1 coth(x) + 10\|- 1 )(%e ) + 2\|- 1 coth(x) + \|- 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R Type: Expression Integer +--E 55 + +--S 56 of 526 +t0409:= (a+b*sech(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (56) \|b sech(x) + a +--R Type: Expression Integer +--E 56 + +--S 57 of 526 +r0409:= -b^(1/2)*atan(coth(x)*(a+b*sech(x)^2)^(1/2)/b^(1/2))+a^(1/2)*atanh(a^(1/2)*tanh(x)/(a+b*sech(x)^2)^(1/2)) +--R +--R +--R +--------------+ +--R +-+ | 2 +--R +-+ tanh(x)\|a +-+ coth(x)\|b sech(x) + a +--R (57) \|a atanh(-----------------) - \|b atan(------------------------) +--R +--------------+ +-+ +--R | 2 \|b +--R \|b sech(x) + a +--R Type: Expression Integer +--E 57 + +--S 58 of 526 +a0409:= integrate(t0409,x) +--R +--R +--R (58) +--R [ +--R - +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +---+ +-+ +--R 2\|- b \|a +--R * +--R log +--R 4 3 +--R (2b + 2a)sinh(x) + (8b + 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((12b + 12a)cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R ((8b + 8a)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (2b + 2a)cosh(x) + 2a cosh(x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (4a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) - 2b - 4a b - 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (- 8b - 16a b - 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 24a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (- 8b - 16a b - 12a )cosh(x) +--R + +--R 2 +--R (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (- 2b - 4a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 6 2 5 +--R (- 2a b - 2a )sinh(x) + (- 12a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a b - 30a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 +--R ((- 40a b - 40a )cosh(x) + (- 24a b - 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 +--R (- 30a b - 30a )cosh(x) + (- 36a b - 24a )cosh(x) +--R + +--R 2 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 16a )cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 2a b - 2a )cosh(x) + (- 6a b - 4a )cosh(x) +--R + +--R 2 2 +--R - 2a cosh(x) +--R * +--R +---+ +--R \|- b +--R / +--R 2 4 2 3 +--R (2a b + a )sinh(x) + (8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b + 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b + 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b + a )cosh(x) + (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 30b - 30a b - 15a )cosh(x) - 2b - 6a b - 3a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 +--R (- 40b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 24a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 36a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 8b - 24a b - 12a )cosh(x) + (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b - 2a b - a )cosh(x) + (- 2b - 6a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R / +--R +-+ +--R 2\|a +--R , +--R +--R - +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R - +--R +-+ +-+ +--R 4\|a \|b +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|a \|b +--R / +--R +-+ +--R 2\|a +--R ] +--R Type: Union(List Expression Integer,...) +--E 58 + +--S 59 of 526 +m0409a:= a0409.1-r0409 +--R +--R +--R (59) +--R - +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +---+ +-+ +--R 2\|- b \|a +--R * +--R log +--R 4 3 +--R (2b + 2a)sinh(x) + (8b + 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((12b + 12a)cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R ((8b + 8a)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (2b + 2a)cosh(x) + 2a cosh(x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (4a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) - 2b - 4a b - 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (- 8b - 16a b - 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (30b - 15a )cosh(x) + (- 12b - 24a b - 18a )cosh(x) +--R + +--R 2 +--R - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (- 8b - 16a b - 12a )cosh(x) +--R + +--R 2 +--R (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (- 2b - 4a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 6 2 5 +--R (- 2a b - 2a )sinh(x) + (- 12a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a b - 30a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 3 +--R ((- 40a b - 40a )cosh(x) + (- 24a b - 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 +--R (- 30a b - 30a )cosh(x) + (- 36a b - 24a )cosh(x) +--R + +--R 2 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 16a )cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (- 2a b - 2a )cosh(x) + (- 6a b - 4a )cosh(x) - 2a cosh(x) +--R * +--R +---+ +--R \|- b +--R / +--R 2 4 2 3 +--R (2a b + a )sinh(x) + (8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b + 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b + 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b + a )cosh(x) + (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 30b - 30a b - 15a )cosh(x) - 2b - 6a b - 3a )sinh(x) +--R + +--R 2 2 3 +--R (- 40b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 24a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 36a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 8b - 24a b - 12a )cosh(x) + (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b - 2a b - a )cosh(x) + (- 2b - 6a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +--------------+ +--R +-+ | 2 +--R tanh(x)\|a +-+ +-+ coth(x)\|b sech(x) + a +--R - 2a atanh(-----------------) + 2\|a \|b atan(------------------------) +--R +--------------+ +-+ +--R | 2 \|b +--R \|b sech(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression Integer +--E 59 + +--S 60 of 526 +--d0409a:= D(m0409a,x) +--E 60 + +--S 61 of 526 +m0409b:= a0409.2-r0409 +--R +--R +--R (60) +--R - +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +--------------+ +--R +-+ | 2 +--R tanh(x)\|a +-+ +-+ coth(x)\|b sech(x) + a +--R - 2a atanh(-----------------) + 2\|a \|b atan(------------------------) +--R +--------------+ +-+ +--R | 2 \|b +--R \|b sech(x) + a +--R + +--R - +--R +-+ +-+ +--R 4\|a \|b +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|a \|b +--R / +--R +-+ +--R 2\|a +--R Type: Expression Integer +--E 61 + +--S 62 of 526 +--d0409b:= D(m0409b,x) +--E 62 + +--S 63 of 526 +t0410:= 1/(1+sech(x)^2)^(1/2) +--R +--R +--R 1 +--R (61) --------------- +--R +------------+ +--R | 2 +--R \|sech(x) + 1 +--R Type: Expression Integer +--E 63 + +--S 64 of 526 +r0410:= atanh(tanh(x)/(2-tanh(x)^2)^(1/2)) +--R +--R +--R tanh(x) +--R (62) atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R Type: Expression Integer +--E 64 + +--S 65 of 526 +a0410:= integrate(t0410,x) +--R +--R +--R (63) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 65 + +--S 66 of 526 +m0410:= a0410-r0410 +--R +--R +--R (64) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R tanh(x) +--R - 2atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R / +--R 2 +--R Type: Expression Integer +--E 66 + +--S 67 of 526 +d0410:= D(m0410,x) +--R +--R +--R (65) +--R 8 7 6 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 9sinh(x) +--R + +--R 3 5 +--R (4cosh(x) - 10cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (4cosh(x) + 9cosh(x) - 10)sinh(x) +--R + +--R 5 3 3 +--R (4cosh(x) + 20cosh(x) )sinh(x) +--R + +--R 4 2 2 +--R (9cosh(x) + 20cosh(x) - 3)sinh(x) +--R + +--R 7 5 8 +--R (- 4cosh(x) - 10cosh(x) + 6cosh(x))sinh(x) - 2cosh(x) +--R + +--R 6 4 2 +--R - 9cosh(x) - 10cosh(x) - 3cosh(x) +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R + +--R 8 7 6 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 12sinh(x) +--R + +--R 3 5 +--R (4cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (4cosh(x) + 12cosh(x) - 18)sinh(x) +--R + +--R 5 3 3 4 2 2 +--R (4cosh(x) + 24cosh(x) )sinh(x) + (12cosh(x) + 36cosh(x) )sinh(x) +--R + +--R 7 5 8 6 4 +--R (- 4cosh(x) - 12cosh(x) )sinh(x) - 2cosh(x) - 12cosh(x) - 18cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 10 9 2 8 +--R sinh(x) + 4cosh(x)sinh(x) + (5cosh(x) + 5)sinh(x) +--R + +--R 7 4 2 6 +--R 16cosh(x)sinh(x) + (- 6cosh(x) + 12cosh(x) + 13)sinh(x) +--R + +--R 5 3 5 +--R (- 8cosh(x) - 16cosh(x) + 16cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 6cosh(x) - 34cosh(x) - 5cosh(x) + 27)sinh(x) +--R + +--R 5 3 3 +--R (- 16cosh(x) - 16cosh(x) + 24cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (5cosh(x) + 12cosh(x) - 5cosh(x) - 6cosh(x) + 18)sinh(x) +--R + +--R 9 7 5 3 +--R (4cosh(x) + 16cosh(x) + 16cosh(x) + 24cosh(x) + 36cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) + 5cosh(x) + 13cosh(x) + 27cosh(x) + 18cosh(x) +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R + +--R 10 9 2 8 +--R sinh(x) + 4cosh(x)sinh(x) + (5cosh(x) + 8)sinh(x) +--R + +--R 7 4 2 6 +--R 22cosh(x)sinh(x) + (- 6cosh(x) + 12cosh(x) + 20)sinh(x) +--R + +--R 5 3 5 +--R (- 8cosh(x) - 22cosh(x) + 34cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 6cosh(x) - 40cosh(x) - 12cosh(x) + 22)sinh(x) +--R + +--R 5 3 3 +--R (- 22cosh(x) - 52cosh(x) + 26cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (5cosh(x) + 12cosh(x) - 12cosh(x) + 8cosh(x) + 27)sinh(x) +--R + +--R 9 7 5 3 +--R (4cosh(x) + 22cosh(x) + 34cosh(x) + 26cosh(x) + 42cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) + 8cosh(x) + 20cosh(x) + 22cosh(x) + 27cosh(x) + 18 +--R / +--R 8 7 6 +--R 2sinh(x) + 4cosh(x)sinh(x) + 12sinh(x) +--R + +--R 3 5 +--R (- 4cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 4cosh(x) - 12cosh(x) + 18)sinh(x) +--R + +--R 5 3 3 +--R (- 4cosh(x) - 24cosh(x) )sinh(x) +--R + +--R 4 2 2 7 5 +--R (- 12cosh(x) - 36cosh(x) )sinh(x) + (4cosh(x) + 12cosh(x) )sinh(x) +--R + +--R 8 6 4 +--R 2cosh(x) + 12cosh(x) + 18cosh(x) +--R * +--R +-------------------------------------+ +--R +--------------+ | 2 2 +--R | 2 | 2sinh(x) + 2cosh(x) + 6 +--R \|- tanh(x) + 2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 10 9 2 8 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 5cosh(x) - 8)sinh(x) +--R + +--R 7 4 2 6 +--R - 22cosh(x)sinh(x) + (6cosh(x) - 12cosh(x) - 20)sinh(x) +--R + +--R 5 3 5 +--R (8cosh(x) + 22cosh(x) - 34cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (6cosh(x) + 40cosh(x) + 12cosh(x) - 22)sinh(x) +--R + +--R 5 3 3 +--R (22cosh(x) + 52cosh(x) - 26cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 5cosh(x) - 12cosh(x) + 12cosh(x) - 8cosh(x) - 27)sinh(x) +--R + +--R 9 7 5 3 +--R (- 4cosh(x) - 22cosh(x) - 34cosh(x) - 26cosh(x) - 42cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - cosh(x) - 8cosh(x) - 20cosh(x) - 22cosh(x) - 27cosh(x) - 18 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R Type: Expression Integer +--E 67 + +--S 68 of 526 +t0411:= 1/(1-sech(x)^2)^(1/2) +--R +--R +--R 1 +--R (66) ----------------- +--R +--------------+ +--R | 2 +--R \|- sech(x) + 1 +--R Type: Expression Integer +--E 68 + +--S 69 of 526 +r0411:= log(sinh(x))*tanh(x)/(tanh(x)^2)^(1/2) +--R +--R +--R tanh(x)log(sinh(x)) +--R (67) ------------------- +--R +--------+ +--R | 2 +--R \|tanh(x) +--R Type: Expression Integer +--E 69 + +--S 70 of 526 +a0411:= integrate(t0411,x) +--R +--R +--R 2sinh(x) +--R (68) log(- -----------------) - x +--R sinh(x) - cosh(x) +--R Type: Union(Expression Integer,...) +--E 70 + +--S 71 of 526 +m0411:= a0411-r0411 +--R +--R +--R +--------+ +--R 2sinh(x) | 2 +--R (log(- -----------------) - x)\|tanh(x) - tanh(x)log(sinh(x)) +--R sinh(x) - cosh(x) +--R (69) --------------------------------------------------------------- +--R +--------+ +--R | 2 +--R \|tanh(x) +--R Type: Expression Integer +--E 71 + +--S 72 of 526 +d0411:= D(m0411,x) +--R +--R +--R +--------+ +--R | 2 +--R cosh(x)\|tanh(x) - cosh(x)tanh(x) +--R (70) ----------------------------------- +--R +--------+ +--R | 2 +--R sinh(x)\|tanh(x) +--R Type: Expression Integer +--E 72 + +--S 73 of 526 +t0412:= 1/(-1+sech(x)^2)^(1/2) +--R +--R +--R 1 +--R (71) --------------- +--R +------------+ +--R | 2 +--R \|sech(x) - 1 +--R Type: Expression Integer +--E 73 + +--S 74 of 526 +r0412:= log(sinh(x))*tanh(x)/(-tanh(x)^2)^(1/2) +--R +--R +--R tanh(x)log(sinh(x)) +--R (72) ------------------- +--R +----------+ +--R | 2 +--R \|- tanh(x) +--R Type: Expression Integer +--E 74 + +--S 75 of 526 +a0412:= integrate(t0412,x) +--R +--R +--R (73) 0 +--R Type: Union(Expression Integer,...) +--E 75 + +--S 76 of 526 +m0412:= a0412-r0412 +--R +--R +--R tanh(x)log(sinh(x)) +--R (74) - ------------------- +--R +----------+ +--R | 2 +--R \|- tanh(x) +--R Type: Expression Integer +--E 76 + +--S 77 of 526 +d0412:= D(m0412,x) +--R +--R +--R cosh(x)tanh(x) +--R (75) - -------------------- +--R +----------+ +--R | 2 +--R sinh(x)\|- tanh(x) +--R Type: Expression Integer +--E 77 + +--S 78 of 526 +t0413:= 1/(-1-sech(x)^2)^(1/2) +--R +--R +--R 1 +--R (76) ----------------- +--R +--------------+ +--R | 2 +--R \|- sech(x) - 1 +--R Type: Expression Integer +--E 78 + +--S 79 of 526 +r0413:= atan(tanh(x)/(-2+tanh(x)^2)^(1/2)) +--R +--R +--R tanh(x) +--R (77) atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R Type: Expression Integer +--E 79 + +--S 80 of 526 +a0413:= integrate(t0413,x) +--R +--R +--R (78) +--R +----------------------+ +--R +---+ | x 4 x 2 x 2 +--R +---+ \|- 1 \|- (%e ) - 6(%e ) - 1 + (%e ) + 1 +--R \|- 1 log(--------------------------------------------) +--R +---+ x 2 +--R \|- 1 (%e ) +--R + +--R - +--R +---+ +--R \|- 1 +--R * +--R log +--R +----------------------+ +--R x 2 | x 4 x 2 +---+ x 4 +--R (2(%e ) + 2)\|- (%e ) - 6(%e ) - 1 + 2\|- 1 (%e ) +--R + +--R +---+ x 2 +---+ +--R - 8\|- 1 (%e ) - 2\|- 1 +--R / +--R +---+ x 4 +--R \|- 1 (%e ) +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 80 + +--S 81 of 526 +m0413:= a0413-r0413 +--R +--R +--R (79) +--R +----------------------+ +--R +---+ | x 4 x 2 x 2 +--R +---+ \|- 1 \|- (%e ) - 6(%e ) - 1 + (%e ) + 1 +--R \|- 1 log(--------------------------------------------) +--R +---+ x 2 +--R \|- 1 (%e ) +--R + +--R - +--R +---+ +--R \|- 1 +--R * +--R log +--R +----------------------+ +--R x 2 | x 4 x 2 +---+ x 4 +--R (2(%e ) + 2)\|- (%e ) - 6(%e ) - 1 + 2\|- 1 (%e ) +--R + +--R +---+ x 2 +---+ +--R - 8\|- 1 (%e ) - 2\|- 1 +--R / +--R +---+ x 4 +--R \|- 1 (%e ) +--R + +--R tanh(x) +--R - 2atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R / +--R 2 +--R Type: Expression Integer +--E 81 + +--S 82 of 526 +d0413:= D(m0413,x) +--R +--R +--R (80) +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (5\|- 1 (%e ) + 11\|- 1 (%e ) + 7\|- 1 (%e ) + \|- 1 ) +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R x 8 x 6 x 4 x 2 +--R 3(%e ) + 22(%e ) + 28(%e ) + 10(%e ) + 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (- 3(%e ) - 19(%e ) - 9(%e ) - 1)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R 5\|- 1 (%e ) + 36\|- 1 (%e ) + 42\|- 1 (%e ) + 12\|- 1 (%e ) + \|- 1 +--R / +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (3(%e ) + 19(%e ) + 9(%e ) + 1)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 5\|- 1 (%e ) - 36\|- 1 (%e ) - 42\|- 1 (%e ) - 12\|- 1 (%e ) +--R + +--R +---+ +--R - \|- 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R Type: Expression Integer +--E 82 + +--S 83 of 526 +t0414:= 1/(a+b*sech(x)^2)^(1/2) +--R +--R +--R 1 +--R (81) ----------------- +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R Type: Expression Integer +--E 83 + +--S 84 of 526 +r0414:= atanh(a^(1/2)*tanh(x)/(a+b*sech(x)^2)^(1/2))/a^(1/2) +--R +--R +--R +-+ +--R tanh(x)\|a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R (82) ------------------------ +--R +-+ +--R \|a +--R Type: Expression Integer +--E 84 + +--S 85 of 526 +a0414:= integrate(t0414,x) +--R +--R +--R (83) +--R - +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) + 4cosh(x) sinh(x) +--R + +--R 4 +--R cosh(x) +--R / +--R +-+ +--R 2\|a +--R Type: Union(Expression Integer,...) +--E 85 + +--S 86 of 526 +m0414:= a0414-r0414 +--R +--R +--R (84) +--R - +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) + 4cosh(x) sinh(x) +--R + +--R 4 +--R cosh(x) +--R + +--R +-+ +--R tanh(x)\|a +--R - 2atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression Integer +--E 86 + +--S 87 of 526 +d0414:= D(m0414,x) +--R +--R +--R (85) +--R 8 2 2 2 6 +--R - a b sinh(x) + (4a b cosh(x) - 2b - 2a b - 2a )sinh(x) +--R + +--R 2 5 +--R (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 4 2 2 2 2 +--R - 6a b cosh(x) + (2b + 2a b + 2a )cosh(x) - 2b - 5a b +--R + +--R 2 +--R - 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 3 +--R ((8b + 8a b)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 6 2 2 4 +--R 4a b cosh(x) + (2b + 2a b + 2a )cosh(x) +--R + +--R 2 2 2 +--R (4b + 10a b)cosh(x) - 4a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 +--R ((- 4b - 4a b)cosh(x) + 4a cosh(x) + (8a b + 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 2 2 6 +--R - a b cosh(x) + (- 2b - 2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 2 +--R (- 2b - 5a b - 4a )cosh(x) + (- 4a b - 2a )cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 3 8 2 3 7 +--R (4a b + a )sinh(x) + (8a b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 3 6 +--R (8a b + 6a b + 3a )sinh(x) +--R + +--R 2 3 3 2 2 3 5 +--R ((- 8a b - 2a )cosh(x) + (16a b + 12a b + 2a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 2 3 2 2 +--R (- 8a b - 2a )cosh(x) + (- 8a b - 6a b - 3a )cosh(x) + 4a b +--R + +--R 3 +--R 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 2 2 3 3 +--R (- 8a b - 2a )cosh(x) + (- 32a b - 24a b - 4a )cosh(x) +--R + +--R 3 +--R - 2a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 4 2 3 2 2 +--R (- 8a b - 6a b - 3a )cosh(x) + (- 8a b + 2a )cosh(x) + 10a b +--R + +--R 3 +--R 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 7 2 2 3 5 +--R (8a b + 2a )cosh(x) + (16a b + 12a b + 2a )cosh(x) +--R + +--R 3 3 2 3 +--R - 2a cosh(x) + (- 4a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 8 2 2 3 6 +--R (4a b + a )cosh(x) + (8a b + 6a b + 3a )cosh(x) +--R + +--R 2 3 4 2 3 2 2 2 3 +--R (4a b + 5a )cosh(x) + (10a b + 5a )cosh(x) + 8a b + 8a b + 2a +--R * +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R 2 3 6 +--R (- 4a b - 2a )sinh(x) +--R + +--R 2 3 2 2 2 3 4 +--R ((4a b + 2a )cosh(x) - 8a b - 8a b - 4a )sinh(x) +--R + +--R 3 3 +--R 4a cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 2 2 3 +--R ((4a b + 2a )cosh(x) + (16a b + 16a b)cosh(x) - 4a b - 2a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 3 2 3 6 +--R (4a cosh(x) + (8a b + 4a )cosh(x))sinh(x) + (- 4a b - 2a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 +--R (- 8a b - 8a b - 4a )cosh(x) + (- 4a b - 2a )cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 10 2 9 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 8 +--R (- 5a b cosh(x) - 2a b + a b + a )sinh(x) +--R + +--R 2 3 7 +--R (- 8a b + 2a )cosh(x)sinh(x) +--R + +--R 2 4 2 2 2 2 2 3 +--R (6a b cosh(x) + (- 8a b - 4a b)cosh(x) + 4a b + 9a b + 3a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 3 +--R 8a b cosh(x) + (8a b - 2a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 12a b + 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 2 3 4 +--R 6a b cosh(x) + (20a b + 6a b - 2a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 4a b - a b - 3a )cosh(x) + 14a b + 11a b + 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 2 2 3 3 +--R (8a b - 2a )cosh(x) + (- 16a b - 8a b - 4a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 8a b - 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R - 5a b cosh(x) + (- 8a b - 4a b)cosh(x) +--R + +--R 2 2 3 4 2 2 3 2 +--R (- 4a b - a b - 3a )cosh(x) + (4a b - 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 +--R 8b + 8a b + 12a b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 3 7 +--R - 4a b cosh(x) + (- 8a b + 2a )cosh(x) +--R + +--R 2 2 3 5 2 2 3 3 +--R (8a b + 12a b + 2a )cosh(x) + (16a b + 8a b - 2a )cosh(x) +--R + +--R 3 2 3 +--R (16b + 16a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 2 3 8 +--R - a b cosh(x) + (- 2a b + a b + a )cosh(x) +--R + +--R 2 2 3 6 2 2 3 4 +--R (4a b + 9a b + 3a )cosh(x) + (14a b + 11a b + 5a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (8b + 8a b + 12a b + 5a )cosh(x) + 8a b + 8a b + 2a +--R * +--R +-+ +--R \|a +--R / +--R 2 3 6 +--R (4a b + 2a )sinh(x) +--R + +--R 2 3 2 2 2 3 4 +--R ((- 4a b - 2a )cosh(x) + 8a b + 8a b + 4a )sinh(x) +--R + +--R 3 3 +--R - 4a cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 2 2 +--R (- 4a b - 2a )cosh(x) + (- 16a b - 16a b)cosh(x) + 4a b +--R + +--R 3 +--R 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 3 +--R (- 4a cosh(x) + (- 8a b - 4a )cosh(x))sinh(x) +--R + +--R 2 3 6 2 2 3 4 +--R (4a b + 2a )cosh(x) + (8a b + 8a b + 4a )cosh(x) +--R + +--R 2 3 2 +--R (4a b + 2a )cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 10 2 9 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 8 +--R (5a b cosh(x) + 2a b - a b - a )sinh(x) +--R + +--R 2 3 7 +--R (8a b - 2a )cosh(x)sinh(x) +--R + +--R 2 4 2 2 2 2 2 3 +--R (- 6a b cosh(x) + (8a b + 4a b)cosh(x) - 4a b - 9a b - 3a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 3 +--R - 8a b cosh(x) + (- 8a b + 2a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 12a b - 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 2 3 4 +--R - 6a b cosh(x) + (- 20a b - 6a b + 2a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (4a b + a b + 3a )cosh(x) - 14a b - 11a b - 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 2 2 3 3 +--R (- 8a b + 2a )cosh(x) + (16a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 +--R (- 16a b - 8a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R 5a b cosh(x) + (8a b + 4a b)cosh(x) +--R + +--R 2 2 3 4 2 2 3 2 +--R (4a b + a b + 3a )cosh(x) + (- 4a b + 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 +--R - 8b - 8a b - 12a b - 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 3 7 +--R 4a b cosh(x) + (8a b - 2a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 8a b - 12a b - 2a )cosh(x) +--R + +--R 2 2 3 3 3 2 3 +--R (- 16a b - 8a b + 2a )cosh(x) + (- 16b - 16a b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 2 3 8 +--R a b cosh(x) + (2a b - a b - a )cosh(x) +--R + +--R 2 2 3 6 2 2 3 4 +--R (- 4a b - 9a b - 3a )cosh(x) + (- 14a b - 11a b - 5a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 8b - 8a b - 12a b - 5a )cosh(x) - 8a b - 8a b - 2a +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R Type: Expression Integer +--E 87 + +--S 88 of 526 +t0415:= (1+sech(x)^2)^(3/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (86) (sech(x) + 1)\|sech(x) + 1 +--R Type: Expression Integer +--E 88 + +--S 89 of 526 +r0415:= 2*asin(1/2*2^(1/2)*tanh(x))+atanh(tanh(x)/(2-tanh(x)^2)^(1/2))+1/2*tanh(x)*(2-tanh(x)^2)^(1/2) +--R +--R +--R (87) +--R +--------------+ +-+ +--R tanh(x) | 2 \|2 tanh(x) +--R 2atanh(-----------------) + tanh(x)\|- tanh(x) + 2 + 4asin(-----------) +--R +--------------+ 2 +--R | 2 +--R \|- tanh(x) + 2 +--R ------------------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 89 + +--S 90 of 526 +a0415:= integrate(t0415,x) +--R +--R +--R (88) +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) + 5)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) + 20cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) + 30cosh(x) + 7)sinh(x) +--R + +--R 5 3 6 +--R (6cosh(x) + 20cosh(x) + 14cosh(x))sinh(x) + cosh(x) +--R + +--R 4 2 +--R 5cosh(x) + 7cosh(x) + 3 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - sinh(x) - 8cosh(x)sinh(x) + (- 28cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (- 56cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70cosh(x) - 120cosh(x) - 18)sinh(x) +--R + +--R 5 3 3 +--R (- 56cosh(x) - 160cosh(x) - 72cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28cosh(x) - 120cosh(x) - 108cosh(x) - 16)sinh(x) +--R + +--R 7 5 3 8 +--R (- 8cosh(x) - 48cosh(x) - 72cosh(x) - 32cosh(x))sinh(x) - cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) - 18cosh(x) - 16cosh(x) - 5 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R + +--R 6 5 2 4 +--R - sinh(x) - 6cosh(x)sinh(x) + (- 15cosh(x) - 5)sinh(x) +--R + +--R 3 3 +--R (- 20cosh(x) - 20cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 15cosh(x) - 30cosh(x) - 7)sinh(x) +--R + +--R 5 3 6 +--R (- 6cosh(x) - 20cosh(x) - 14cosh(x))sinh(x) - cosh(x) +--R + +--R 4 2 +--R - 5cosh(x) - 7cosh(x) - 3 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R sinh(x) + 8cosh(x)sinh(x) + (28cosh(x) + 8)sinh(x) +--R + +--R 3 5 +--R (56cosh(x) + 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70cosh(x) + 120cosh(x) + 18)sinh(x) +--R + +--R 5 3 3 +--R (56cosh(x) + 160cosh(x) + 72cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28cosh(x) + 120cosh(x) + 108cosh(x) + 16)sinh(x) +--R + +--R 7 5 3 8 +--R (8cosh(x) + 48cosh(x) + 72cosh(x) + 32cosh(x))sinh(x) + cosh(x) +--R + +--R 6 4 2 +--R 8cosh(x) + 18cosh(x) + 16cosh(x) + 5 +--R * +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) + 40)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) + 160cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) + 240cosh(x) + 56)sinh(x) +--R + +--R 5 3 6 +--R (48cosh(x) + 160cosh(x) + 112cosh(x))sinh(x) + 8cosh(x) +--R + +--R 4 2 +--R 40cosh(x) + 56cosh(x) + 24 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 8sinh(x) - 64cosh(x)sinh(x) + (- 224cosh(x) - 64)sinh(x) +--R + +--R 3 5 +--R (- 448cosh(x) - 384cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 560cosh(x) - 960cosh(x) - 144)sinh(x) +--R + +--R 5 3 3 +--R (- 448cosh(x) - 1280cosh(x) - 576cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 224cosh(x) - 960cosh(x) - 864cosh(x) - 128)sinh(x) +--R + +--R 7 5 3 +--R (- 64cosh(x) - 384cosh(x) - 576cosh(x) - 256cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 8cosh(x) - 64cosh(x) - 144cosh(x) - 128cosh(x) - 40 +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R / +--R 2 +--R + +--R 2 2 +--R (8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) + 8) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R - 8sinh(x) - 32cosh(x)sinh(x) + (- 48cosh(x) - 32)sinh(x) +--R + +--R 3 4 2 +--R (- 32cosh(x) - 64cosh(x))sinh(x) - 8cosh(x) - 32cosh(x) - 8 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 10)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) + 40cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) + 60cosh(x) + 14)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 40cosh(x) + 28cosh(x))sinh(x) + 2cosh(x) + 10cosh(x) +--R + +--R 2 +--R 14cosh(x) + 6 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) - 16)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) - 96cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) - 240cosh(x) - 36)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) - 320cosh(x) - 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) - 240cosh(x) - 216cosh(x) - 32)sinh(x) +--R + +--R 7 5 3 8 +--R (- 16cosh(x) - 96cosh(x) - 144cosh(x) - 64cosh(x))sinh(x) - 2cosh(x) +--R + +--R 6 4 2 +--R - 16cosh(x) - 36cosh(x) - 32cosh(x) - 10 +--R Type: Union(Expression Integer,...) +--E 90 + +--S 91 of 526 +--m0415:= a0415-r0415 +--E 91 + +--S 92 of 526 +--d0415:= D(m0415,x) +--E 92 + +--S 93 of 526 +t0416:= (1-sech(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (89) (- sech(x) + 1)\|- sech(x) + 1 +--R Type: Expression Integer +--E 93 + +--S 94 of 526 +r0416:= 1/2*coth(x)*(tanh(x)^2)^(1/2)*(2*log(cosh(x))-tanh(x)^2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (2coth(x)log(cosh(x)) - coth(x)tanh(x) )\|tanh(x) +--R (90) --------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 94 + +--S 95 of 526 +a0416:= integrate(t0416,x) +--R +--R +--R (91) +--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 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R - x sinh(x) - 4x cosh(x)sinh(x) + (- 6x cosh(x) - 2x + 2)sinh(x) +--R + +--R 3 4 +--R (- 4x cosh(x) + (- 4x + 4)cosh(x))sinh(x) - x cosh(x) +--R + +--R 2 +--R (- 2x + 2)cosh(x) - 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 95 + +--S 96 of 526 +m0416:= a0416-r0416 +--R +--R +--R (92) +--R 4 3 +--R - 2coth(x)sinh(x) - 8cosh(x)coth(x)sinh(x) +--R + +--R 2 2 +--R (- 12cosh(x) - 4)coth(x)sinh(x) +--R + +--R 3 +--R (- 8cosh(x) - 8cosh(x))coth(x)sinh(x) +--R + +--R 4 2 +--R (- 2cosh(x) - 4cosh(x) - 2)coth(x) +--R * +--R log(cosh(x)) +--R + +--R 4 3 +--R coth(x)sinh(x) + 4cosh(x)coth(x)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) + 2)coth(x)sinh(x) +--R + +--R 3 +--R (4cosh(x) + 4cosh(x))coth(x)sinh(x) +--R + +--R 4 2 +--R (cosh(x) + 2cosh(x) + 1)coth(x) +--R * +--R 2 +--R tanh(x) +--R * +--R +--------+ +--R | 2 +--R \|tanh(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 * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R - 2x sinh(x) - 8x cosh(x)sinh(x) + (- 12x cosh(x) - 4x + 4)sinh(x) +--R + +--R 3 4 +--R (- 8x cosh(x) + (- 8x + 8)cosh(x))sinh(x) - 2x cosh(x) +--R + +--R 2 +--R (- 4x + 4)cosh(x) - 2x +--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 96 + +--S 97 of 526 +d0416:= D(m0416,x) +--R +--R +--R (93) +--R 7 6 2 5 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 6)sinh(x) +--R + +--R 3 4 +--R (40cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (30cosh(x) + 4cosh(x) + 6)sinh(x) +--R + +--R 5 3 2 +--R (12cosh(x) - 24cosh(x) + 20cosh(x))sinh(x) +--R + +--R 6 4 2 5 +--R (2cosh(x) - 26cosh(x) + 22cosh(x) + 2)sinh(x) - 8cosh(x) +--R + +--R 3 +--R 8cosh(x) +--R * +--R +--------+ +--R | 2 +--R \|tanh(x) +--R + +--R 6 2 5 +--R 2cosh(x)coth(x)sinh(x) + 12cosh(x) coth(x)sinh(x) +--R + +--R 3 4 +--R (30cosh(x) + 6cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (40cosh(x) + 24cosh(x) )coth(x)sinh(x) +--R + +--R 5 3 2 +--R (30cosh(x) + 36cosh(x) + 6cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (12cosh(x) + 24cosh(x) + 12cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (2cosh(x) + 6cosh(x) + 6cosh(x) + 2cosh(x))coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 2 6 +--R (2cosh(x)coth(x) - 2cosh(x))sinh(x) +--R + +--R 2 2 2 5 +--R (12cosh(x) coth(x) - 12cosh(x) )sinh(x) +--R + +--R 3 2 3 4 +--R ((30cosh(x) + 6cosh(x))coth(x) - 30cosh(x) - 6cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R ((40cosh(x) + 24cosh(x) )coth(x) - 40cosh(x) - 24cosh(x) ) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (30cosh(x) + 36cosh(x) + 6cosh(x))coth(x) - 30cosh(x) +--R + +--R 3 +--R - 36cosh(x) - 6cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (12cosh(x) + 24cosh(x) + 12cosh(x) )coth(x) - 12cosh(x) +--R + +--R 4 2 +--R - 24cosh(x) - 12cosh(x) +--R * +--R sinh(x) +--R + +--R 7 5 3 2 +--R (2cosh(x) + 6cosh(x) + 6cosh(x) + 2cosh(x))coth(x) +--R + +--R 7 5 3 +--R - 2cosh(x) - 6cosh(x) - 6cosh(x) - 2cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 6 2 5 +--R - 2cosh(x)coth(x)sinh(x) - 12cosh(x) coth(x)sinh(x) +--R + +--R 3 4 +--R (- 30cosh(x) - 6cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (- 40cosh(x) - 24cosh(x) )coth(x)sinh(x) +--R + +--R 5 3 2 +--R (- 30cosh(x) - 36cosh(x) - 6cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (- 12cosh(x) - 24cosh(x) - 12cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (- 2cosh(x) - 6cosh(x) - 6cosh(x) - 2cosh(x))coth(x) +--R * +--R tanh(x) +--R * +--R log(cosh(x)) +--R + +--R 6 2 5 +--R - 3cosh(x)coth(x)sinh(x) - 18cosh(x) coth(x)sinh(x) +--R + +--R 3 4 +--R (- 45cosh(x) - 9cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (- 60cosh(x) - 36cosh(x) )coth(x)sinh(x) +--R + +--R 5 3 2 +--R (- 45cosh(x) - 54cosh(x) - 9cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (- 18cosh(x) - 36cosh(x) - 18cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (- 3cosh(x) - 9cosh(x) - 9cosh(x) - 3cosh(x))coth(x) +--R * +--R 5 +--R tanh(x) +--R + +--R 2 6 +--R (- cosh(x)coth(x) + cosh(x))sinh(x) +--R + +--R 2 2 2 5 +--R (- 6cosh(x) coth(x) + 6cosh(x) )sinh(x) +--R + +--R 3 2 3 4 +--R ((- 15cosh(x) - 3cosh(x))coth(x) + 15cosh(x) + 3cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R ((- 20cosh(x) - 12cosh(x) )coth(x) + 20cosh(x) + 12cosh(x) ) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 15cosh(x) - 18cosh(x) - 3cosh(x))coth(x) + 15cosh(x) +--R + +--R 3 +--R 18cosh(x) + 3cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (- 6cosh(x) - 12cosh(x) - 6cosh(x) )coth(x) + 6cosh(x) +--R + +--R 4 2 +--R 12cosh(x) + 6cosh(x) +--R * +--R sinh(x) +--R + +--R 7 5 3 2 7 +--R (- cosh(x) - 3cosh(x) - 3cosh(x) - cosh(x))coth(x) + cosh(x) +--R + +--R 5 3 +--R 3cosh(x) + 3cosh(x) + cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 6 2 5 +--R 3cosh(x)coth(x)sinh(x) + 18cosh(x) coth(x)sinh(x) +--R + +--R 3 4 +--R (45cosh(x) + 9cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (60cosh(x) + 36cosh(x) )coth(x)sinh(x) +--R + +--R 5 3 2 +--R (45cosh(x) + 54cosh(x) + 9cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (18cosh(x) + 36cosh(x) + 18cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (3cosh(x) + 9cosh(x) + 9cosh(x) + 3cosh(x))coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 7 6 +--R - 2coth(x)sinh(x) - 12cosh(x)coth(x)sinh(x) +--R + +--R 2 5 +--R (- 30cosh(x) - 6)coth(x)sinh(x) +--R + +--R 3 4 +--R (- 40cosh(x) - 24cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (- 30cosh(x) - 36cosh(x) - 6)coth(x)sinh(x) +--R + +--R 5 3 2 +--R (- 12cosh(x) - 24cosh(x) - 12cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (- 2cosh(x) - 6cosh(x) - 6cosh(x) - 2)coth(x)sinh(x) +--R * +--R 2 +--R tanh(x) +--R / +--R 6 2 5 3 4 +--R 2cosh(x)sinh(x) + 12cosh(x) sinh(x) + (30cosh(x) + 6cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (40cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 5 3 2 +--R (30cosh(x) + 36cosh(x) + 6cosh(x))sinh(x) +--R + +--R 6 4 2 7 5 +--R (12cosh(x) + 24cosh(x) + 12cosh(x) )sinh(x) + 2cosh(x) + 6cosh(x) +--R + +--R 3 +--R 6cosh(x) + 2cosh(x) +--R * +--R +--------+ +--R | 2 +--R \|tanh(x) +--R Type: Expression Integer +--E 97 + +--S 98 of 526 +t0417:= (-1+sech(x)^2)^(3/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (94) (sech(x) - 1)\|sech(x) - 1 +--R Type: Expression Integer +--E 98 + +--S 99 of 526 +r0417:= -1/2*coth(x)*(-tanh(x)^2)^(1/2)*(2*log(cosh(x))-tanh(x)^2) +--R +--R +--R +----------+ +--R 2 | 2 +--R (- 2coth(x)log(cosh(x)) + coth(x)tanh(x) )\|- tanh(x) +--R (95) ------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 99 + +--S 100 of 526 +a0417:= integrate(t0417,x) +--R +--R +--R (96) 0 +--R Type: Union(Expression Integer,...) +--E 100 + +--S 101 of 526 +m0417:= a0417-r0417 +--R +--R +--R +----------+ +--R 2 | 2 +--R (2coth(x)log(cosh(x)) - coth(x)tanh(x) )\|- tanh(x) +--R (97) ----------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 101 + +--S 102 of 526 +d0417:= D(m0417,x) +--R +--R +--R (98) +--R 3 2 2 +--R 2cosh(x)coth(x)tanh(x) + (2cosh(x)coth(x) - 2cosh(x))tanh(x) +--R + +--R - 2cosh(x)coth(x)tanh(x) +--R * +--R log(cosh(x)) +--R + +--R 5 2 4 +--R - 3cosh(x)coth(x)tanh(x) + (- cosh(x)coth(x) + cosh(x))tanh(x) +--R + +--R 3 2 +--R 3cosh(x)coth(x)tanh(x) - 2coth(x)sinh(x)tanh(x) +--R / +--R +----------+ +--R | 2 +--R 2cosh(x)\|- tanh(x) +--R Type: Expression Integer +--E 102 + +--S 103 of 526 +t0418:= (-1-sech(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (99) (- sech(x) - 1)\|- sech(x) - 1 +--R Type: Expression Integer +--E 103 + +--S 104 of 526 +r0418:= atan(tanh(x)/(-2+tanh(x)^2)^(1/2))+2*atanh(coth(x)*(-2+tanh(x)^2)^(1/2))-1/2*tanh(x)*(-2+tanh(x)^2)^(1/2) +--R +--R +--R (100) +--R +------------+ +--R | 2 tanh(x) +--R 4atanh(coth(x)\|tanh(x) - 2 ) + 2atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R +------------+ +--R | 2 +--R - tanh(x)\|tanh(x) - 2 +--R / +--R 2 +--R Type: Expression Integer +--E 104 + +--S 105 of 526 +a0418:= integrate(t0418,x) +--R +--R +--R (101) +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (12(%e ) + 28(%e ) + 20(%e ) + 4)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 20\|- 1 (%e ) - 64\|- 1 (%e ) - 72\|- 1 (%e ) - 32\|- 1 (%e ) +--R + +--R +---+ +--R - 4\|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 + 2)(%e ) - \|- 1 +--R log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (3\|- 1 (%e ) + 7\|- 1 (%e ) + 5\|- 1 (%e ) + \|- 1 ) +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R x 8 x 6 x 4 x 2 +--R 5(%e ) + 16(%e ) + 18(%e ) + 8(%e ) + 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 - \|- 1 (%e ) - \|- 1 +--R log(-------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (- 12(%e ) - 28(%e ) - 20(%e ) - 4)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R 20\|- 1 (%e ) + 64\|- 1 (%e ) + 72\|- 1 (%e ) + 32\|- 1 (%e ) +--R + +--R +---+ +--R 4\|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 - 2)(%e ) - \|- 1 +--R log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (- 3\|- 1 (%e ) - 7\|- 1 (%e ) - 5\|- 1 (%e ) - \|- 1 ) +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R x 8 x 6 x 4 x 2 +--R - 5(%e ) - 16(%e ) - 18(%e ) - 8(%e ) - 1 +--R * +--R log +--R +----------------------+ +--R +---+ x 2 +---+ | x 4 x 2 x 4 +--R (- 2\|- 1 (%e ) - 2\|- 1 )\|- (%e ) - 6(%e ) - 1 + 2(%e ) +--R + +--R x 2 +--R - 8(%e ) - 2 +--R / +--R x 4 +--R (%e ) +--R + +--R +----------------------+ +--R +---+ x 6 +---+ x 4 | x 4 x 2 x 8 +--R (8\|- 1 (%e ) + 8\|- 1 (%e ) )\|- (%e ) - 6(%e ) - 1 + 8(%e ) +--R + +--R x 6 x 4 +--R 32(%e ) + 8(%e ) +--R / +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (6(%e ) + 14(%e ) + 10(%e ) + 2)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 10\|- 1 (%e ) - 32\|- 1 (%e ) - 36\|- 1 (%e ) - 16\|- 1 (%e ) +--R + +--R +---+ +--R - 2\|- 1 +--R Type: Union(Expression Integer,...) +--E 105 + +--S 106 of 526 +m0418:= a0418-r0418 +--R +--R +--R (102) +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (12(%e ) + 28(%e ) + 20(%e ) + 4)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 20\|- 1 (%e ) - 64\|- 1 (%e ) - 72\|- 1 (%e ) - 32\|- 1 (%e ) +--R + +--R +---+ +--R - 4\|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 + 2)(%e ) - \|- 1 +--R log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (3\|- 1 (%e ) + 7\|- 1 (%e ) + 5\|- 1 (%e ) + \|- 1 ) +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R x 8 x 6 x 4 x 2 +--R 5(%e ) + 16(%e ) + 18(%e ) + 8(%e ) + 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 - \|- 1 (%e ) - \|- 1 +--R log(-------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (- 12(%e ) - 28(%e ) - 20(%e ) - 4)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R 20\|- 1 (%e ) + 64\|- 1 (%e ) + 72\|- 1 (%e ) + 32\|- 1 (%e ) +--R + +--R +---+ +--R 4\|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 - 2)(%e ) - \|- 1 +--R log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (- 3\|- 1 (%e ) - 7\|- 1 (%e ) - 5\|- 1 (%e ) - \|- 1 ) +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R x 8 x 6 x 4 x 2 +--R - 5(%e ) - 16(%e ) - 18(%e ) - 8(%e ) - 1 +--R * +--R log +--R +----------------------+ +--R +---+ x 2 +---+ | x 4 x 2 x 4 +--R (- 2\|- 1 (%e ) - 2\|- 1 )\|- (%e ) - 6(%e ) - 1 + 2(%e ) +--R + +--R x 2 +--R - 8(%e ) - 2 +--R / +--R x 4 +--R (%e ) +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (- 12(%e ) - 28(%e ) - 20(%e ) - 4)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R 20\|- 1 (%e ) + 64\|- 1 (%e ) + 72\|- 1 (%e ) + 32\|- 1 (%e ) +--R + +--R +---+ +--R 4\|- 1 +--R * +--R +------------+ +--R | 2 +--R atanh(coth(x)\|tanh(x) - 2 ) +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (- 6(%e ) - 14(%e ) - 10(%e ) - 2)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R 10\|- 1 (%e ) + 32\|- 1 (%e ) + 36\|- 1 (%e ) + 16\|- 1 (%e ) +--R + +--R +---+ +--R 2\|- 1 +--R * +--R tanh(x) +--R atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (3(%e ) + 7(%e ) + 5(%e ) + 1)tanh(x)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 5\|- 1 (%e ) - 16\|- 1 (%e ) - 18\|- 1 (%e ) - 8\|- 1 (%e ) +--R + +--R +---+ +--R - \|- 1 +--R * +--R tanh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R +----------------------+ +--R +---+ x 6 +---+ x 4 | x 4 x 2 x 8 +--R (8\|- 1 (%e ) + 8\|- 1 (%e ) )\|- (%e ) - 6(%e ) - 1 + 8(%e ) +--R + +--R x 6 x 4 +--R 32(%e ) + 8(%e ) +--R / +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (6(%e ) + 14(%e ) + 10(%e ) + 2)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 10\|- 1 (%e ) - 32\|- 1 (%e ) - 36\|- 1 (%e ) - 16\|- 1 (%e ) +--R + +--R +---+ +--R - 2\|- 1 +--R Type: Expression Integer +--E 106 + +--S 107 of 526 +d0418:= D(m0418,x) +--R +--R +--R (103) +--R +---+ 2 x 18 +---+ 2 x 16 +--R 129\|- 1 coth(x) (%e ) + 1663\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 14 +---+ 2 x 12 +--R 7290\|- 1 coth(x) (%e ) + 13482\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 10 +---+ 2 x 8 +--R 12348\|- 1 coth(x) (%e ) + 6216\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 6 +---+ 2 x 4 +--R 1806\|- 1 coth(x) (%e ) + 302\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 2 +---+ 2 +--R 27\|- 1 coth(x) (%e ) + \|- 1 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 18 +--R (- 258\|- 1 coth(x) - 129\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (- 3326\|- 1 coth(x) - 1663\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (- 14580\|- 1 coth(x) - 7290\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (- 26964\|- 1 coth(x) - 13482\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (- 24696\|- 1 coth(x) - 12348\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (- 12432\|- 1 coth(x) - 6216\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (- 3612\|- 1 coth(x) - 1806\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (- 604\|- 1 coth(x) - 302\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 54\|- 1 coth(x) - 27\|- 1 )(%e ) - 2\|- 1 coth(x) - \|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R 2 x 20 2 x 18 2 x 16 +--R 127coth(x) (%e ) + 2046coth(x) (%e ) + 11789coth(x) (%e ) +--R + +--R 2 x 14 2 x 12 +--R 30168coth(x) (%e ) + 38118coth(x) (%e ) +--R + +--R 2 x 10 2 x 8 2 x 6 +--R 26388coth(x) (%e ) + 10706coth(x) (%e ) + 2616coth(x) (%e ) +--R + +--R 2 x 4 2 x 2 2 +--R 379coth(x) (%e ) + 30coth(x) (%e ) + coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 x 20 2 x 18 +--R (- 254coth(x) - 127)(%e ) + (- 4092coth(x) - 2046)(%e ) +--R + +--R 2 x 16 2 x 14 +--R (- 23578coth(x) - 11789)(%e ) + (- 60336coth(x) - 30168)(%e ) +--R + +--R 2 x 12 2 x 10 +--R (- 76236coth(x) - 38118)(%e ) + (- 52776coth(x) - 26388)(%e ) +--R + +--R 2 x 8 2 x 6 +--R (- 21412coth(x) - 10706)(%e ) + (- 5232coth(x) - 2616)(%e ) +--R + +--R 2 x 4 2 x 2 2 +--R (- 758coth(x) - 379)(%e ) + (- 60coth(x) - 30)(%e ) - 2coth(x) - 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R 2 x 18 2 x 16 2 x 14 +--R - 127coth(x) (%e ) - 903coth(x) (%e ) - 2646coth(x) (%e ) +--R + +--R 2 x 12 2 x 10 2 x 8 +--R - 4210coth(x) (%e ) - 4004coth(x) (%e ) - 2352coth(x) (%e ) +--R + +--R 2 x 6 2 x 4 2 x 2 +--R - 850coth(x) (%e ) - 182coth(x) (%e ) - 21coth(x) (%e ) +--R + +--R 2 +--R - coth(x) +--R * +--R 6 +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R (508coth(x) + 127)(%e ) + (3612coth(x) + 903)(%e ) +--R + +--R 2 x 14 2 x 12 +--R (10584coth(x) + 2646)(%e ) + (16840coth(x) + 4210)(%e ) +--R + +--R 2 x 10 2 x 8 +--R (16016coth(x) + 4004)(%e ) + (9408coth(x) + 2352)(%e ) +--R + +--R 2 x 6 2 x 4 +--R (3400coth(x) + 850)(%e ) + (728coth(x) + 182)(%e ) +--R + +--R 2 x 2 2 +--R (84coth(x) + 21)(%e ) + 4coth(x) + 1 +--R * +--R 4 +--R tanh(x) +--R + +--R x 18 x 16 x 14 +--R - 254coth(x)(%e ) - 1806coth(x)(%e ) - 5292coth(x)(%e ) +--R + +--R x 12 x 10 x 8 +--R - 8420coth(x)(%e ) - 8008coth(x)(%e ) - 4704coth(x)(%e ) +--R + +--R x 6 x 4 x 2 +--R - 1700coth(x)(%e ) - 364coth(x)(%e ) - 42coth(x)(%e ) - 2coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R - 1016coth(x) (%e ) - 7224coth(x) (%e ) +--R + +--R 2 x 14 2 x 12 +--R - 21168coth(x) (%e ) - 33680coth(x) (%e ) +--R + +--R 2 x 10 2 x 8 2 x 6 +--R - 32032coth(x) (%e ) - 18816coth(x) (%e ) - 6800coth(x) (%e ) +--R + +--R 2 x 4 2 x 2 2 +--R - 1456coth(x) (%e ) - 168coth(x) (%e ) - 8coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R x 18 x 16 x 14 +--R 254coth(x)(%e ) + 1806coth(x)(%e ) + 5292coth(x)(%e ) +--R + +--R x 12 x 10 x 8 +--R 8420coth(x)(%e ) + 8008coth(x)(%e ) + 4704coth(x)(%e ) +--R + +--R x 6 x 4 x 2 +--R 1700coth(x)(%e ) + 364coth(x)(%e ) + 42coth(x)(%e ) + 2coth(x) +--R * +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R (1016coth(x) - 254)(%e ) + (7224coth(x) - 1806)(%e ) +--R + +--R 2 x 14 2 x 12 +--R (21168coth(x) - 5292)(%e ) + (33680coth(x) - 8420)(%e ) +--R + +--R 2 x 10 2 x 8 +--R (32032coth(x) - 8008)(%e ) + (18816coth(x) - 4704)(%e ) +--R + +--R 2 x 6 2 x 4 +--R (6800coth(x) - 1700)(%e ) + (1456coth(x) - 364)(%e ) +--R + +--R 2 x 2 2 +--R (168coth(x) - 42)(%e ) + 8coth(x) - 2 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ 2 x 20 +---+ 2 x 18 +--R 129\|- 1 coth(x) (%e ) + 1276\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 16 +---+ 2 x 14 +--R 4881\|- 1 coth(x) (%e ) + 9908\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 12 +---+ 2 x 10 +--R 11998\|- 1 coth(x) (%e ) + 9100\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 8 +---+ 2 x 6 +--R 4382\|- 1 coth(x) (%e ) + 1324\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 4 +---+ 2 x 2 +---+ 2 +--R 241\|- 1 coth(x) (%e ) + 24\|- 1 coth(x) (%e ) + \|- 1 coth(x) +--R * +--R 6 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 20 +--R (- 516\|- 1 coth(x) - 129\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 18 +--R (- 5104\|- 1 coth(x) - 1276\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (- 19524\|- 1 coth(x) - 4881\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (- 39632\|- 1 coth(x) - 9908\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (- 47992\|- 1 coth(x) - 11998\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (- 36400\|- 1 coth(x) - 9100\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (- 17528\|- 1 coth(x) - 4382\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (- 5296\|- 1 coth(x) - 1324\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (- 964\|- 1 coth(x) - 241\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 96\|- 1 coth(x) - 24\|- 1 )(%e ) - 4\|- 1 coth(x) - \|- 1 +--R * +--R 4 +--R tanh(x) +--R + +--R +---+ x 20 +---+ x 18 +--R 258\|- 1 coth(x)(%e ) + 2552\|- 1 coth(x)(%e ) +--R + +--R +---+ x 16 +---+ x 14 +--R 9762\|- 1 coth(x)(%e ) + 19816\|- 1 coth(x)(%e ) +--R + +--R +---+ x 12 +---+ x 10 +--R 23996\|- 1 coth(x)(%e ) + 18200\|- 1 coth(x)(%e ) +--R + +--R +---+ x 8 +---+ x 6 +--R 8764\|- 1 coth(x)(%e ) + 2648\|- 1 coth(x)(%e ) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R 482\|- 1 coth(x)(%e ) + 48\|- 1 coth(x)(%e ) + 2\|- 1 coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R +---+ 2 x 20 +---+ 2 x 18 +--R 1032\|- 1 coth(x) (%e ) + 10208\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 16 +---+ 2 x 14 +--R 39048\|- 1 coth(x) (%e ) + 79264\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 12 +---+ 2 x 10 +--R 95984\|- 1 coth(x) (%e ) + 72800\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 8 +---+ 2 x 6 +--R 35056\|- 1 coth(x) (%e ) + 10592\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 4 +---+ 2 x 2 +---+ 2 +--R 1928\|- 1 coth(x) (%e ) + 192\|- 1 coth(x) (%e ) + 8\|- 1 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ x 20 +---+ x 18 +--R - 258\|- 1 coth(x)(%e ) - 2552\|- 1 coth(x)(%e ) +--R + +--R +---+ x 16 +---+ x 14 +--R - 9762\|- 1 coth(x)(%e ) - 19816\|- 1 coth(x)(%e ) +--R + +--R +---+ x 12 +---+ x 10 +--R - 23996\|- 1 coth(x)(%e ) - 18200\|- 1 coth(x)(%e ) +--R + +--R +---+ x 8 +---+ x 6 +--R - 8764\|- 1 coth(x)(%e ) - 2648\|- 1 coth(x)(%e ) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R - 482\|- 1 coth(x)(%e ) - 48\|- 1 coth(x)(%e ) - 2\|- 1 coth(x) +--R * +--R tanh(x) +--R + +--R +---+ 2 +---+ x 20 +--R (- 1032\|- 1 coth(x) + 258\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 18 +--R (- 10208\|- 1 coth(x) + 2552\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (- 39048\|- 1 coth(x) + 9762\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (- 79264\|- 1 coth(x) + 19816\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (- 95984\|- 1 coth(x) + 23996\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (- 72800\|- 1 coth(x) + 18200\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (- 35056\|- 1 coth(x) + 8764\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (- 10592\|- 1 coth(x) + 2648\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (- 1928\|- 1 coth(x) + 482\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 192\|- 1 coth(x) + 48\|- 1 )(%e ) - 8\|- 1 coth(x) + 2\|- 1 +--R / +--R 2 x 18 2 x 16 2 x 14 +--R 127coth(x) (%e ) + 903coth(x) (%e ) + 2646coth(x) (%e ) +--R + +--R 2 x 12 2 x 10 2 x 8 +--R 4210coth(x) (%e ) + 4004coth(x) (%e ) + 2352coth(x) (%e ) +--R + +--R 2 x 6 2 x 4 2 x 2 +--R 850coth(x) (%e ) + 182coth(x) (%e ) + 21coth(x) (%e ) +--R + +--R 2 +--R coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R (- 254coth(x) - 127)(%e ) + (- 1806coth(x) - 903)(%e ) +--R + +--R 2 x 14 2 x 12 +--R (- 5292coth(x) - 2646)(%e ) + (- 8420coth(x) - 4210)(%e ) +--R + +--R 2 x 10 2 x 8 +--R (- 8008coth(x) - 4004)(%e ) + (- 4704coth(x) - 2352)(%e ) +--R + +--R 2 x 6 2 x 4 +--R (- 1700coth(x) - 850)(%e ) + (- 364coth(x) - 182)(%e ) +--R + +--R 2 x 2 2 +--R (- 42coth(x) - 21)(%e ) - 2coth(x) - 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ 2 x 20 +---+ 2 x 18 +--R - 129\|- 1 coth(x) (%e ) - 1276\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 16 +---+ 2 x 14 +--R - 4881\|- 1 coth(x) (%e ) - 9908\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 12 +---+ 2 x 10 +--R - 11998\|- 1 coth(x) (%e ) - 9100\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 8 +---+ 2 x 6 +--R - 4382\|- 1 coth(x) (%e ) - 1324\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 4 +---+ 2 x 2 +---+ 2 +--R - 241\|- 1 coth(x) (%e ) - 24\|- 1 coth(x) (%e ) - \|- 1 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 20 +--R (258\|- 1 coth(x) + 129\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 18 +--R (2552\|- 1 coth(x) + 1276\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (9762\|- 1 coth(x) + 4881\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (19816\|- 1 coth(x) + 9908\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (23996\|- 1 coth(x) + 11998\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (18200\|- 1 coth(x) + 9100\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (8764\|- 1 coth(x) + 4382\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (2648\|- 1 coth(x) + 1324\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (482\|- 1 coth(x) + 241\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (48\|- 1 coth(x) + 24\|- 1 )(%e ) + 2\|- 1 coth(x) + \|- 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R Type: Expression Integer +--E 107 + +--S 108 of 526 +t0419:= (a+b*sech(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (104) (b sech(x) + a)\|b sech(x) + a +--R Type: Expression Integer +--E 108 + +--S 109 of 526 +r0419:= -3/2*a*b^(1/2)*atan(coth(x)*(a+b*sech(x)^2)^(1/2)/b^(1/2))-1/2*b^(3/2)*atan(coth(x)*(a+b*sech(x)^2)^(1/2)/b^(1/2))+a^(3/2)*atanh(a^(1/2)*tanh(x)/(a+b*sech(x)^2)^(1/2))+1/2*b*(a+b*sech(x)^2)^(1/2)*tanh(x) +--R +--R +--R (105) +--R +-+ +--R +-+ tanh(x)\|a +--R 2a\|a atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R +--------------+ +--R | 2 +--------------+ +--R +-+ coth(x)\|b sech(x) + a | 2 +--R (- b - 3a)\|b atan(------------------------) + b tanh(x)\|b sech(x) + a +--R +-+ +--R \|b +--R / +--R 2 +--R Type: Expression Integer +--E 109 + +--S 110 of 526 +a0419:= integrate(t0419,x) +--R +--R +--R (106) +--R [ +--R 2 3 6 2 3 5 +--R (- 2a b - a )sinh(x) + (- 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b - 15a )cosh(x) - 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b - 20a )cosh(x) + (- 16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b - 15a )cosh(x) + (- 24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b - 6a )cosh(x) + (- 16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b - a )cosh(x) + (- 4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b - 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b + 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b + 56a b + 28a )cosh(x) + 4a b + 8a b + 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b + 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b + 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b + 120a b + 60a )cosh(x) + 2a b + 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b + 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b + 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b + 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b + 60a b + 36a )cosh(x) + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b + 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b + 40a b + 24a )cosh(x) + (8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b + 2a b + a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b + 10a b + 6a )cosh(x) + (4a b + 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 2 6 +--R (2b + 7a b + 3a )sinh(x) +--R + +--R 2 2 5 +--R (12b + 42a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 105a b + 45a )cosh(x) + 4b + 15a b + 9a )sinh(x) +--R + +--R 2 2 3 +--R (40b + 140a b + 60a )cosh(x) +--R + +--R 2 2 +--R (16b + 60a b + 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 105a b + 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b + 90a b + 54a )cosh(x) + 2b + 9a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (12b + 42a b + 18a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (16b + 60a b + 36a )cosh(x) + (4b + 18a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + 7a b + 3a )cosh(x) + (4b + 15a b + 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 9a b + 9a )cosh(x) + a b + 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +---+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|- b \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) - 4b - 20a b +--R + +--R 2 3 +--R - 28a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 560a b - 490a b - 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) - 2b - 16a b +--R + +--R 2 3 +--R - 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80b - 400a b - 560a b - 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 12b - 96a b - 216a b - 108a )cosh(x) - 4a b - 16a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 32a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 4b - 20a b - 28a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b - 16a b - 36a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4a b - 16a b - 12a )cosh(x) - a b - 3a +--R * +--R +---+ +--R \|- b +--R * +--R log +--R 4 3 +--R (2b + 2a)sinh(x) + (8b + 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((12b + 12a)cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R ((8b + 8a)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (2b + 2a)cosh(x) + 2a cosh(x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (4a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) - 2b - 4a b - 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (- 8b - 16a b - 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 24a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (- 8b - 16a b - 12a )cosh(x) +--R + +--R 2 +--R (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (- 2b - 4a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 6 2 5 +--R (- 2a b - 2a )sinh(x) + (- 12a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a b - 30a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 +--R ((- 40a b - 40a )cosh(x) + (- 24a b - 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 +--R (- 30a b - 30a )cosh(x) + (- 36a b - 24a )cosh(x) +--R + +--R 2 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 16a )cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 2a b - 2a )cosh(x) + (- 6a b - 4a )cosh(x) +--R + +--R 2 2 +--R - 2a cosh(x) +--R * +--R +---+ +--R \|- b +--R / +--R 2 4 2 3 +--R (2a b + a )sinh(x) + (8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b + 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b + 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b + a )cosh(x) + (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 30b - 30a b - 15a )cosh(x) - 2b - 6a b - 3a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 +--R (- 40b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 24a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 36a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 8b - 24a b - 12a )cosh(x) + (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b - 2a b - a )cosh(x) + (- 2b - 6a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 3 6 2 3 5 +--R (2a b + a )sinh(x) + (12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b + 15a )cosh(x) + 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b + 20a )cosh(x) + (16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (30a b + 15a )cosh(x) + (24a b + 18a )cosh(x) + 2a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b + 6a )cosh(x) + (16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (2a b + a )cosh(x) + (4a b + 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (2a b + 3a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b - 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 56a b - 56a b - 28a )cosh(x) - 4a b - 8a b - 4a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b - 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b - 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b - 120a b - 60a )cosh(x) - 2a b - 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b - 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b - 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b - 60a b - 36a )cosh(x) - 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b - 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) + (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b - 2a b - a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b - 10a b - 6a )cosh(x) + (- 4a b - 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) + 6b + 2a)sinh(x) +--R + +--R 3 4 +--R (- 8b cosh(x) + (12b + 4a)cosh(x))sinh(x) - 2b cosh(x) +--R + +--R 2 +--R (6b + 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 3 2 2 6 +--R (- 2b - 4a b - 2a b)sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((- 30b - 60a b - 30a b)cosh(x) + 2b - 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 +--R (- 40b - 80a b - 40a b)cosh(x) +--R + +--R 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 30b - 60a b - 30a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b - 36a b - 24a b)cosh(x) + 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) + (4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 2b - 4a b - 2a b)cosh(x) + (2b - 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b - 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (2b + 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 112a b + 56a b)cosh(x) + 12b + 14a b + 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (72b + 84a b + 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (180b + 210a b + 90a b)cosh(x) - 6b + 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (240b + 280a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (180b + 210a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b + 48a b + 36a b)cosh(x) - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 32a b + 16a b)cosh(x) +--R + +--R 3 2 2 5 +--R (72b + 84a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) + (- 4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 4a b + 2a b)cosh(x) + (12b + 14a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b + 8a b + 6a b)cosh(x) + (- 2a b + 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b + 2a)sinh(x) + (24b + 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b + 30a)cosh(x) + 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b + 40a)cosh(x) + (32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b + 30a)cosh(x) + (48b + 36a)cosh(x) + 4b + 6a)sinh(x) +--R + +--R 5 3 +--R ((24b + 12a)cosh(x) + (32b + 24a)cosh(x) + (8b + 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b + 2a)cosh(x) + (8b + 6a)cosh(x) + (4b + 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b - 4a b - 2a )sinh(x) + (- 32b - 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b - 112a b - 56a )cosh(x) - 8b - 16a b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b - 224a b - 112a )cosh(x) + (- 48b - 96a b - 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 280b - 280a b - 140a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) - 4b - 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 224b - 224a b - 112a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 160b - 320a b - 160a )cosh(x) + (- 16b - 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 +--R (- 112b - 112a b - 56a )cosh(x) +--R + +--R 2 2 4 +--R (- 120b - 240a b - 120a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 24b - 120a b - 72a )cosh(x) - 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b - 32a b - 16a )cosh(x) + (- 48b - 96a b - 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b - 80a b - 48a )cosh(x) + (- 16a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b - 4a b - 2a )cosh(x) + (- 8b - 16a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b - 20a b - 12a )cosh(x) + (- 8a b - 8a )cosh(x) - 2a +--R , +--R +--R 2 3 6 2 3 5 +--R (- 2a b - a )sinh(x) + (- 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b - 15a )cosh(x) - 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b - 20a )cosh(x) + (- 16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b - 15a )cosh(x) + (- 24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b - 6a )cosh(x) + (- 16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b - a )cosh(x) + (- 4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b - 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b + 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b + 56a b + 28a )cosh(x) + 4a b + 8a b + 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b + 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b + 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b + 120a b + 60a )cosh(x) + 2a b + 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b + 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b + 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b + 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b + 60a b + 36a )cosh(x) + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b + 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b + 40a b + 24a )cosh(x) + (8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b + 2a b + a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b + 10a b + 6a )cosh(x) + (4a b + 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 3 6 2 3 5 +--R (2a b + a )sinh(x) + (12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b + 15a )cosh(x) + 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b + 20a )cosh(x) + (16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (30a b + 15a )cosh(x) + (24a b + 18a )cosh(x) + 2a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b + 6a )cosh(x) + (16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (2a b + a )cosh(x) + (4a b + 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (2a b + 3a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b - 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 56a b - 56a b - 28a )cosh(x) - 4a b - 8a b - 4a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b - 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b - 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b - 120a b - 60a )cosh(x) - 2a b - 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b - 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b - 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b - 60a b - 36a )cosh(x) - 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b - 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) + (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b - 2a b - a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b - 10a b - 6a )cosh(x) + (- 4a b - 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) + 6b + 2a)sinh(x) +--R + +--R 3 4 +--R (- 8b cosh(x) + (12b + 4a)cosh(x))sinh(x) - 2b cosh(x) +--R + +--R 2 +--R (6b + 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 2 6 +--R (- 4b - 14a b - 6a )sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 84a b - 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 60b - 210a b - 90a )cosh(x) - 8b - 30a b - 18a )sinh(x) +--R + +--R 2 2 3 +--R (- 80b - 280a b - 120a )cosh(x) +--R + +--R 2 2 +--R (- 32b - 120a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 60b - 210a b - 90a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 48b - 180a b - 108a )cosh(x) - 4b - 18a b - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 84a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R (- 32b - 120a b - 72a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 4b - 14a b - 6a )cosh(x) + (- 8b - 30a b - 18a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 4b - 18a b - 18a )cosh(x) - 2a b - 6a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (4b + 16a b + 14a b + 6a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 128a b + 112a b + 48a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (112b + 448a b + 392a b + 168a )cosh(x) + 8b + 40a b +--R + +--R 2 3 +--R 56a b + 24a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (224b + 896a b + 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 +--R (48b + 240a b + 336a b + 144a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (280b + 1120a b + 980a b + 420a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (120b + 600a b + 840a b + 360a )cosh(x) + 4b + 32a b +--R + +--R 2 3 +--R 72a b + 36a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (224b + 896a b + 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (160b + 800a b + 1120a b + 480a )cosh(x) +--R + +--R 3 2 2 3 +--R (16b + 128a b + 288a b + 144a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (112b + 448a b + 392a b + 168a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (120b + 600a b + 840a b + 360a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (24b + 192a b + 432a b + 216a )cosh(x) + 8a b + 32a b +--R + +--R 3 +--R 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 128a b + 112a b + 48a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (48b + 240a b + 336a b + 144a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (16b + 128a b + 288a b + 144a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 64a b + 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (4b + 16a b + 14a b + 6a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (8b + 40a b + 56a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4b + 32a b + 72a b + 36a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (8a b + 32a b + 24a )cosh(x) + 2a b + 6a +--R * +--R +-+ +--R \|b +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|a \|b +--R + +--R 3 2 2 6 +--R (- 2b - 4a b - 2a b)sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((- 30b - 60a b - 30a b)cosh(x) + 2b - 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 +--R (- 40b - 80a b - 40a b)cosh(x) +--R + +--R 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 30b - 60a b - 30a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b - 36a b - 24a b)cosh(x) + 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) + (4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 2b - 4a b - 2a b)cosh(x) + (2b - 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b - 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (2b + 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 112a b + 56a b)cosh(x) + 12b + 14a b + 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (72b + 84a b + 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (180b + 210a b + 90a b)cosh(x) - 6b + 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (240b + 280a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (180b + 210a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b + 48a b + 36a b)cosh(x) - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 32a b + 16a b)cosh(x) +--R + +--R 3 2 2 5 +--R (72b + 84a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) + (- 4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 4a b + 2a b)cosh(x) + (12b + 14a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b + 8a b + 6a b)cosh(x) + (- 2a b + 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b + 2a)sinh(x) + (24b + 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b + 30a)cosh(x) + 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b + 40a)cosh(x) + (32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b + 30a)cosh(x) + (48b + 36a)cosh(x) + 4b + 6a)sinh(x) +--R + +--R 5 3 +--R ((24b + 12a)cosh(x) + (32b + 24a)cosh(x) + (8b + 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b + 2a)cosh(x) + (8b + 6a)cosh(x) + (4b + 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b - 4a b - 2a )sinh(x) + (- 32b - 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b - 112a b - 56a )cosh(x) - 8b - 16a b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b - 224a b - 112a )cosh(x) + (- 48b - 96a b - 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 280b - 280a b - 140a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) - 4b - 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 224b - 224a b - 112a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 160b - 320a b - 160a )cosh(x) + (- 16b - 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 +--R (- 112b - 112a b - 56a )cosh(x) +--R + +--R 2 2 4 +--R (- 120b - 240a b - 120a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 24b - 120a b - 72a )cosh(x) - 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b - 32a b - 16a )cosh(x) + (- 48b - 96a b - 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b - 80a b - 48a )cosh(x) + (- 16a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b - 4a b - 2a )cosh(x) + (- 8b - 16a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b - 20a b - 12a )cosh(x) + (- 8a b - 8a )cosh(x) - 2a +--R ] +--R Type: Union(List Expression Integer,...) +--E 110 + +--S 111 of 526 +m0419a:= a0419.1-r0419 +--R +--R +--R (107) +--R 2 3 6 2 3 5 +--R (- 2a b - a )sinh(x) + (- 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b - 15a )cosh(x) - 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b - 20a )cosh(x) + (- 16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b - 15a )cosh(x) + (- 24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b - 6a )cosh(x) + (- 16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b - a )cosh(x) + (- 4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b - 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b + 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b + 56a b + 28a )cosh(x) + 4a b + 8a b + 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b + 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b + 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b + 120a b + 60a )cosh(x) + 2a b + 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b + 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b + 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b + 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b + 60a b + 36a )cosh(x) + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b + 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b + 40a b + 24a )cosh(x) + (8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b + 2a b + a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b + 10a b + 6a )cosh(x) + (4a b + 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 2 6 2 2 5 +--R (2b + 7a b + 3a )sinh(x) + (12b + 42a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 105a b + 45a )cosh(x) + 4b + 15a b + 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 140a b + 60a )cosh(x) + (16b + 60a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 105a b + 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b + 90a b + 54a )cosh(x) + 2b + 9a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 42a b + 18a )cosh(x) + (16b + 60a b + 36a )cosh(x) +--R + +--R 2 2 +--R (4b + 18a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + 7a b + 3a )cosh(x) + (4b + 15a b + 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 9a b + 9a )cosh(x) + a b + 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +---+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|- b \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) - 4b - 20a b +--R + +--R 2 3 +--R - 28a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 560a b - 490a b - 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) - 2b - 16a b +--R + +--R 2 3 +--R - 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80b - 400a b - 560a b - 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 12b - 96a b - 216a b - 108a )cosh(x) - 4a b - 16a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 32a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 4b - 20a b - 28a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b - 16a b - 36a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4a b - 16a b - 12a )cosh(x) - a b - 3a +--R * +--R +---+ +--R \|- b +--R * +--R log +--R 4 3 +--R (2b + 2a)sinh(x) + (8b + 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((12b + 12a)cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R ((8b + 8a)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (2b + 2a)cosh(x) + 2a cosh(x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (4a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) - 2b - 4a b - 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (- 8b - 16a b - 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (30b - 15a )cosh(x) + (- 12b - 24a b - 18a )cosh(x) +--R + +--R 2 +--R - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (- 8b - 16a b - 12a )cosh(x) +--R + +--R 2 +--R (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (- 2b - 4a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 6 2 5 +--R (- 2a b - 2a )sinh(x) + (- 12a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a b - 30a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 3 +--R ((- 40a b - 40a )cosh(x) + (- 24a b - 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 +--R (- 30a b - 30a )cosh(x) + (- 36a b - 24a )cosh(x) +--R + +--R 2 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 16a )cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (- 2a b - 2a )cosh(x) + (- 6a b - 4a )cosh(x) - 2a cosh(x) +--R * +--R +---+ +--R \|- b +--R / +--R 2 4 2 3 +--R (2a b + a )sinh(x) + (8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b + 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b + 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b + a )cosh(x) + (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 30b - 30a b - 15a )cosh(x) - 2b - 6a b - 3a )sinh(x) +--R + +--R 2 2 3 +--R (- 40b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 24a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 36a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 8b - 24a b - 12a )cosh(x) + (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b - 2a b - a )cosh(x) + (- 2b - 6a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 3 6 2 3 5 +--R (2a b + a )sinh(x) + (12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b + 15a )cosh(x) + 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b + 20a )cosh(x) + (16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R ((30a b + 15a )cosh(x) + (24a b + 18a )cosh(x) + 2a b + 3a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b + 6a )cosh(x) + (16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 2 3 2 +--R (2a b + a )cosh(x) + (4a b + 3a )cosh(x) + (2a b + 3a )cosh(x) +--R + +--R 3 +--R a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b - 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((- 56a b - 56a b - 28a )cosh(x) - 4a b - 8a b - 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b - 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b - 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b - 120a b - 60a )cosh(x) - 2a b - 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b - 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b - 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b - 60a b - 36a )cosh(x) - 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b - 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) + (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b - 2a b - a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b - 10a b - 6a )cosh(x) + (- 4a b - 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) + 6b + 2a)sinh(x) +--R + +--R 3 4 +--R (- 8b cosh(x) + (12b + 4a)cosh(x))sinh(x) - 2b cosh(x) +--R + +--R 2 +--R (6b + 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 3 6 2 3 5 +--R (- 4a b - 2a )sinh(x) + (- 24a b - 12a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 60a b - 30a )cosh(x) - 8a b - 6a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 80a b - 40a )cosh(x) + (- 32a b - 24a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 60a b - 30a )cosh(x) + (- 48a b - 36a )cosh(x) - 4a b +--R + +--R 3 +--R - 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 24a b - 12a )cosh(x) + (- 32a b - 24a )cosh(x) +--R + +--R 2 3 +--R (- 8a b - 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 4a b - 2a )cosh(x) + (- 8a b - 6a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 4a b - 6a )cosh(x) - 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (4a b + 4a b + 2a )sinh(x) +--R + +--R 2 2 3 7 +--R (32a b + 32a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((112a b + 112a b + 56a )cosh(x) + 8a b + 16a b + 8a )sinh(x) +--R + +--R 2 2 3 3 +--R (224a b + 224a b + 112a )cosh(x) +--R + +--R 2 2 3 +--R (48a b + 96a b + 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (280a b + 280a b + 140a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (120a b + 240a b + 120a )cosh(x) + 4a b + 20a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (224a b + 224a b + 112a )cosh(x) +--R + +--R 2 2 3 3 +--R (160a b + 320a b + 160a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 80a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 4 +--R (120a b + 240a b + 120a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (24a b + 120a b + 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (32a b + 32a b + 16a )cosh(x) +--R + +--R 2 2 3 5 +--R (48a b + 96a b + 48a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (16a b + 80a b + 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (4a b + 4a b + 2a )cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (4a b + 20a b + 12a )cosh(x) + (8a b + 8a )cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R tanh(x)\|a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R 2 2 6 2 2 5 +--R (2b + 7a b + 3a )sinh(x) + (12b + 42a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 105a b + 45a )cosh(x) + 4b + 15a b + 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 140a b + 60a )cosh(x) + (16b + 60a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 105a b + 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b + 90a b + 54a )cosh(x) + 2b + 9a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 42a b + 18a )cosh(x) + (16b + 60a b + 36a )cosh(x) +--R + +--R 2 2 +--R (4b + 18a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + 7a b + 3a )cosh(x) + (4b + 15a b + 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 9a b + 9a )cosh(x) + a b + 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) - 4b - 20a b +--R + +--R 2 3 +--R - 28a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 560a b - 490a b - 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) - 2b - 16a b +--R + +--R 2 3 +--R - 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80b - 400a b - 560a b - 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 12b - 96a b - 216a b - 108a )cosh(x) - 4a b - 16a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 32a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 4b - 20a b - 28a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b - 16a b - 36a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4a b - 16a b - 12a )cosh(x) - a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R +--------------+ +--R | 2 +--R coth(x)\|b sech(x) + a +--R atan(------------------------) +--R +-+ +--R \|b +--R + +--R 2 6 2 5 +--R (- 2b - a b)sinh(x) + (- 12b - 6a b)cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30b - 15a b)cosh(x) - 4b - 3a b)sinh(x) +--R + +--R 2 3 2 3 +--R ((- 40b - 20a b)cosh(x) + (- 16b - 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 30b - 15a b)cosh(x) + (- 24b - 18a b)cosh(x) - 2b +--R + +--R - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12b - 6a b)cosh(x) + (- 16b - 12a b)cosh(x) +--R + +--R 2 +--R (- 4b - 6a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 2b - a b)cosh(x) + (- 4b - 3a b)cosh(x) +--R + +--R 2 2 +--R (- 2b - 3a b)cosh(x) - a b +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R tanh(x)\|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (2b + 2a b + a b)sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 16a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 56a b + 28a b)cosh(x) + 4b + 8a b + 4a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 +--R (24b + 48a b + 24a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 140a b + 70a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (60b + 120a b + 60a b)cosh(x) + 2b + 10a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 +--R (80b + 160a b + 80a b)cosh(x) +--R + +--R 3 2 2 +--R (8b + 40a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 56a b + 28a b)cosh(x) +--R + +--R 3 2 2 4 +--R (60b + 120a b + 60a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b + 60a b + 36a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 16a b + 8a b)cosh(x) +--R + +--R 3 2 2 5 +--R (24b + 48a b + 24a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b + 40a b + 24a b)cosh(x) + (8a b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 2a b + a b)cosh(x) + (4b + 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 2 +--R (2b + 10a b + 6a b)cosh(x) + (4a b + 4a b)cosh(x) + a b +--R * +--R tanh(x) +--R * +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R 3 2 2 6 +--R (- 2b - 4a b - 2a b)sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((- 30b - 60a b - 30a b)cosh(x) + 2b - 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 3 2 2 +--R ((- 40b - 80a b - 40a b)cosh(x) + (8b - 24a b - 16a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 30b - 60a b - 30a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b - 36a b - 24a b)cosh(x) + 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) + (4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 2b - 4a b - 2a b)cosh(x) + (2b - 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b - 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (2b + 4a b + 2a b)sinh(x) + (16b + 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 112a b + 56a b)cosh(x) + 12b + 14a b + 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (72b + 84a b + 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (180b + 210a b + 90a b)cosh(x) - 6b + 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (240b + 280a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (180b + 210a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b + 48a b + 36a b)cosh(x) - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 5 +--R (16b + 32a b + 16a b)cosh(x) + (72b + 84a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) + (- 4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 4a b + 2a b)cosh(x) + (12b + 14a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b + 8a b + 6a b)cosh(x) + (- 2a b + 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b + 2a)sinh(x) + (24b + 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b + 30a)cosh(x) + 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b + 40a)cosh(x) + (32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b + 30a)cosh(x) + (48b + 36a)cosh(x) + 4b + 6a)sinh(x) +--R + +--R 5 3 +--R ((24b + 12a)cosh(x) + (32b + 24a)cosh(x) + (8b + 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b + 2a)cosh(x) + (8b + 6a)cosh(x) + (4b + 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b - 4a b - 2a )sinh(x) + (- 32b - 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b - 112a b - 56a )cosh(x) - 8b - 16a b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b - 224a b - 112a )cosh(x) + (- 48b - 96a b - 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 280b - 280a b - 140a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) - 4b - 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 224b - 224a b - 112a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 160b - 320a b - 160a )cosh(x) + (- 16b - 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 +--R (- 112b - 112a b - 56a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) + (- 24b - 120a b - 72a )cosh(x) +--R + +--R 2 +--R - 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b - 32a b - 16a )cosh(x) + (- 48b - 96a b - 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b - 80a b - 48a )cosh(x) + (- 16a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b - 4a b - 2a )cosh(x) + (- 8b - 16a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b - 20a b - 12a )cosh(x) + (- 8a b - 8a )cosh(x) - 2a +--R Type: Expression Integer +--E 111 + +--S 112 of 526 +--d0419a:= D(m0419a,x) +--E 112 + +--S 113 of 526 +m0419b:= a0419.2-r0419 +--R +--R +--R (108) +--R 2 3 6 2 3 5 +--R (- 2a b - a )sinh(x) + (- 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b - 15a )cosh(x) - 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b - 20a )cosh(x) + (- 16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b - 15a )cosh(x) + (- 24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b - 6a )cosh(x) + (- 16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b - a )cosh(x) + (- 4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b - 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b + 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b + 56a b + 28a )cosh(x) + 4a b + 8a b + 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b + 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b + 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b + 120a b + 60a )cosh(x) + 2a b + 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b + 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b + 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b + 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b + 60a b + 36a )cosh(x) + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b + 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b + 40a b + 24a )cosh(x) + (8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b + 2a b + a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b + 10a b + 6a )cosh(x) + (4a b + 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 3 6 2 3 5 +--R (2a b + a )sinh(x) + (12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b + 15a )cosh(x) + 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b + 20a )cosh(x) + (16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R ((30a b + 15a )cosh(x) + (24a b + 18a )cosh(x) + 2a b + 3a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b + 6a )cosh(x) + (16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 2 3 2 +--R (2a b + a )cosh(x) + (4a b + 3a )cosh(x) + (2a b + 3a )cosh(x) +--R + +--R 3 +--R a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b - 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((- 56a b - 56a b - 28a )cosh(x) - 4a b - 8a b - 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b - 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b - 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b - 120a b - 60a )cosh(x) - 2a b - 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b - 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b - 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b - 60a b - 36a )cosh(x) - 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b - 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) + (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b - 2a b - a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b - 10a b - 6a )cosh(x) + (- 4a b - 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) + 6b + 2a)sinh(x) +--R + +--R 3 4 +--R (- 8b cosh(x) + (12b + 4a)cosh(x))sinh(x) - 2b cosh(x) +--R + +--R 2 +--R (6b + 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 3 6 2 3 5 +--R (- 4a b - 2a )sinh(x) + (- 24a b - 12a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 60a b - 30a )cosh(x) - 8a b - 6a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 80a b - 40a )cosh(x) + (- 32a b - 24a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 60a b - 30a )cosh(x) + (- 48a b - 36a )cosh(x) - 4a b +--R + +--R 3 +--R - 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 24a b - 12a )cosh(x) + (- 32a b - 24a )cosh(x) +--R + +--R 2 3 +--R (- 8a b - 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 4a b - 2a )cosh(x) + (- 8a b - 6a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 4a b - 6a )cosh(x) - 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (4a b + 4a b + 2a )sinh(x) +--R + +--R 2 2 3 7 +--R (32a b + 32a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((112a b + 112a b + 56a )cosh(x) + 8a b + 16a b + 8a )sinh(x) +--R + +--R 2 2 3 3 +--R (224a b + 224a b + 112a )cosh(x) +--R + +--R 2 2 3 +--R (48a b + 96a b + 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (280a b + 280a b + 140a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (120a b + 240a b + 120a )cosh(x) + 4a b + 20a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (224a b + 224a b + 112a )cosh(x) +--R + +--R 2 2 3 3 +--R (160a b + 320a b + 160a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 80a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 4 +--R (120a b + 240a b + 120a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (24a b + 120a b + 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (32a b + 32a b + 16a )cosh(x) +--R + +--R 2 2 3 5 +--R (48a b + 96a b + 48a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (16a b + 80a b + 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (4a b + 4a b + 2a )cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (4a b + 20a b + 12a )cosh(x) + (8a b + 8a )cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R tanh(x)\|a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R 2 2 6 2 2 5 +--R (2b + 7a b + 3a )sinh(x) + (12b + 42a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 105a b + 45a )cosh(x) + 4b + 15a b + 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 140a b + 60a )cosh(x) + (16b + 60a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 105a b + 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b + 90a b + 54a )cosh(x) + 2b + 9a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 42a b + 18a )cosh(x) + (16b + 60a b + 36a )cosh(x) +--R + +--R 2 2 +--R (4b + 18a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + 7a b + 3a )cosh(x) + (4b + 15a b + 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 9a b + 9a )cosh(x) + a b + 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) - 4b - 20a b +--R + +--R 2 3 +--R - 28a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 560a b - 490a b - 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) - 2b - 16a b +--R + +--R 2 3 +--R - 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80b - 400a b - 560a b - 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 12b - 96a b - 216a b - 108a )cosh(x) - 4a b - 16a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 32a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 4b - 20a b - 28a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b - 16a b - 36a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4a b - 16a b - 12a )cosh(x) - a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R +--------------+ +--R | 2 +--R coth(x)\|b sech(x) + a +--R atan(------------------------) +--R +-+ +--R \|b +--R + +--R 2 2 6 +--R (- 4b - 14a b - 6a )sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 84a b - 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 60b - 210a b - 90a )cosh(x) - 8b - 30a b - 18a )sinh(x) +--R + +--R 2 2 3 +--R (- 80b - 280a b - 120a )cosh(x) +--R + +--R 2 2 +--R (- 32b - 120a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 60b - 210a b - 90a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 48b - 180a b - 108a )cosh(x) - 4b - 18a b - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 84a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R (- 32b - 120a b - 72a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 4b - 14a b - 6a )cosh(x) + (- 8b - 30a b - 18a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 4b - 18a b - 18a )cosh(x) - 2a b - 6a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (4b + 16a b + 14a b + 6a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 128a b + 112a b + 48a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (112b + 448a b + 392a b + 168a )cosh(x) + 8b + 40a b +--R + +--R 2 3 +--R 56a b + 24a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (224b + 896a b + 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 +--R (48b + 240a b + 336a b + 144a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (280b + 1120a b + 980a b + 420a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (120b + 600a b + 840a b + 360a )cosh(x) + 4b + 32a b +--R + +--R 2 3 +--R 72a b + 36a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (224b + 896a b + 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (160b + 800a b + 1120a b + 480a )cosh(x) +--R + +--R 3 2 2 3 +--R (16b + 128a b + 288a b + 144a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (112b + 448a b + 392a b + 168a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (120b + 600a b + 840a b + 360a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (24b + 192a b + 432a b + 216a )cosh(x) + 8a b + 32a b +--R + +--R 3 +--R 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 128a b + 112a b + 48a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (48b + 240a b + 336a b + 144a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (16b + 128a b + 288a b + 144a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 64a b + 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (4b + 16a b + 14a b + 6a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (8b + 40a b + 56a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4b + 32a b + 72a b + 36a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (8a b + 32a b + 24a )cosh(x) + 2a b + 6a +--R * +--R +-+ +--R \|b +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|a \|b +--R + +--R 2 6 2 5 +--R (- 2b - a b)sinh(x) + (- 12b - 6a b)cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30b - 15a b)cosh(x) - 4b - 3a b)sinh(x) +--R + +--R 2 3 2 3 +--R ((- 40b - 20a b)cosh(x) + (- 16b - 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 30b - 15a b)cosh(x) + (- 24b - 18a b)cosh(x) - 2b +--R + +--R - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12b - 6a b)cosh(x) + (- 16b - 12a b)cosh(x) +--R + +--R 2 +--R (- 4b - 6a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 2b - a b)cosh(x) + (- 4b - 3a b)cosh(x) +--R + +--R 2 2 +--R (- 2b - 3a b)cosh(x) - a b +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R tanh(x)\|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (2b + 2a b + a b)sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 16a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 56a b + 28a b)cosh(x) + 4b + 8a b + 4a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 +--R (24b + 48a b + 24a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 140a b + 70a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (60b + 120a b + 60a b)cosh(x) + 2b + 10a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 +--R (80b + 160a b + 80a b)cosh(x) +--R + +--R 3 2 2 +--R (8b + 40a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 56a b + 28a b)cosh(x) +--R + +--R 3 2 2 4 +--R (60b + 120a b + 60a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b + 60a b + 36a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 16a b + 8a b)cosh(x) +--R + +--R 3 2 2 5 +--R (24b + 48a b + 24a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b + 40a b + 24a b)cosh(x) + (8a b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 2a b + a b)cosh(x) + (4b + 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 2 +--R (2b + 10a b + 6a b)cosh(x) + (4a b + 4a b)cosh(x) + a b +--R * +--R tanh(x) +--R * +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R 3 2 2 6 +--R (- 2b - 4a b - 2a b)sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((- 30b - 60a b - 30a b)cosh(x) + 2b - 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 3 2 2 +--R ((- 40b - 80a b - 40a b)cosh(x) + (8b - 24a b - 16a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 30b - 60a b - 30a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b - 36a b - 24a b)cosh(x) + 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) + (4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 2b - 4a b - 2a b)cosh(x) + (2b - 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b - 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (2b + 4a b + 2a b)sinh(x) + (16b + 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 112a b + 56a b)cosh(x) + 12b + 14a b + 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (72b + 84a b + 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (180b + 210a b + 90a b)cosh(x) - 6b + 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (240b + 280a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (180b + 210a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b + 48a b + 36a b)cosh(x) - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 5 +--R (16b + 32a b + 16a b)cosh(x) + (72b + 84a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) + (- 4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 4a b + 2a b)cosh(x) + (12b + 14a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b + 8a b + 6a b)cosh(x) + (- 2a b + 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b + 2a)sinh(x) + (24b + 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b + 30a)cosh(x) + 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b + 40a)cosh(x) + (32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b + 30a)cosh(x) + (48b + 36a)cosh(x) + 4b + 6a)sinh(x) +--R + +--R 5 3 +--R ((24b + 12a)cosh(x) + (32b + 24a)cosh(x) + (8b + 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b + 2a)cosh(x) + (8b + 6a)cosh(x) + (4b + 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b - 4a b - 2a )sinh(x) + (- 32b - 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b - 112a b - 56a )cosh(x) - 8b - 16a b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b - 224a b - 112a )cosh(x) + (- 48b - 96a b - 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 280b - 280a b - 140a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) - 4b - 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 224b - 224a b - 112a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 160b - 320a b - 160a )cosh(x) + (- 16b - 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 +--R (- 112b - 112a b - 56a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) + (- 24b - 120a b - 72a )cosh(x) +--R + +--R 2 +--R - 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b - 32a b - 16a )cosh(x) + (- 48b - 96a b - 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b - 80a b - 48a )cosh(x) + (- 16a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b - 4a b - 2a )cosh(x) + (- 8b - 16a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b - 20a b - 12a )cosh(x) + (- 8a b - 8a )cosh(x) - 2a +--R Type: Expression Integer +--E 113 + +--S 114 of 526 +--d0419b:= D(m0419b,x) +--E 114 + +--S 115 of 526 +t0420:= x/sech(x)^(3/2)-1/3*x*sech(x)^(1/2) +--R +--R +--R 2 +--R - x sech(x) + 3x +--R (109) ------------------ +--R +-------+ +--R 3sech(x)\|sech(x) +--R Type: Expression Integer +--E 115 + +--S 116 of 526 +r0420:= -2/9*(2*cosh(x)-3*x*sinh(x))/(1/cosh(x))^(1/2) +--R +--R +--R 6x sinh(x) - 4cosh(x) +--R (110) --------------------- +--R +-------+ +--R | 1 +--R 9 |------- +--R \|cosh(x) +--R Type: Expression Integer +--E 116 + +--S 117 of 526 +a0420:= integrate(t0420,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 117 + +--S 118 of 526 +m0420:= a0420-r0420 +--R +--R +--R +-------+ +--R | 1 +--R 9a0420 |------- - 6x sinh(x) + 4cosh(x) +--R \|cosh(x) +--R (111) ---------------------------------------- +--R +-------+ +--R | 1 +--R 9 |------- +--R \|cosh(x) +--R Type: Expression Integer +--E 118 + +--S 119 of 526 +d0420:= D(m0420,x) +--R +--R +--R 2 2 +--R - x sinh(x) - 2x cosh(x) +--R (112) -------------------------- +--R +-------+ +--R | 1 +--R 3cosh(x) |------- +--R \|cosh(x) +--R Type: Expression Integer +--E 119 + +--S 120 of 526 +t0421:= x/sech(x)^(5/2)-3/5*x/sech(x)^(1/2) +--R +--R +--R 2 +--R - 3x sech(x) + 5x +--R (113) ------------------- +--R 2 +-------+ +--R 5sech(x) \|sech(x) +--R Type: Expression Integer +--E 120 + +--S 121 of 526 +r0421:= -4/25/sech(x)^(5/2)+2/5*x*sinh(x)/sech(x)^(3/2) +--R +--R +--R 10x sech(x)sinh(x) - 4 +--R (114) ---------------------- +--R 2 +-------+ +--R 25sech(x) \|sech(x) +--R Type: Expression Integer +--E 121 + +--S 122 of 526 +--a0421:= integrate(t0421,x) +--E 122 + +--S 123 of 526 +--m0421:= a0421-r0421 +--E 123 + +--S 124 of 526 +--d0421:= D(m0421,x) +--E 124 + +--S 125 of 526 +t0422:= x/sech(x)^(7/2)-5/21*x*sech(x)^(1/2) +--R +--R +--R 4 +--R - 5x sech(x) + 21x +--R (115) -------------------- +--R 3 +-------+ +--R 21sech(x) \|sech(x) +--R Type: Expression Integer +--E 125 + +--S 126 of 526 +r0422:= -2/441*(18*cosh(x)^3+70*cosh(x)-63*x*sinh(x)*cosh(x)^2-105*x*sinh(x))/(1/cosh(x))^(1/2) +--R +--R +--R 2 3 +--R (126x cosh(x) + 210x)sinh(x) - 36cosh(x) - 140cosh(x) +--R (116) ------------------------------------------------------- +--R +-------+ +--R | 1 +--R 441 |------- +--R \|cosh(x) +--R Type: Expression Integer +--E 126 + +--S 127 of 526 +a0422:= integrate(t0422,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 127 + +--S 128 of 526 +m0422:= a0422-r0422 +--R +--R +--R (117) +--R +-------+ +--R | 1 2 3 +--R 441a0422 |------- + (- 126x cosh(x) - 210x)sinh(x) + 36cosh(x) +--R \|cosh(x) +--R + +--R 140cosh(x) +--R / +--R +-------+ +--R | 1 +--R 441 |------- +--R \|cosh(x) +--R Type: Expression Integer +--E 128 + +--S 129 of 526 +d0422:= D(m0422,x) +--R +--R +--R 2 2 4 2 +--R (- 15x cosh(x) - 5x)sinh(x) - 6x cosh(x) - 10x cosh(x) +--R (118) ---------------------------------------------------------- +--R +-------+ +--R | 1 +--R 21cosh(x) |------- +--R \|cosh(x) +--R Type: Expression Integer +--E 129 + +--S 130 of 526 +t0423:= x^2/sech(x)^(3/2)-1/3*x^2*sech(x)^(1/2) +--R +--R +--R 2 2 2 +--R - x sech(x) + 3x +--R (119) ------------------ +--R +-------+ +--R 3sech(x)\|sech(x) +--R Type: Expression Integer +--E 130 + +--S 131 of 526 +r0423:= -8/9*x/sech(x)^(3/2)-16/27*%i*cosh(x)^(1/2)*EllipticF(1/2*%i*x,2)*sech(x)^(1/2)+16/27*sinh(x)/sech(x)^(1/2)+2/3*x^2*sinh(x)/sech(x)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Complex Fraction Integer +--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 131 + +--S 132 of 526 +--a0423:= integrate(t0423,x) +--E 132 + +--S 133 of 526 +--m0423:= a0423-r0423 +--E 133 + +--S 134 of 526 +--d0423:= D(m0423,x) +--E 134 + +--S 135 of 526 +t0424:= csch(a+b*x) +--R +--R +--R (120) csch(b x + a) +--R Type: Expression Integer +--E 135 + +--S 136 of 526 +r0424:= -acoth(cosh(a+b*x))/b +--R +--R +--R acoth(cosh(b x + a)) +--R (121) - -------------------- +--R b +--R Type: Expression Integer +--E 136 + +--S 137 of 526 +a0424:= integrate(t0424,x) +--R +--R +--R (122) +--R - log(sinh(b x + a) + cosh(b x + a) + 1) +--R + +--R log(sinh(b x + a) + cosh(b x + a) - 1) +--R / +--R b +--R Type: Union(Expression Integer,...) +--E 137 + +--S 138 of 526 +m0424:= a0424-r0424 +--R +--R +--R (123) +--R - log(sinh(b x + a) + cosh(b x + a) + 1) +--R + +--R log(sinh(b x + a) + cosh(b x + a) - 1) + acoth(cosh(b x + a)) +--R / +--R b +--R Type: Expression Integer +--E 138 + +--S 139 of 526 +d0424:= D(m0424,x) +--R +--R +--R (124) +--R 3 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R (cosh(b x + a) - 1)sinh(b x + a) + 2cosh(b x + a) - 2cosh(b x + a) +--R / +--R 2 2 +--R (cosh(b x + a) - 1)sinh(b x + a) +--R + +--R 3 4 +--R (2cosh(b x + a) - 2cosh(b x + a))sinh(b x + a) + cosh(b x + a) +--R + +--R 2 +--R - 2cosh(b x + a) + 1 +--R Type: Expression Integer +--E 139 + +--S 140 of 526 +t0425:= csch(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (125) \|csch(b x + a) +--R Type: Expression Integer +--E 140 + +--S 141 of 526 +r0425:= -2*%i*csch(a+b*x)^(1/2)*EllipticF(-1/4*%pi+1/2*%i*(a+b*x),2)*(%i*sinh(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 141 + +--S 142 of 526 +a0425:= integrate(t0425,x) +--R +--R +--R x +--R ++ +--------------+ +--R (126) | \|csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 142 + +--S 143 of 526 +--m0425:= a0425-r0425 +--E 143 + +--S 144 of 526 +--d0425:= D(m0425,x) +--E 144 + +--S 145 of 526 +t0426:= csch(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (127) csch(b x + a)\|csch(b x + a) +--R Type: Expression Integer +--E 145 + +--S 146 of 526 +r0426:= -2*cosh(a+b*x)*csch(a+b*x)^(1/2)/b-2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)/b/csch(a+b*x)^(1/2)/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 146 + +--S 147 of 526 +a0426:= integrate(t0426,x) +--R +--R +--R x +--R ++ +--------------+ +--R (128) | csch(%R b + a)\|csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 147 + +--S 148 of 526 +--m0426:= a0426-r0426 +--E 148 + +--S 149 of 526 +--d0426:= D(m0426,x) +--E 149 + +--S 150 of 526 +t0427:= csch(a+b*x)^(5/2) +--R +--R +--R 2 +-------------+ +--R (129) csch(b x + a) \|csch(b x + a) +--R Type: Expression Integer +--E 150 + +--S 151 of 526 +r0427:= -2/3*cosh(a+b*x)*csch(a+b*x)^(3/2)/b+2/3*%i*csch(a+b*x)^(1/2)*EllipticF(-1/4*%pi+1/2*%i*(a+b*x),2)*(%i*sinh(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 151 + +--S 152 of 526 +a0427:= integrate(t0427,x) +--R +--R +--R x +--R ++ 2 +--------------+ +--R (130) | csch(%R b + a) \|csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 152 + +--S 153 of 526 +--m0427:= a0427-r0427 +--E 153 + +--S 154 of 526 +--d0427:= D(m0427,x) +--E 154 + +--S 155 of 526 +t0428:= 1/csch(a+b*x)^(1/2) +--R +--R +--R 1 +--R (131) ---------------- +--R +-------------+ +--R \|csch(b x + a) +--R Type: Expression Integer +--E 155 + +--S 156 of 526 +r0428:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)/b/csch(a+b*x)^(1/2)/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 156 + +--S 157 of 526 +a0428:= integrate(t0428,x) +--R +--R +--R x +--R ++ 1 +--R (132) | ----------------- d%R +--R ++ +--------------+ +--R \|csch(%R b + a) +--R Type: Union(Expression Integer,...) +--E 157 + +--S 158 of 526 +--m0428:= a0428-r0428 +--E 158 + +--S 159 of 526 +--d0428:= D(m0428,x) +--E 159 + +--S 160 of 526 +t0429:= 1/csch(a+b*x)^(3/2) +--R +--R +--R 1 +--R (133) ----------------------------- +--R +-------------+ +--R csch(b x + a)\|csch(b x + a) +--R Type: Expression Integer +--E 160 + +--S 161 of 526 +r0429:= 2/3*cosh(a+b*x)/b/csch(a+b*x)^(1/2)+2/3*%i*csch(a+b*x)^(1/2)*EllipticF(-1/4*%pi+1/2*%i*(a+b*x),2)*(%i*sinh(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 161 + +--S 162 of 526 +a0429:= integrate(t0429,x) +--R +--R +--R x +--R ++ 1 +--R (134) | ------------------------------- d%R +--R ++ +--------------+ +--R csch(%R b + a)\|csch(%R b + a) +--R Type: Union(Expression Integer,...) +--E 162 + +--S 163 of 526 +--m0429:= a0429-r0429 +--E 163 + +--S 164 of 526 +--d0429:= D(m0429,x) +--E 164 + +--S 165 of 526 +t0430:= 1/csch(a+b*x)^(5/2) +--R +--R +--R 1 +--R (135) ------------------------------ +--R 2 +-------------+ +--R csch(b x + a) \|csch(b x + a) +--R Type: Expression Integer +--E 165 + +--S 166 of 526 +r0430:= 2/5*cosh(a+b*x)/b/csch(a+b*x)^(3/2)+6/5*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)/b/csch(a+b*x)^(1/2)/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 166 + +--S 167 of 526 +a0430:= integrate(t0430,x) +--R +--R +--R x +--R ++ 1 +--R (136) | -------------------------------- d%R +--R ++ 2 +--------------+ +--R csch(%R b + a) \|csch(%R b + a) +--R Type: Union(Expression Integer,...) +--E 167 + +--S 168 of 526 +--m0430:= a0430-r0430 +--E 168 + +--S 169 of 526 +--d0430:= D(m0430,x) +--E 169 + +--S 170 of 526 +t0431:= x*csch(a+b*x) +--R +--R +--R (137) x csch(b x + a) +--R Type: Expression Integer +--E 170 + +--S 171 of 526 +r0431:= -(2*x*atanh(exp(a+b*x))*b+polylog(2,-exp(a+b*x))-polylog(2,exp(a+b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 171 + +--S 172 of 526 +a0431:= integrate(t0431,x) +--R +--R +--R x +--R ++ +--R (138) | %R csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 172 + +--S 173 of 526 +--m0431:= a0431-r0431 +--E 173 + +--S 174 of 526 +--d0431:= D(m0431,x) +--E 174 + +--S 175 of 526 +t0432:= x^2*csch(a+b*x) +--R +--R +--R 2 +--R (139) x csch(b x + a) +--R Type: Expression Integer +--E 175 + +--S 176 of 526 +r0432:= -2*(x^2*atanh(exp(a+b*x))*b^2+polylog(2,-exp(a+b*x))*x*b-polylog(2,exp(a+b*x))*x*b-polylog(3,-exp(a+b*x))+polylog(3,exp(a+b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 176 + +--S 177 of 526 +a0432:= integrate(t0432,x) +--R +--R +--R x +--R ++ 2 +--R (140) | %R csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 177 + +--S 178 of 526 +--m0432:= a0432-r0432 +--E 178 + +--S 179 of 526 +--d0432:= D(m0432,x) +--E 179 + +--S 180 of 526 +t0433:= x^3*csch(a+b*x) +--R +--R +--R 3 +--R (141) x csch(b x + a) +--R Type: Expression Integer +--E 180 + +--S 181 of 526 +r0433:= -(2*x^3*atanh(exp(a+b*x))*b^3+3*polylog(2,-exp(a+b*x))*x^2*b^2-3*polylog(2,exp(a+b*x))*x^2*b^2-6*polylog(3,-exp(a+b*x))*x*b+6*polylog(3,exp(a+b*x))*x*b+6*polylog(4,-exp(a+b*x))-6*polylog(4,exp(a+b*x)))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 181 + +--S 182 of 526 +a0433:= integrate(t0433,x) +--R +--R +--R x +--R ++ 3 +--R (142) | %R csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 182 + +--S 183 of 526 +--m0433:= a0433-r0433 +--E 183 + +--S 184 of 526 +--d0433:= D(m0433,x) +--E 184 + +--S 185 of 526 +t0434:= x*csch(a+b*x)^2 +--R +--R +--R 2 +--R (143) x csch(b x + a) +--R Type: Expression Integer +--E 185 + +--S 186 of 526 +r0434:= -x*coth(a+b*x)/b+log(sinh(a+b*x))/b^2 +--R +--R +--R log(sinh(b x + a)) - b x coth(b x + a) +--R (144) -------------------------------------- +--R 2 +--R b +--R Type: Expression Integer +--E 186 + +--S 187 of 526 +a0434:= integrate(t0434,x) +--R +--R +--R (145) +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1) +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R - 2b x sinh(b x + a) - 4b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Union(Expression Integer,...) +--E 187 + +--S 188 of 526 +m0434:= a0434-r0434 +--R +--R +--R (146) +--R 2 2 +--R (- sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) + 1) +--R * +--R log(sinh(b x + a)) +--R + +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1) +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R (b x coth(b x + a) - 2b x)sinh(b x + a) +--R + +--R (2b x cosh(b x + a)coth(b x + a) - 4b x cosh(b x + a))sinh(b x + a) +--R + +--R 2 2 +--R (b x cosh(b x + a) - b x)coth(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Expression Integer +--E 188 + +--S 189 of 526 +d0434:= D(m0434,x) +--R +--R +--R (147) +--R 2 4 +--R (- b x coth(b x + a) + coth(b x + a) + b x - 1)sinh(b x + a) +--R + +--R 2 +--R - 4b x cosh(b x + a)coth(b x + a) + 4cosh(b x + a)coth(b x + a) +--R + +--R (4b x - 4)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 2 2 +--R (- 6b x cosh(b x + a) + 2b x)coth(b x + a) +--R + +--R 2 2 +--R (6cosh(b x + a) - 2)coth(b x + a) + (6b x - 6)cosh(b x + a) + 2b x +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 3 2 +--R (- 4b x cosh(b x + a) + 4b x cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R (4cosh(b x + a) - 4cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R (4b x - 4)cosh(b x + a) + 4b x cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (- b x cosh(b x + a) + 2b x cosh(b x + a) - b x)coth(b x + a) +--R + +--R 4 2 +--R (cosh(b x + a) - 2cosh(b x + a) + 1)coth(b x + a) +--R + +--R 4 2 +--R (b x - 1)cosh(b x + a) + 2b x cosh(b x + a) + b x + 1 +--R / +--R 4 3 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (6b cosh(b x + a) - 2b)sinh(b x + a) +--R + +--R 3 4 +--R (4b cosh(b x + a) - 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 2 +--R - 2b cosh(b x + a) + b +--R Type: Expression Integer +--E 189 + +--S 190 of 526 +t0435:= x^2*csch(a+b*x)^2 +--R +--R +--R 2 2 +--R (148) x csch(b x + a) +--R Type: Expression Integer +--E 190 + +--S 191 of 526 +r0435:= -(b^2*x^2+x^2*coth(a+b*x)*b^2-2*x*log(1-exp(2*a+2*b*x))*b-polylog(2,exp(2*a+2*b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 191 + +--S 192 of 526 +a0435:= integrate(t0435,x) +--R +--R +--R x +--R ++ 2 2 +--R (149) | %R csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 192 + +--S 193 of 526 +--m0435:= a0435-r0435 +--E 193 + +--S 194 of 526 +--d0435:= D(m0435,x) +--E 194 + +--S 195 of 526 +t0436:= x^3*csch(a+b*x)^2 +--R +--R +--R 3 2 +--R (150) x csch(b x + a) +--R Type: Expression Integer +--E 195 + +--S 196 of 526 +r0436:= -1/2*(2*b^3*x^3+2*x^3*coth(a+b*x)*b^3-6*x^2*log(1-exp(2*a+2*b*x))*b^2-6*x*polylog(2,exp(2*a+2*b*x))*b+3*polylog(3,exp(2*a+2*b*x)))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 196 + +--S 197 of 526 +a0436:= integrate(t0436,x) +--R +--R +--R x +--R ++ 3 2 +--R (151) | %R csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 197 + +--S 198 of 526 +--m0436:= a0436-r0436 +--E 198 + +--S 199 of 526 +--d0436:= D(m0436,x) +--E 199 + +--S 200 of 526 +t0437:= x*csch(a+b*x)^3 +--R +--R +--R 3 +--R (152) x csch(b x + a) +--R Type: Expression Integer +--E 200 + +--S 201 of 526 +r0437:= x*atanh(exp(1)^(a+b*x))/b-1/2*csch(a+b*x)/b^2-1/2*x*coth(a+b*x)*csch(a+b*x)/b+1/2*polylog(2,-exp(1)^(a+b*x))/b^2-1/2*polylog(2,exp(1)^(a+b*x))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 201 + +--S 202 of 526 +a0437:= integrate(t0437,x) +--R +--R +--R x +--R ++ 3 +--R (153) | %R csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 202 + +--S 203 of 526 +--m0437:= a0437-r0437 +--E 203 + +--S 204 of 526 +--d0437:= D(m0437,x) +--E 204 + +--S 205 of 526 +t0438:= x^2*csch(a+b*x)^3 +--R +--R +--R 2 3 +--R (154) x csch(b x + a) +--R Type: Expression Integer +--E 205 + +--S 206 of 526 +r0438:= -acoth(cosh(a+b*x))/b^3+x^2*atanh(exp(1)^(a+b*x))/b-x*csch(a+b*x)/b^2-1/2*x^2*coth(a+b*x)*csch(a+b*x)/b+x*polylog(2,-exp(1)^(a+b*x))/b^2-x*polylog(2,exp(1)^(a+b*x))/b^2-polylog(3,-exp(1)^(a+b*x))/b^3+polylog(3,exp(1)^(a+b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 206 + +--S 207 of 526 +a0438:= integrate(t0438,x) +--R +--R +--R x +--R ++ 2 3 +--R (155) | %R csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 207 + +--S 208 of 526 +--m0438:= a0438-r0438 +--E 208 + +--S 209 of 526 +--d0438:= D(m0438,x) +--E 209 + +--S 210 of 526 +t0439:= (c+d*x)*csch(a+b*x) +--R +--R +--R (156) (d x + c)csch(b x + a) +--R Type: Expression Integer +--E 210 + +--S 211 of 526 +r0439:= -(2*atanh(exp(a+b*x))*c*b+2*atanh(exp(a+b*x))*d*x*b+d*polylog(2,-exp(a+b*x))-d*polylog(2,exp(a+b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 526 +a0439:= integrate(t0439,x) +--R +--R +--R x +--R ++ +--R (157) | (%R d + c)csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 212 + +--S 213 of 526 +--m0439:= a0439-r0439 +--E 213 + +--S 214 of 526 +--d0439:= D(m0439,x) +--E 214 + +--S 215 of 526 +t0440:= (c+d*x)^2*csch(a+b*x) +--R +--R +--R 2 2 2 +--R (158) (d x + 2c d x + c )csch(b x + a) +--R Type: Expression Integer +--E 215 + +--S 216 of 526 +r0440:= -2*(c+d*x)^2*atanh(exp(1)^(a+b*x))/b-2*d*(c+d*x)*polylog(2,-exp(1)^(a+b*x))/b^2+2*d*(c+d*x)*polylog(2,exp(1)^(a+b*x))/b^2+2*d^2*polylog(3,-exp(1)^(a+b*x))/b^3-2*d^2*polylog(3,exp(1)^(a+b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 216 + +--S 217 of 526 +a0440:= integrate(t0440,x) +--R +--R +--R x +--R ++ 2 2 2 +--R (159) | (%R d + 2%R c d + c )csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 217 + +--S 218 of 526 +--m0440:= a0440-r0440 +--E 218 + +--S 219 of 526 +--d0440:= D(m0440,x) +--E 219 + +--S 220 of 526 +t0441:= (c+d*x)^3*csch(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R (160) (d x + 3c d x + 3c d x + c )csch(b x + a) +--R Type: Expression Integer +--E 220 + +--S 221 of 526 +r0441:= -2*(c+d*x)^3*atanh(exp(1)^(a+b*x))/b-3*d*(c+d*x)^2*polylog(2,-exp(1)^(a+b*x))/b^2+3*d*(c+d*x)^2*polylog(2,exp(1)^(a+b*x))/b^2+6*d^2*(c+d*x)*polylog(3,-exp(1)^(a+b*x))/b^3-6*d^2*(c+d*x)*polylog(3,exp(1)^(a+b*x))/b^3-6*d^3*polylog(4,-exp(1)^(a+b*x))/b^4+6*d^3*polylog(4,exp(1)^(a+b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 221 + +--S 222 of 526 +a0441:= integrate(t0441,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 +--R (161) | (%R d + 3%R c d + 3%R c d + c )csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 222 + +--S 223 of 526 +--m0441:= a0441-r0441 +--E 223 + +--S 224 of 526 +--d0441:= D(m0441,x) +--E 224 + +--S 225 of 526 +t0442:= (c+d*x)*csch(a+b*x)^2 +--R +--R +--R 2 +--R (162) (d x + c)csch(b x + a) +--R Type: Expression Integer +--E 225 + +--S 226 of 526 +r0442:= -(c+d*x)*coth(a+b*x)/b+d*log(sinh(a+b*x))/b^2 +--R +--R +--R d log(sinh(b x + a)) + (- b d x - b c)coth(b x + a) +--R (163) --------------------------------------------------- +--R 2 +--R b +--R Type: Expression Integer +--E 226 + +--S 227 of 526 +a0442:= integrate(t0442,x) +--R +--R +--R (164) +--R 2 2 +--R d sinh(b x + a) + 2d cosh(b x + a)sinh(b x + a) + d cosh(b x + a) +--R + +--R - d +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R - 2b d x sinh(b x + a) - 4b d x cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R - 2b d x cosh(b x + a) - 2b c +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Union(Expression Integer,...) +--E 227 + +--S 228 of 526 +m0442:= a0442-r0442 +--R +--R +--R (165) +--R 2 2 +--R - d sinh(b x + a) - 2d cosh(b x + a)sinh(b x + a) - d cosh(b x + a) +--R + +--R d +--R * +--R log(sinh(b x + a)) +--R + +--R 2 2 +--R d sinh(b x + a) + 2d cosh(b x + a)sinh(b x + a) + d cosh(b x + a) +--R + +--R - d +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R ((b d x + b c)coth(b x + a) - 2b d x)sinh(b x + a) +--R + +--R ((2b d x + 2b c)cosh(b x + a)coth(b x + a) - 4b d x cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 2 +--R ((b d x + b c)cosh(b x + a) - b d x - b c)coth(b x + a) +--R + +--R 2 +--R - 2b d x cosh(b x + a) - 2b c +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Expression Integer +--E 228 + +--S 229 of 526 +d0442:= D(m0442,x) +--R +--R +--R (166) +--R 2 +--R ((- b d x - b c)coth(b x + a) + d coth(b x + a) + b d x - d + b c) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 2 +--R (- 4b d x - 4b c)cosh(b x + a)coth(b x + a) +--R + +--R 4d cosh(b x + a)coth(b x + a) + (4b d x - 4d + 4b c)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 2 2 +--R ((- 6b d x - 6b c)cosh(b x + a) + 2b d x + 2b c)coth(b x + a) +--R + +--R 2 +--R (6d cosh(b x + a) - 2d)coth(b x + a) +--R + +--R 2 +--R (6b d x - 6d + 6b c)cosh(b x + a) + 2b d x + 2b c +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 3 +--R ((- 4b d x - 4b c)cosh(b x + a) + (4b d x + 4b c)cosh(b x + a)) +--R * +--R 2 +--R coth(b x + a) +--R + +--R 3 +--R (4d cosh(b x + a) - 4d cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R (4b d x - 4d + 4b c)cosh(b x + a) + (4b d x + 4b c)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 4 2 +--R (- b d x - b c)cosh(b x + a) + (2b d x + 2b c)cosh(b x + a) - b d x +--R + +--R - b c +--R * +--R 2 +--R coth(b x + a) +--R + +--R 4 2 +--R (d cosh(b x + a) - 2d cosh(b x + a) + d)coth(b x + a) +--R + +--R 4 2 +--R (b d x - d + b c)cosh(b x + a) + (2b d x + 2b c)cosh(b x + a) + b d x +--R + +--R d + b c +--R / +--R 4 3 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (6b cosh(b x + a) - 2b)sinh(b x + a) +--R + +--R 3 4 +--R (4b cosh(b x + a) - 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 2 +--R - 2b cosh(b x + a) + b +--R Type: Expression Integer +--E 229 + +--S 230 of 526 +t0443:= (c+d*x)^2*csch(a+b*x)^2 +--R +--R +--R 2 2 2 2 +--R (167) (d x + 2c d x + c )csch(b x + a) +--R Type: Expression Integer +--E 230 + +--S 231 of 526 +r0443:= -(c+d*x)^2/b-(c+d*x)^2*coth(a+b*x)/b+2*d*(c+d*x)*log(1-exp(1)^(2*a+2*b*x))/b^2+d^2*polylog(2,exp(1)^(2*a+2*b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 231 + +--S 232 of 526 +a0443:= integrate(t0443,x) +--R +--R +--R x +--R ++ 2 2 2 2 +--R (168) | (%R d + 2%R c d + c )csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 232 + +--S 233 of 526 +--m0443:= a0443-r0443 +--E 233 + +--S 234 of 526 +--d0443:= D(m0443,x) +--E 234 + +--S 235 of 526 +t0444:= (c+d*x)^3*csch(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 2 +--R (169) (d x + 3c d x + 3c d x + c )csch(b x + a) +--R Type: Expression Integer +--E 235 + +--S 236 of 526 +r0444:= -(c+d*x)^3/b-(c+d*x)^3*coth(a+b*x)/b+3*d*(c+d*x)^2*log(1-exp(1)^(2*a+2*b*x))/b^2+3*d^2*(c+d*x)*polylog(2,exp(1)^(2*a+2*b*x))/b^3-3/2*d^3*polylog(3,exp(1)^(2*a+2*b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 236 + +--S 237 of 526 +a0444:= integrate(t0444,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 2 +--R (170) | (%R d + 3%R c d + 3%R c d + c )csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 237 + +--S 238 of 526 +--m0444:= a0444-r0444 +--E 238 + +--S 239 of 526 +--d0444:= D(m0444,x) +--E 239 + +--S 240 of 526 +t0445:= (c+d*x)*csch(a+b*x)^3 +--R +--R +--R 3 +--R (171) (d x + c)csch(b x + a) +--R Type: Expression Integer +--E 240 + +--S 241 of 526 +r0445:= (c+d*x)*atanh(exp(1)^(a+b*x))/b-1/2*d*csch(a+b*x)/b^2-1/2*(c+d*x)*coth(a+b*x)*csch(a+b*x)/b+1/2*d*polylog(2,-exp(1)^(a+b*x))/b^2-1/2*d*polylog(2,exp(1)^(a+b*x))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 241 + +--S 242 of 526 +a0445:= integrate(t0445,x) +--R +--R +--R x +--R ++ 3 +--R (172) | (%R d + c)csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 242 + +--S 243 of 526 +--m0445:= a0445-r0445 +--E 243 + +--S 244 of 526 +--d0445:= D(m0445,x) +--E 244 + +--S 245 of 526 +t0446:= (c+d*x)^2*csch(a+b*x)^3 +--R +--R +--R 2 2 2 3 +--R (173) (d x + 2c d x + c )csch(b x + a) +--R Type: Expression Integer +--E 245 + +--S 246 of 526 +r0446:= -d^2*acoth(cosh(a+b*x))/b^3+(c+d*x)^2*atanh(exp(1)^(a+b*x))/b-d*(c+d*x)*csch(a+b*x)/b^2-1/2*(c+d*x)^2*coth(a+b*x)*csch(a+b*x)/b+d*(c+d*x)*polylog(2,-exp(1)^(a+b*x))/b^2-d*(c+d*x)*polylog(2,exp(1)^(a+b*x))/b^2-d^2*polylog(3,-exp(1)^(a+b*x))/b^3+d^2*polylog(3,exp(1)^(a+b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 246 + +--S 247 of 526 +a0446:= integrate(t0446,x) +--R +--R +--R x +--R ++ 2 2 2 3 +--R (174) | (%R d + 2%R c d + c )csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 247 + +--S 248 of 526 +--m0446:= a0446-r0446 +--E 248 + +--S 249 of 526 +--d0446:= D(m0446,x) +--E 249 + +--S 250 of 526 +t0447:= csch(x)^(1/2) +--R +--R +--R +-------+ +--R (175) \|csch(x) +--R Type: Expression Integer +--E 250 + +--S 251 of 526 +r0447:= -2*%i*csch(x)^(1/2)*EllipticF(-1/4*%pi+1/2*%i*x,2)*(%i*sinh(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 251 + +--S 252 of 526 +a0447:= integrate(t0447,x) +--R +--R +--R x +--R ++ +--------+ +--R (176) | \|csch(%R) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 252 + +--S 253 of 526 +--m0447:= a0447-r0447 +--E 253 + +--S 254 of 526 +--d0447:= D(m0447,x) +--E 254 + +--S 255 of 526 +t0448:= (-csch(x)^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (177) \|- csch(x) +--R Type: Expression Integer +--E 255 + +--S 256 of 526 +r0448:= acsc(tanh(x)) +--R +--R +--R (178) acsc(tanh(x)) +--R Type: Expression Integer +--E 256 + +--S 257 of 526 +a0448:= integrate(t0448,x) +--R +--R +--R +---+ x +---+ x +--R (179) - \|- 1 log(%e + 1) + \|- 1 log(%e - 1) +--R Type: Union(Expression Integer,...) +--E 257 + +--S 258 of 526 +m0448:= a0448-r0448 +--R +--R +--R +---+ x +---+ x +--R (180) - \|- 1 log(%e + 1) + \|- 1 log(%e - 1) - acsc(tanh(x)) +--R Type: Expression Integer +--E 258 + +--S 259 of 526 +d0448:= D(m0448,x) +--R +--R +--R (181) +--R +------------+ +--R +---+ x | 2 x 2 2 x 2 +--R 2\|- 1 %e tanh(x)\|tanh(x) - 1 + (- (%e ) + 1)tanh(x) + (%e ) - 1 +--R ---------------------------------------------------------------------- +--R +------------+ +--R x 2 | 2 +--R ((%e ) - 1)tanh(x)\|tanh(x) - 1 +--R Type: Expression Integer +--E 259 + +--S 260 of 526 +t0449:= (csch(x)^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R (182) \|csch(x) +--R Type: Expression Integer +--E 260 + +--S 261 of 526 +r0449:= -acoth(cosh(x))*csgn(1/sinh(x)) +--R +--R There are no library operations named csgn +--R Use HyperDoc Browse or issue +--R )what op csgn +--R to learn if there is any operation containing " csgn " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named csgn +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 261 + +--S 262 of 526 +a0449:= integrate(t0449,x) +--R +--R +--R (183) - log(sinh(x) + cosh(x) + 1) + log(sinh(x) + cosh(x) - 1) +--R Type: Union(Expression Integer,...) +--E 262 + +--S 263 of 526 +--m0449:= a0449-r0449 +--E 263 + +--S 264 of 526 +--d0449:= D(m0449,x) +--E 264 + +--S 265 of 526 +t0450:= (csch(x)^3)^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R (184) \|csch(x) +--R Type: Expression Integer +--E 265 + +--S 266 of 526 +r0450:= -2*(csch(x)^3)^(1/2)*(coth(x)+%i*EllipticE(-1/4*%pi+1/2*%i*x,2)/(%i*sinh(x))^(1/2))*sinh(x)^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Complex Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 266 + +--S 267 of 526 +a0450:= integrate(t0450,x) +--R +--R +--R x +---------+ +--R ++ | 3 +--R (185) | \|csch(%R) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 267 + +--S 268 of 526 +--m0450:= a0450-r0450 +--E 268 + +--S 269 of 526 +--d0450:= D(m0450,x) +--E 269 + +--S 270 of 526 +t0451:= (csch(x)^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (186) \|csch(x) +--R Type: Expression Integer +--E 270 + +--S 271 of 526 +r0451:= -cosh(x)*csgn(1/sinh(x)^2)/sinh(x) +--R +--R There are no library operations named csgn +--R Use HyperDoc Browse or issue +--R )what op csgn +--R to learn if there is any operation containing " csgn " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named csgn +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 271 + +--S 272 of 526 +a0451:= integrate(t0451,x) +--R +--R +--R 2 +--R (187) - ----------------------------------------- +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Union(Expression Integer,...) +--E 272 + +--S 273 of 526 +--m0451:= a0451-r0451 +--E 273 + +--S 274 of 526 +--d0451:= D(m0451,x) +--E 274 + +--S 275 of 526 +t0452:= 1/(a+%i*a*csch(a+b*x)) +--R +--R +--R %i +--R (188) - ---------------------- +--R a csch(b x + a) - %i a +--R Type: Expression Complex Integer +--E 275 + +--S 276 of 526 +r0452:= x/a+%i*cosh(a+b*x)/a/b/(1-%i*sinh(a+b*x)) +--R +--R +--R b x sinh(b x + a) - cosh(b x + a) + %i b x +--R (189) ------------------------------------------ +--R a b sinh(b x + a) + %i a b +--R Type: Expression Complex Integer +--E 276 + +--S 277 of 526 +a0452:= integrate(t0452,x) +--R +--R +--R b x sinh(b x + a) + b x cosh(b x + a) + %i b x + 2%i +--R (190) ---------------------------------------------------- +--R a b sinh(b x + a) + a b cosh(b x + a) + %i a b +--R Type: Union(Expression Complex Integer,...) +--E 277 + +--S 278 of 526 +m0452:= a0452-r0452 +--R +--R +--R (191) +--R 2 +--R (cosh(b x + a) + 2%i)sinh(b x + a) + cosh(b x + a) + %i cosh(b x + a) - 2 +--R / +--R 2 +--R a b sinh(b x + a) + (a b cosh(b x + a) + 2%i a b)sinh(b x + a) +--R + +--R %i a b cosh(b x + a) - a b +--R Type: Expression Complex Integer +--E 278 + +--S 279 of 526 +d0452:= D(m0452,x) +--R +--R +--R (192) +--R 4 3 +--R sinh(b x + a) + (2cosh(b x + a) + %i)sinh(b x + a) +--R + +--R 2 +--R (2%i cosh(b x + a) + 1)sinh(b x + a) +--R + +--R 3 2 +--R (- 2cosh(b x + a) - %i cosh(b x + a) + 2cosh(b x + a) + %i) +--R * +--R sinh(b x + a) +--R + +--R 4 3 2 +--R - cosh(b x + a) - 2%i cosh(b x + a) + cosh(b x + a) + 2%i cosh(b x + a) +--R / +--R 4 3 +--R a sinh(b x + a) + (2a cosh(b x + a) + 4%i a)sinh(b x + a) +--R + +--R 2 2 +--R (a cosh(b x + a) + 6%i a cosh(b x + a) - 6a)sinh(b x + a) +--R + +--R 2 +--R (2%i a cosh(b x + a) - 6a cosh(b x + a) - 4%i a)sinh(b x + a) +--R + +--R 2 +--R - a cosh(b x + a) - 2%i a cosh(b x + a) + a +--R Type: Expression Complex Integer +--E 279 + +--S 280 of 526 +t0453:= 1/(a-%i*a*csch(a+b*x)) +--R +--R +--R %i +--R (193) ---------------------- +--R a csch(b x + a) + %i a +--R Type: Expression Complex Integer +--E 280 + +--S 281 of 526 +r0453:= x/a-%i*cosh(a+b*x)/a/b/(1+%i*sinh(a+b*x)) +--R +--R +--R b x sinh(b x + a) - cosh(b x + a) - %i b x +--R (194) ------------------------------------------ +--R a b sinh(b x + a) - %i a b +--R Type: Expression Complex Integer +--E 281 + +--S 282 of 526 +a0453:= integrate(t0453,x) +--R +--R +--R b x sinh(b x + a) + b x cosh(b x + a) - %i b x - 2%i +--R (195) ---------------------------------------------------- +--R a b sinh(b x + a) + a b cosh(b x + a) - %i a b +--R Type: Union(Expression Complex Integer,...) +--E 282 + +--S 283 of 526 +m0453:= a0453-r0453 +--R +--R +--R (196) +--R 2 +--R (cosh(b x + a) - 2%i)sinh(b x + a) + cosh(b x + a) - %i cosh(b x + a) - 2 +--R / +--R 2 +--R a b sinh(b x + a) + (a b cosh(b x + a) - 2%i a b)sinh(b x + a) +--R + +--R - %i a b cosh(b x + a) - a b +--R Type: Expression Complex Integer +--E 283 + +--S 284 of 526 +d0453:= D(m0453,x) +--R +--R +--R (197) +--R 4 3 +--R sinh(b x + a) + (2cosh(b x + a) - %i)sinh(b x + a) +--R + +--R 2 +--R (- 2%i cosh(b x + a) + 1)sinh(b x + a) +--R + +--R 3 2 +--R (- 2cosh(b x + a) + %i cosh(b x + a) + 2cosh(b x + a) - %i) +--R * +--R sinh(b x + a) +--R + +--R 4 3 2 +--R - cosh(b x + a) + 2%i cosh(b x + a) + cosh(b x + a) - 2%i cosh(b x + a) +--R / +--R 4 3 +--R a sinh(b x + a) + (2a cosh(b x + a) - 4%i a)sinh(b x + a) +--R + +--R 2 2 +--R (a cosh(b x + a) - 6%i a cosh(b x + a) - 6a)sinh(b x + a) +--R + +--R 2 +--R (- 2%i a cosh(b x + a) - 6a cosh(b x + a) + 4%i a)sinh(b x + a) +--R + +--R 2 +--R - a cosh(b x + a) + 2%i a cosh(b x + a) + a +--R Type: Expression Complex Integer +--E 284 + +--S 285 of 526 +t0454:= (3+3*%i*csch(x))^(1/2) +--R +--R +--R +---------------+ +--R (198) \|3%i csch(x) + 3 +--R Type: Expression Complex Integer +--E 285 + +--S 286 of 526 +r0454:= 2*3^(1/2)*atan((-1+%i*csch(x))^(1/2))*coth(x)/(-1+%i*csch(x))^(1/2)/(1+%i*csch(x))^(1/2) +--R +--R +--R +-+ +--------------+ +--R 2\|3 coth(x)atan(\|%i csch(x) - 1 ) +--R (199) ----------------------------------- +--R +--------------+ +--------------+ +--R \|%i csch(x) - 1 \|%i csch(x) + 1 +--R Type: Expression Complex Integer +--E 286 + +--S 287 of 526 +a0454:= integrate(t0454,x) +--R +--R +--R (200) +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- - \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R - \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R \|3 +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) - 2%i cosh(x) +--R + +--R - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R - %i\|3 sinh(x) + (- 3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (- 3%i\|3 cosh(x) - 2\|3 cosh(x) + %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - %i\|3 cosh(x) - \|3 cosh(x) + %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression Complex Integer,...) +--E 287 + +--S 288 of 526 +m0454:= a0454-r0454 +--R +--R +--R (201) +--R - +--R +-+ +--------------+ +--------------+ +--R \|3 \|%i csch(x) - 1 \|%i csch(x) + 1 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- - \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R - \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--------------+ +--------------+ +--R \|3 \|%i csch(x) - 1 \|%i csch(x) + 1 +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R - %i\|3 sinh(x) + (- 3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (- 3%i\|3 cosh(x) - 2\|3 cosh(x) + %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - %i\|3 cosh(x) - \|3 cosh(x) + %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--------------+ +--R - 2\|3 coth(x)atan(\|%i csch(x) - 1 ) +--R / +--R +--------------+ +--------------+ +--R \|%i csch(x) - 1 \|%i csch(x) + 1 +--R Type: Expression Complex Integer +--E 288 + +--S 289 of 526 +d0454:= D(m0454,x) +--R +--R +--R (202) +--R 2 2 6 +--R (- 6csch(x) + 6coth(x) - 6)sinh(x) +--R + +--R 2 2 5 +--R (- 36cosh(x)csch(x) + 36cosh(x)coth(x) - 36cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R (- 90cosh(x) - 6)csch(x) + (90cosh(x) + 6)coth(x) +--R + +--R 2 +--R - 90cosh(x) - 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 120cosh(x) - 24cosh(x))csch(x) +--R + +--R 3 2 3 +--R (120cosh(x) + 24cosh(x))coth(x) - 120cosh(x) - 24cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 90cosh(x) - 36cosh(x) + 36)csch(x) +--R + +--R 4 2 2 4 +--R (90cosh(x) + 36cosh(x) - 36)coth(x) - 90cosh(x) +--R + +--R 2 +--R - 36cosh(x) + 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 36cosh(x) - 24cosh(x) + 72cosh(x))csch(x) +--R + +--R 5 3 2 5 +--R (36cosh(x) + 24cosh(x) - 72cosh(x))coth(x) - 36cosh(x) +--R + +--R 3 +--R - 24cosh(x) + 72cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 6cosh(x) - 6cosh(x) + 36cosh(x) - 24)csch(x) +--R + +--R 6 4 2 2 6 +--R (6cosh(x) + 6cosh(x) - 36cosh(x) + 24)coth(x) - 6cosh(x) +--R + +--R 4 2 +--R - 6cosh(x) + 36cosh(x) - 24 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 +-+ 6 +--R (6%i\|3 csch(x) - 6%i\|3 coth(x) + 6%i\|3 )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R 36%i\|3 cosh(x)csch(x) - 36%i\|3 cosh(x)coth(x) +--R + +--R +-+ +--R 36%i\|3 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 6%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (- 90%i\|3 cosh(x) + 6%i\|3 )coth(x) + 90%i\|3 cosh(x) - 6%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (120%i\|3 cosh(x) - 24%i\|3 cosh(x))csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 120%i\|3 cosh(x) + 24%i\|3 cosh(x))coth(x) +--R + +--R +-+ 3 +-+ +--R 120%i\|3 cosh(x) - 24%i\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 )coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x))coth(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 ) +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 ) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 +--R * +--R +--------------+ +--R atan(\|%i csch(x) - 1 ) +--R + +--R 2 6 +--R (- 6csch(x) - 6)sinh(x) +--R + +--R 2 5 +--R ((- 36cosh(x) + 18%i)csch(x) - 36cosh(x) + 18%i)sinh(x) +--R + +--R 2 2 2 +--R (- 90cosh(x) + 90%i cosh(x) - 3)csch(x) - 90cosh(x) +--R + +--R 90%i cosh(x) - 3 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 120cosh(x) + 180%i cosh(x) - 12cosh(x) - 30%i)csch(x) +--R + +--R 3 2 +--R - 120cosh(x) + 180%i cosh(x) - 12cosh(x) - 30%i +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R - 90cosh(x) + 180%i cosh(x) - 18cosh(x) - 90%i cosh(x) +--R + +--R 24 +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R - 90cosh(x) + 180%i cosh(x) - 18cosh(x) - 90%i cosh(x) + 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 36cosh(x) + 90%i cosh(x) - 12cosh(x) - 90%i cosh(x) +--R + +--R 48cosh(x) + 12%i +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 2 +--R - 36cosh(x) + 90%i cosh(x) - 12cosh(x) - 90%i cosh(x) +--R + +--R 48cosh(x) + 12%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 6cosh(x) + 18%i cosh(x) - 3cosh(x) - 30%i cosh(x) +--R + +--R 2 +--R 24cosh(x) + 12%i cosh(x) - 12 +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R - 6cosh(x) + 18%i cosh(x) - 3cosh(x) - 30%i cosh(x) +--R + +--R 2 +--R 24cosh(x) + 12%i cosh(x) - 12 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 6 +--R (3%i\|3 csch(x) + 3%i\|3 )sinh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ 5 +--R ((18%i\|3 cosh(x) + 6\|3 )csch(x) + 18%i\|3 cosh(x) + 6\|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R (45%i\|3 cosh(x) + 30\|3 cosh(x) - 3%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ +-+ +--R 45%i\|3 cosh(x) + 30\|3 cosh(x) - 3%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (60%i\|3 cosh(x) + 60\|3 cosh(x) - 12%i\|3 cosh(x) - 24\|3 ) +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 60%i\|3 cosh(x) + 60\|3 cosh(x) - 12%i\|3 cosh(x) - 24\|3 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 45%i\|3 cosh(x) + 60\|3 cosh(x) - 18%i\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72\|3 cosh(x) - 18%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 45%i\|3 cosh(x) + 60\|3 cosh(x) - 18%i\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72\|3 cosh(x) - 18%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 18%i\|3 cosh(x) + 30\|3 cosh(x) - 12%i\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72\|3 cosh(x) - 36%i\|3 cosh(x) + 12\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 18%i\|3 cosh(x) + 30\|3 cosh(x) - 12%i\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72\|3 cosh(x) - 36%i\|3 cosh(x) + 12\|3 +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 3%i\|3 cosh(x) + 6\|3 cosh(x) - 3%i\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24\|3 cosh(x) - 18%i\|3 cosh(x) + 12\|3 cosh(x) + 12%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 3%i\|3 cosh(x) + 6\|3 cosh(x) - 3%i\|3 cosh(x) - 24\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 18%i\|3 cosh(x) + 12\|3 cosh(x) + 12%i\|3 +--R * +--R +--------------+ +--------------+ +--R \|%i csch(x) - 1 \|%i csch(x) + 1 +--R + +--R 2 2 6 +--R (- 3%i coth(x) csch(x) - 3coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (- 18%i cosh(x)coth(x) csch(x) - 18cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 +--R (- 45%i cosh(x) - 3%i)coth(x) csch(x) +--R + +--R 2 2 +--R (- 45cosh(x) - 3)coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 60%i cosh(x) - 12%i cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (- 60cosh(x) - 12cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 45%i cosh(x) - 18%i cosh(x) + 18%i)coth(x) csch(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) - 18cosh(x) + 18)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) - 12%i cosh(x) + 36%i cosh(x))coth(x) +--R * +--R csch(x) +--R + +--R 5 3 2 +--R (- 18cosh(x) - 12cosh(x) + 36cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) - 3%i cosh(x) + 18%i cosh(x) - 12%i)coth(x) +--R * +--R csch(x) +--R + +--R 6 4 2 2 +--R (- 3cosh(x) - 3cosh(x) + 18cosh(x) - 12)coth(x) +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 6 +--R (- 3\|3 coth(x) csch(x) + 3%i\|3 coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 5 +--R (- 18\|3 cosh(x)coth(x) csch(x) + 18%i\|3 cosh(x)coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 45\|3 cosh(x) + 3\|3 )coth(x) csch(x) +--R + +--R +-+ 2 +-+ 2 +--R (45%i\|3 cosh(x) - 3%i\|3 )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 60\|3 cosh(x) + 12\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (60%i\|3 cosh(x) - 12%i\|3 cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 45\|3 cosh(x) + 18\|3 cosh(x) + 12\|3 )coth(x) csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (45%i\|3 cosh(x) - 18%i\|3 cosh(x) - 12%i\|3 )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 18\|3 cosh(x) + 12\|3 cosh(x) + 24\|3 cosh(x))coth(x) +--R * +--R csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (18%i\|3 cosh(x) - 12%i\|3 cosh(x) - 24%i\|3 cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (- 3\|3 cosh(x) + 3\|3 cosh(x) + 12\|3 cosh(x) - 12\|3 )coth(x) +--R * +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (3%i\|3 cosh(x) - 3%i\|3 cosh(x) - 12%i\|3 cosh(x) + 12%i\|3 ) +--R * +--R 2 +--R coth(x) +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R / +--R +-+ 2 +-+ 6 +--R (\|3 csch(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (6\|3 cosh(x)csch(x) + 6\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((15\|3 cosh(x) + \|3 )csch(x) + 15\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (20\|3 cosh(x) + 4\|3 cosh(x))csch(x) + 20\|3 cosh(x) +--R + +--R +-+ +--R 4\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (\|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 )csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R \|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- 3%i csch(x) - 3%i)sinh(x) +--R + +--R 2 5 +--R (- 18%i cosh(x)csch(x) - 18%i cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 45%i cosh(x) + 3%i)csch(x) - 45%i cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 3 +--R (- 60%i cosh(x) + 12%i cosh(x))csch(x) - 60%i cosh(x) +--R + +--R 12%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 45%i cosh(x) + 18%i cosh(x) + 12%i)csch(x) - 45%i cosh(x) +--R + +--R 2 +--R 18%i cosh(x) + 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x))csch(x) +--R + +--R 5 3 +--R - 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i)csch(x) +--R + +--R 6 4 2 +--R - 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i +--R * +--R +--------------+ +--------------+ +--R \|%i csch(x) - 1 \|%i csch(x) + 1 +--R Type: Expression Complex Integer +--E 289 + +--S 290 of 526 +t0455:= (3-3*%i*csch(x))^(1/2) +--R +--R +--R +-----------------+ +--R (203) \|- 3%i csch(x) + 3 +--R Type: Expression Complex Integer +--E 290 + +--S 291 of 526 +r0455:= 2*3^(1/2)*atan((-1-%i*csch(x))^(1/2))*coth(x)/(-1-%i*csch(x))^(1/2)/(1-%i*csch(x))^(1/2) +--R +--R +--R +-+ +----------------+ +--R 2\|3 coth(x)atan(\|- %i csch(x) - 1 ) +--R (204) -------------------------------------- +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R Type: Expression Complex Integer +--E 291 + +--S 292 of 526 +a0455:= integrate(t0455,x) +--R +--R +--R (205) +--R +-+ +--R \|3 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- + \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|3 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R %i\|3 sinh(x) + (3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (3%i\|3 cosh(x) - 2\|3 cosh(x) - %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R %i\|3 cosh(x) - \|3 cosh(x) - %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression Complex Integer,...) +--E 292 + +--S 293 of 526 +m0455:= a0455-r0455 +--R +--R +--R (206) +--R +-+ +----------------+ +----------------+ +--R \|3 \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- + \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +----------------+ +----------------+ +--R \|3 \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R %i\|3 sinh(x) + (3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (3%i\|3 cosh(x) - 2\|3 cosh(x) - %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R %i\|3 cosh(x) - \|3 cosh(x) - %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +----------------+ +--R - 2\|3 coth(x)atan(\|- %i csch(x) - 1 ) +--R / +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R Type: Expression Complex Integer +--E 293 + +--S 294 of 526 +d0455:= D(m0455,x) +--R +--R +--R (207) +--R 2 2 6 +--R (- 6csch(x) + 6coth(x) - 6)sinh(x) +--R + +--R 2 2 5 +--R (- 36cosh(x)csch(x) + 36cosh(x)coth(x) - 36cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R (- 90cosh(x) - 6)csch(x) + (90cosh(x) + 6)coth(x) +--R + +--R 2 +--R - 90cosh(x) - 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 120cosh(x) - 24cosh(x))csch(x) +--R + +--R 3 2 3 +--R (120cosh(x) + 24cosh(x))coth(x) - 120cosh(x) - 24cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 90cosh(x) - 36cosh(x) + 36)csch(x) +--R + +--R 4 2 2 4 +--R (90cosh(x) + 36cosh(x) - 36)coth(x) - 90cosh(x) +--R + +--R 2 +--R - 36cosh(x) + 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 36cosh(x) - 24cosh(x) + 72cosh(x))csch(x) +--R + +--R 5 3 2 5 +--R (36cosh(x) + 24cosh(x) - 72cosh(x))coth(x) - 36cosh(x) +--R + +--R 3 +--R - 24cosh(x) + 72cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 6cosh(x) - 6cosh(x) + 36cosh(x) - 24)csch(x) +--R + +--R 6 4 2 2 6 +--R (6cosh(x) + 6cosh(x) - 36cosh(x) + 24)coth(x) - 6cosh(x) +--R + +--R 4 2 +--R - 6cosh(x) + 36cosh(x) - 24 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 +-+ 6 +--R (6%i\|3 csch(x) - 6%i\|3 coth(x) + 6%i\|3 )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R 36%i\|3 cosh(x)csch(x) - 36%i\|3 cosh(x)coth(x) +--R + +--R +-+ +--R 36%i\|3 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 6%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (- 90%i\|3 cosh(x) + 6%i\|3 )coth(x) + 90%i\|3 cosh(x) - 6%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (120%i\|3 cosh(x) - 24%i\|3 cosh(x))csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 120%i\|3 cosh(x) + 24%i\|3 cosh(x))coth(x) +--R + +--R +-+ 3 +-+ +--R 120%i\|3 cosh(x) - 24%i\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 )coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x))coth(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 ) +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 ) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 +--R * +--R +----------------+ +--R atan(\|- %i csch(x) - 1 ) +--R + +--R 2 6 +--R (6csch(x) + 6)sinh(x) +--R + +--R 2 5 +--R ((36cosh(x) + 18%i)csch(x) + 36cosh(x) + 18%i)sinh(x) +--R + +--R 2 2 2 +--R (90cosh(x) + 90%i cosh(x) + 3)csch(x) + 90cosh(x) +--R + +--R 90%i cosh(x) + 3 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (120cosh(x) + 180%i cosh(x) + 12cosh(x) - 30%i)csch(x) +--R + +--R 3 2 +--R 120cosh(x) + 180%i cosh(x) + 12cosh(x) - 30%i +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 90cosh(x) + 180%i cosh(x) + 18cosh(x) - 90%i cosh(x) +--R + +--R - 24 +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R 90cosh(x) + 180%i cosh(x) + 18cosh(x) - 90%i cosh(x) - 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 36cosh(x) + 90%i cosh(x) + 12cosh(x) - 90%i cosh(x) +--R + +--R - 48cosh(x) + 12%i +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 2 +--R 36cosh(x) + 90%i cosh(x) + 12cosh(x) - 90%i cosh(x) +--R + +--R - 48cosh(x) + 12%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R 6cosh(x) + 18%i cosh(x) + 3cosh(x) - 30%i cosh(x) +--R + +--R 2 +--R - 24cosh(x) + 12%i cosh(x) + 12 +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R 6cosh(x) + 18%i cosh(x) + 3cosh(x) - 30%i cosh(x) +--R + +--R 2 +--R - 24cosh(x) + 12%i cosh(x) + 12 +--R * +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R + +--R 2 2 6 +--R (3%i coth(x) csch(x) - 3coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (18%i cosh(x)coth(x) csch(x) - 18cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 +--R (45%i cosh(x) + 3%i)coth(x) csch(x) +--R + +--R 2 2 +--R (- 45cosh(x) - 3)coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (60%i cosh(x) + 12%i cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (- 60cosh(x) - 12cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (45%i cosh(x) + 18%i cosh(x) - 18%i)coth(x) csch(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) - 18cosh(x) + 18)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (18%i cosh(x) + 12%i cosh(x) - 36%i cosh(x))coth(x) csch(x) +--R + +--R 5 3 2 +--R (- 18cosh(x) - 12cosh(x) + 36cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (3%i cosh(x) + 3%i cosh(x) - 18%i cosh(x) + 12%i)coth(x) +--R * +--R csch(x) +--R + +--R 6 4 2 2 +--R (- 3cosh(x) - 3cosh(x) + 18cosh(x) - 12)coth(x) +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 6 +--R (- 3%i\|3 csch(x) - 3%i\|3 )sinh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ +--R ((- 18%i\|3 cosh(x) + 6\|3 )csch(x) - 18%i\|3 cosh(x) + 6\|3 ) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R (- 45%i\|3 cosh(x) + 30\|3 cosh(x) + 3%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 45%i\|3 cosh(x) + 30\|3 cosh(x) + 3%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 60%i\|3 cosh(x) + 60\|3 cosh(x) + 12%i\|3 cosh(x) +--R + +--R +-+ +--R - 24\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 60%i\|3 cosh(x) + 60\|3 cosh(x) + 12%i\|3 cosh(x) - 24\|3 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 45%i\|3 cosh(x) + 60\|3 cosh(x) + 18%i\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72\|3 cosh(x) + 18%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 45%i\|3 cosh(x) + 60\|3 cosh(x) + 18%i\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72\|3 cosh(x) + 18%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 18%i\|3 cosh(x) + 30\|3 cosh(x) + 12%i\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72\|3 cosh(x) + 36%i\|3 cosh(x) + 12\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 18%i\|3 cosh(x) + 30\|3 cosh(x) + 12%i\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72\|3 cosh(x) + 36%i\|3 cosh(x) + 12\|3 +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 3%i\|3 cosh(x) + 6\|3 cosh(x) + 3%i\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24\|3 cosh(x) + 18%i\|3 cosh(x) + 12\|3 cosh(x) - 12%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R - 3%i\|3 cosh(x) + 6\|3 cosh(x) + 3%i\|3 cosh(x) - 24\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 18%i\|3 cosh(x) + 12\|3 cosh(x) - 12%i\|3 +--R * +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R + +--R +-+ 2 +-+ 2 6 +--R (3\|3 coth(x) csch(x) + 3%i\|3 coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 5 +--R (18\|3 cosh(x)coth(x) csch(x) + 18%i\|3 cosh(x)coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (45\|3 cosh(x) - 3\|3 )coth(x) csch(x) +--R + +--R +-+ 2 +-+ 2 +--R (45%i\|3 cosh(x) - 3%i\|3 )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (60\|3 cosh(x) - 12\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (60%i\|3 cosh(x) - 12%i\|3 cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (45\|3 cosh(x) - 18\|3 cosh(x) - 12\|3 )coth(x) csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (45%i\|3 cosh(x) - 18%i\|3 cosh(x) - 12%i\|3 )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (18\|3 cosh(x) - 12\|3 cosh(x) - 24\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (18%i\|3 cosh(x) - 12%i\|3 cosh(x) - 24%i\|3 cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (3\|3 cosh(x) - 3\|3 cosh(x) - 12\|3 cosh(x) + 12\|3 )coth(x) +--R * +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (3%i\|3 cosh(x) - 3%i\|3 cosh(x) - 12%i\|3 cosh(x) + 12%i\|3 ) +--R * +--R 2 +--R coth(x) +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R / +--R +-+ 2 +-+ 6 +--R (\|3 csch(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (6\|3 cosh(x)csch(x) + 6\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((15\|3 cosh(x) + \|3 )csch(x) + 15\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (20\|3 cosh(x) + 4\|3 cosh(x))csch(x) + 20\|3 cosh(x) +--R + +--R +-+ +--R 4\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +-+ 4 +--R (15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 )csch(x) + 15\|3 cosh(x) +--R + +--R +-+ 2 +-+ +--R 6\|3 cosh(x) - 6\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (\|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 )csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R \|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 +--R * +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- 3%i csch(x) - 3%i)sinh(x) +--R + +--R 2 5 +--R (- 18%i cosh(x)csch(x) - 18%i cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 45%i cosh(x) + 3%i)csch(x) - 45%i cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 3 +--R (- 60%i cosh(x) + 12%i cosh(x))csch(x) - 60%i cosh(x) +--R + +--R 12%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 45%i cosh(x) + 18%i cosh(x) + 12%i)csch(x) - 45%i cosh(x) +--R + +--R 2 +--R 18%i cosh(x) + 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x))csch(x) +--R + +--R 5 3 +--R - 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i)csch(x) +--R + +--R 6 4 2 +--R - 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i +--R * +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R Type: Expression Complex Integer +--E 294 + +--S 295 of 526 +t0456:= (-3+3*%i*csch(x))^(1/2) +--R +--R +--R +---------------+ +--R (208) \|3%i csch(x) - 3 +--R Type: Expression Complex Integer +--E 295 + +--S 296 of 526 +r0456:= -2*3^(1/2)*atan((-1-%i*csch(x))^(1/2))*coth(x)/(-1-%i*csch(x))^(1/2)/(-1+%i*csch(x))^(1/2) +--R +--R +--R +-+ +----------------+ +--R 2\|3 coth(x)atan(\|- %i csch(x) - 1 ) +--R (209) - ------------------------------------- +--R +----------------+ +--------------+ +--R \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R Type: Expression Complex Integer +--E 296 + +--S 297 of 526 +a0456:= integrate(t0456,x) +--R +--R +--R (210) +--R +-+ +--R %i\|3 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- + \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R %i\|3 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R %i\|3 sinh(x) + (3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (3%i\|3 cosh(x) - 2\|3 cosh(x) - %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R %i\|3 cosh(x) - \|3 cosh(x) - %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression Complex Integer,...) +--E 297 + +--S 298 of 526 +m0456:= a0456-r0456 +--R +--R +--R (211) +--R +-+ +----------------+ +--------------+ +--R %i\|3 \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- + \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +----------------+ +--------------+ +--R %i\|3 \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R %i\|3 sinh(x) + (3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (3%i\|3 cosh(x) - 2\|3 cosh(x) - %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R %i\|3 cosh(x) - \|3 cosh(x) - %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +----------------+ +--R 2\|3 coth(x)atan(\|- %i csch(x) - 1 ) +--R / +--R +----------------+ +--------------+ +--R \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R Type: Expression Complex Integer +--E 298 + +--S 299 of 526 +d0456:= D(m0456,x) +--R +--R +--R (212) +--R 2 2 6 +--R (6csch(x) - 6coth(x) + 6)sinh(x) +--R + +--R 2 2 5 +--R (36cosh(x)csch(x) - 36cosh(x)coth(x) + 36cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R (90cosh(x) + 6)csch(x) + (- 90cosh(x) - 6)coth(x) +--R + +--R 2 +--R 90cosh(x) + 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (120cosh(x) + 24cosh(x))csch(x) +--R + +--R 3 2 3 +--R (- 120cosh(x) - 24cosh(x))coth(x) + 120cosh(x) + 24cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (90cosh(x) + 36cosh(x) - 36)csch(x) +--R + +--R 4 2 2 4 +--R (- 90cosh(x) - 36cosh(x) + 36)coth(x) + 90cosh(x) +--R + +--R 2 +--R 36cosh(x) - 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (36cosh(x) + 24cosh(x) - 72cosh(x))csch(x) +--R + +--R 5 3 2 5 +--R (- 36cosh(x) - 24cosh(x) + 72cosh(x))coth(x) + 36cosh(x) +--R + +--R 3 +--R 24cosh(x) - 72cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (6cosh(x) + 6cosh(x) - 36cosh(x) + 24)csch(x) +--R + +--R 6 4 2 2 6 +--R (- 6cosh(x) - 6cosh(x) + 36cosh(x) - 24)coth(x) + 6cosh(x) +--R + +--R 4 2 +--R 6cosh(x) - 36cosh(x) + 24 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 +-+ 6 +--R (- 6%i\|3 csch(x) + 6%i\|3 coth(x) - 6%i\|3 )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R - 36%i\|3 cosh(x)csch(x) + 36%i\|3 cosh(x)coth(x) +--R + +--R +-+ +--R - 36%i\|3 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 6%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (90%i\|3 cosh(x) - 6%i\|3 )coth(x) - 90%i\|3 cosh(x) + 6%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 120%i\|3 cosh(x) + 24%i\|3 cosh(x))csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (120%i\|3 cosh(x) - 24%i\|3 cosh(x))coth(x) - 120%i\|3 cosh(x) +--R + +--R +-+ +--R 24%i\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 )coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x))coth(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 ) +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 ) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 +--R * +--R +----------------+ +--R atan(\|- %i csch(x) - 1 ) +--R + +--R 2 6 +--R (6%i csch(x) + 6%i)sinh(x) +--R + +--R 2 5 +--R ((36%i cosh(x) - 18)csch(x) + 36%i cosh(x) - 18)sinh(x) +--R + +--R 2 2 2 +--R (90%i cosh(x) - 90cosh(x) + 3%i)csch(x) + 90%i cosh(x) +--R + +--R - 90cosh(x) + 3%i +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (120%i cosh(x) - 180cosh(x) + 12%i cosh(x) + 30)csch(x) +--R + +--R 3 2 +--R 120%i cosh(x) - 180cosh(x) + 12%i cosh(x) + 30 +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 90%i cosh(x) - 180cosh(x) + 18%i cosh(x) + 90cosh(x) +--R + +--R - 24%i +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R 90%i cosh(x) - 180cosh(x) + 18%i cosh(x) + 90cosh(x) - 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 36%i cosh(x) - 90cosh(x) + 12%i cosh(x) + 90cosh(x) +--R + +--R - 48%i cosh(x) - 12 +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 2 +--R 36%i cosh(x) - 90cosh(x) + 12%i cosh(x) + 90cosh(x) +--R + +--R - 48%i cosh(x) - 12 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R 6%i cosh(x) - 18cosh(x) + 3%i cosh(x) + 30cosh(x) +--R + +--R 2 +--R - 24%i cosh(x) - 12cosh(x) + 12%i +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R 6%i cosh(x) - 18cosh(x) + 3%i cosh(x) + 30cosh(x) +--R + +--R 2 +--R - 24%i cosh(x) - 12cosh(x) + 12%i +--R * +--R +-----------------------------------------+ +--R +----------------+ | 3 +--R \|- %i csch(x) - 1 |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 6 +--R (3\|3 csch(x) + 3\|3 )sinh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ +--R ((18\|3 cosh(x) + 6%i\|3 )csch(x) + 18\|3 cosh(x) + 6%i\|3 ) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R (45\|3 cosh(x) + 30%i\|3 cosh(x) - 3\|3 )csch(x) +--R + +--R +-+ 2 +-+ +-+ +--R 45\|3 cosh(x) + 30%i\|3 cosh(x) - 3\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 60\|3 cosh(x) + 60%i\|3 cosh(x) - 12\|3 cosh(x) +--R + +--R +-+ +--R - 24%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 60\|3 cosh(x) + 60%i\|3 cosh(x) - 12\|3 cosh(x) - 24%i\|3 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 45\|3 cosh(x) + 60%i\|3 cosh(x) - 18\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72%i\|3 cosh(x) - 18\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 45\|3 cosh(x) + 60%i\|3 cosh(x) - 18\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72%i\|3 cosh(x) - 18\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 18\|3 cosh(x) + 30%i\|3 cosh(x) - 12\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72%i\|3 cosh(x) - 36\|3 cosh(x) + 12%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 18\|3 cosh(x) + 30%i\|3 cosh(x) - 12\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72%i\|3 cosh(x) - 36\|3 cosh(x) + 12%i\|3 +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 3\|3 cosh(x) + 6%i\|3 cosh(x) - 3\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24%i\|3 cosh(x) - 18\|3 cosh(x) + 12%i\|3 cosh(x) + 12\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 3\|3 cosh(x) + 6%i\|3 cosh(x) - 3\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24%i\|3 cosh(x) - 18\|3 cosh(x) + 12%i\|3 cosh(x) + 12\|3 +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R + +--R 2 2 6 +--R (- 3%i coth(x) csch(x) + 3coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (- 18%i cosh(x)coth(x) csch(x) + 18cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 2 2 +--R ((- 45%i cosh(x) - 3%i)coth(x) csch(x) + (45cosh(x) + 3)coth(x) ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 60%i cosh(x) - 12%i cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (60cosh(x) + 12cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 45%i cosh(x) - 18%i cosh(x) + 18%i)coth(x) csch(x) +--R + +--R 4 2 2 +--R (45cosh(x) + 18cosh(x) - 18)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) - 12%i cosh(x) + 36%i cosh(x))coth(x) csch(x) +--R + +--R 5 3 2 +--R (18cosh(x) + 12cosh(x) - 36cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) - 3%i cosh(x) + 18%i cosh(x) - 12%i)coth(x) csch(x) +--R + +--R 6 4 2 2 +--R (3cosh(x) + 3cosh(x) - 18cosh(x) + 12)coth(x) +--R * +--R +-----------------------------------------+ +--R +----------------+ | 3 +--R \|- %i csch(x) - 1 |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 6 +--R (- 3\|3 coth(x) csch(x) - 3%i\|3 coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 5 +--R (- 18\|3 cosh(x)coth(x) csch(x) - 18%i\|3 cosh(x)coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 45\|3 cosh(x) + 3\|3 )coth(x) csch(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 45%i\|3 cosh(x) + 3%i\|3 )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 60\|3 cosh(x) + 12\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 60%i\|3 cosh(x) + 12%i\|3 cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 45\|3 cosh(x) + 18\|3 cosh(x) + 12\|3 )coth(x) csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 45%i\|3 cosh(x) + 18%i\|3 cosh(x) + 12%i\|3 )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 18\|3 cosh(x) + 12\|3 cosh(x) + 24\|3 cosh(x))coth(x) +--R * +--R csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 18%i\|3 cosh(x) + 12%i\|3 cosh(x) + 24%i\|3 cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (- 3\|3 cosh(x) + 3\|3 cosh(x) + 12\|3 cosh(x) - 12\|3 )coth(x) +--R * +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 3%i\|3 cosh(x) + 3%i\|3 cosh(x) + 12%i\|3 cosh(x) - 12%i\|3 ) +--R * +--R 2 +--R coth(x) +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R / +--R +-+ 2 +-+ 6 +--R (\|3 csch(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (6\|3 cosh(x)csch(x) + 6\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((15\|3 cosh(x) + \|3 )csch(x) + 15\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (20\|3 cosh(x) + 4\|3 cosh(x))csch(x) + 20\|3 cosh(x) +--R + +--R +-+ +--R 4\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (\|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 )csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R \|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 +--R * +--R +-----------------------------------------+ +--R +----------------+ | 3 +--R \|- %i csch(x) - 1 |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- 3%i csch(x) - 3%i)sinh(x) +--R + +--R 2 5 +--R (- 18%i cosh(x)csch(x) - 18%i cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 45%i cosh(x) + 3%i)csch(x) - 45%i cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 3 +--R (- 60%i cosh(x) + 12%i cosh(x))csch(x) - 60%i cosh(x) +--R + +--R 12%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 45%i cosh(x) + 18%i cosh(x) + 12%i)csch(x) +--R + +--R 4 2 +--R - 45%i cosh(x) + 18%i cosh(x) + 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x))csch(x) +--R + +--R 5 3 +--R - 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i)csch(x) +--R + +--R 6 4 2 +--R - 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R Type: Expression Complex Integer +--E 299 + +--S 300 of 526 +t0457:= (-3-3*%i*csch(x))^(1/2) +--R +--R +--R +-----------------+ +--R (213) \|- 3%i csch(x) - 3 +--R Type: Expression Complex Integer +--E 300 + +--S 301 of 526 +r0457:= -2*3^(1/2)*atan((-1+%i*csch(x))^(1/2))*coth(x)/(-1-%i*csch(x))^(1/2)/(-1+%i*csch(x))^(1/2) +--R +--R +--R +-+ +--------------+ +--R 2\|3 coth(x)atan(\|%i csch(x) - 1 ) +--R (214) - ------------------------------------ +--R +----------------+ +--------------+ +--R \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R Type: Expression Complex Integer +--E 301 + +--S 302 of 526 +a0457:= integrate(t0457,x) +--R +--R +--R (215) +--R - +--R +-+ +--R %i\|3 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- - \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R - \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R %i\|3 +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) - 2%i cosh(x) +--R + +--R - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R - %i\|3 sinh(x) + (- 3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (- 3%i\|3 cosh(x) - 2\|3 cosh(x) + %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - %i\|3 cosh(x) - \|3 cosh(x) + %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression Complex Integer,...) +--E 302 + +--S 303 of 526 +m0457:= a0457-r0457 +--R +--R +--R (216) +--R - +--R +-+ +----------------+ +--------------+ +--R %i\|3 \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- - \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R - \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +----------------+ +--------------+ +--R %i\|3 \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R - %i\|3 sinh(x) + (- 3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (- 3%i\|3 cosh(x) - 2\|3 cosh(x) + %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - %i\|3 cosh(x) - \|3 cosh(x) + %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--------------+ +--R 2\|3 coth(x)atan(\|%i csch(x) - 1 ) +--R / +--R +----------------+ +--------------+ +--R \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R Type: Expression Complex Integer +--E 303 + +--S 304 of 526 +d0457:= D(m0457,x) +--R +--R +--R (217) +--R 2 2 6 +--R (6csch(x) - 6coth(x) + 6)sinh(x) +--R + +--R 2 2 5 +--R (36cosh(x)csch(x) - 36cosh(x)coth(x) + 36cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R (90cosh(x) + 6)csch(x) + (- 90cosh(x) - 6)coth(x) +--R + +--R 2 +--R 90cosh(x) + 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (120cosh(x) + 24cosh(x))csch(x) +--R + +--R 3 2 3 +--R (- 120cosh(x) - 24cosh(x))coth(x) + 120cosh(x) + 24cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (90cosh(x) + 36cosh(x) - 36)csch(x) +--R + +--R 4 2 2 4 +--R (- 90cosh(x) - 36cosh(x) + 36)coth(x) + 90cosh(x) +--R + +--R 2 +--R 36cosh(x) - 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (36cosh(x) + 24cosh(x) - 72cosh(x))csch(x) +--R + +--R 5 3 2 5 +--R (- 36cosh(x) - 24cosh(x) + 72cosh(x))coth(x) + 36cosh(x) +--R + +--R 3 +--R 24cosh(x) - 72cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (6cosh(x) + 6cosh(x) - 36cosh(x) + 24)csch(x) +--R + +--R 6 4 2 2 6 +--R (- 6cosh(x) - 6cosh(x) + 36cosh(x) - 24)coth(x) + 6cosh(x) +--R + +--R 4 2 +--R 6cosh(x) - 36cosh(x) + 24 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 +-+ 6 +--R (- 6%i\|3 csch(x) + 6%i\|3 coth(x) - 6%i\|3 )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R - 36%i\|3 cosh(x)csch(x) + 36%i\|3 cosh(x)coth(x) +--R + +--R +-+ +--R - 36%i\|3 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 6%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (90%i\|3 cosh(x) - 6%i\|3 )coth(x) - 90%i\|3 cosh(x) + 6%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 120%i\|3 cosh(x) + 24%i\|3 cosh(x))csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (120%i\|3 cosh(x) - 24%i\|3 cosh(x))coth(x) - 120%i\|3 cosh(x) +--R + +--R +-+ +--R 24%i\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 )coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x))coth(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 ) +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 ) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 +--R * +--R +--------------+ +--R atan(\|%i csch(x) - 1 ) +--R + +--R 2 6 +--R (- 6%i csch(x) - 6%i)sinh(x) +--R + +--R 2 5 +--R ((- 36%i cosh(x) - 18)csch(x) - 36%i cosh(x) - 18)sinh(x) +--R + +--R 2 2 +--R (- 90%i cosh(x) - 90cosh(x) - 3%i)csch(x) +--R + +--R 2 +--R - 90%i cosh(x) - 90cosh(x) - 3%i +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 120%i cosh(x) - 180cosh(x) - 12%i cosh(x) + 30) +--R * +--R 2 +--R csch(x) +--R + +--R 3 2 +--R - 120%i cosh(x) - 180cosh(x) - 12%i cosh(x) + 30 +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R - 90%i cosh(x) - 180cosh(x) - 18%i cosh(x) +--R + +--R 90cosh(x) + 24%i +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R - 90%i cosh(x) - 180cosh(x) - 18%i cosh(x) + 90cosh(x) +--R + +--R 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R - 36%i cosh(x) - 90cosh(x) - 12%i cosh(x) +--R + +--R 2 +--R 90cosh(x) + 48%i cosh(x) - 12 +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 2 +--R - 36%i cosh(x) - 90cosh(x) - 12%i cosh(x) + 90cosh(x) +--R + +--R 48%i cosh(x) - 12 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 6%i cosh(x) - 18cosh(x) - 3%i cosh(x) + 30cosh(x) +--R + +--R 2 +--R 24%i cosh(x) - 12cosh(x) - 12%i +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R - 6%i cosh(x) - 18cosh(x) - 3%i cosh(x) + 30cosh(x) +--R + +--R 2 +--R 24%i cosh(x) - 12cosh(x) - 12%i +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R + +--R 2 2 6 +--R (3%i coth(x) csch(x) + 3coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (18%i cosh(x)coth(x) csch(x) + 18cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 +--R (45%i cosh(x) + 3%i)coth(x) csch(x) +--R + +--R 2 2 +--R (45cosh(x) + 3)coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (60%i cosh(x) + 12%i cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (60cosh(x) + 12cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (45%i cosh(x) + 18%i cosh(x) - 18%i)coth(x) csch(x) +--R + +--R 4 2 2 +--R (45cosh(x) + 18cosh(x) - 18)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (18%i cosh(x) + 12%i cosh(x) - 36%i cosh(x))coth(x) csch(x) +--R + +--R 5 3 2 +--R (18cosh(x) + 12cosh(x) - 36cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (3%i cosh(x) + 3%i cosh(x) - 18%i cosh(x) + 12%i)coth(x) +--R * +--R csch(x) +--R + +--R 6 4 2 2 +--R (3cosh(x) + 3cosh(x) - 18cosh(x) + 12)coth(x) +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 6 +--R (- 3\|3 csch(x) - 3\|3 )sinh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ +--R ((- 18\|3 cosh(x) + 6%i\|3 )csch(x) - 18\|3 cosh(x) + 6%i\|3 ) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R (- 45\|3 cosh(x) + 30%i\|3 cosh(x) + 3\|3 )csch(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 45\|3 cosh(x) + 30%i\|3 cosh(x) + 3\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 60\|3 cosh(x) + 60%i\|3 cosh(x) + 12\|3 cosh(x) +--R + +--R +-+ +--R - 24%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 60\|3 cosh(x) + 60%i\|3 cosh(x) + 12\|3 cosh(x) - 24%i\|3 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 45\|3 cosh(x) + 60%i\|3 cosh(x) + 18\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72%i\|3 cosh(x) + 18\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 45\|3 cosh(x) + 60%i\|3 cosh(x) + 18\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72%i\|3 cosh(x) + 18\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 18\|3 cosh(x) + 30%i\|3 cosh(x) + 12\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72%i\|3 cosh(x) + 36\|3 cosh(x) + 12%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 18\|3 cosh(x) + 30%i\|3 cosh(x) + 12\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72%i\|3 cosh(x) + 36\|3 cosh(x) + 12%i\|3 +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 3\|3 cosh(x) + 6%i\|3 cosh(x) + 3\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24%i\|3 cosh(x) + 18\|3 cosh(x) + 12%i\|3 cosh(x) - 12\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 3\|3 cosh(x) + 6%i\|3 cosh(x) + 3\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24%i\|3 cosh(x) + 18\|3 cosh(x) + 12%i\|3 cosh(x) - 12\|3 +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R + +--R +-+ 2 +-+ 2 6 +--R (3\|3 coth(x) csch(x) - 3%i\|3 coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 5 +--R (18\|3 cosh(x)coth(x) csch(x) - 18%i\|3 cosh(x)coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (45\|3 cosh(x) - 3\|3 )coth(x) csch(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 45%i\|3 cosh(x) + 3%i\|3 )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (60\|3 cosh(x) - 12\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 60%i\|3 cosh(x) + 12%i\|3 cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (45\|3 cosh(x) - 18\|3 cosh(x) - 12\|3 )coth(x) csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 45%i\|3 cosh(x) + 18%i\|3 cosh(x) + 12%i\|3 )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (18\|3 cosh(x) - 12\|3 cosh(x) - 24\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 18%i\|3 cosh(x) + 12%i\|3 cosh(x) + 24%i\|3 cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (3\|3 cosh(x) - 3\|3 cosh(x) - 12\|3 cosh(x) + 12\|3 )coth(x) +--R * +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 3%i\|3 cosh(x) + 3%i\|3 cosh(x) + 12%i\|3 cosh(x) - 12%i\|3 ) +--R * +--R 2 +--R coth(x) +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R / +--R +-+ 2 +-+ 6 +--R (\|3 csch(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (6\|3 cosh(x)csch(x) + 6\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((15\|3 cosh(x) + \|3 )csch(x) + 15\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (20\|3 cosh(x) + 4\|3 cosh(x))csch(x) + 20\|3 cosh(x) +--R + +--R +-+ +--R 4\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (\|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 )csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R \|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 +--R * +--R +-----------------------------------------+ +--R +----------------+ | 3 +--R \|- %i csch(x) - 1 |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- 3%i csch(x) - 3%i)sinh(x) +--R + +--R 2 5 +--R (- 18%i cosh(x)csch(x) - 18%i cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 45%i cosh(x) + 3%i)csch(x) - 45%i cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 3 +--R (- 60%i cosh(x) + 12%i cosh(x))csch(x) - 60%i cosh(x) +--R + +--R 12%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 45%i cosh(x) + 18%i cosh(x) + 12%i)csch(x) +--R + +--R 4 2 +--R - 45%i cosh(x) + 18%i cosh(x) + 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x))csch(x) +--R + +--R 5 3 +--R - 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i)csch(x) +--R + +--R 6 4 2 +--R - 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R Type: Expression Complex Integer +--E 304 + +--S 305 of 526 +t0458:= (a+%i*a*csch(x))^(1/2) +--R +--R +--R +----------------+ +--R (218) \|%i a csch(x) + a +--R Type: Expression Complex Integer +--E 305 + +--S 306 of 526 +r0458:= 2*a*atan((-1+%i*csch(x))^(1/2))*coth(x)/(-1+%i*csch(x))^(1/2)/(a+%i*a*csch(x))^(1/2) +--R +--R +--R +--------------+ +--R 2a coth(x)atan(\|%i csch(x) - 1 ) +--R (219) ------------------------------------ +--R +--------------+ +----------------+ +--R \|%i csch(x) - 1 \|%i a csch(x) + a +--R Type: Expression Complex Integer +--E 306 + +--S 307 of 526 +a0458:= integrate(t0458,x) +--R +--R +--R (220) +--R - +--R +-+ +--R \|a +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +--R (- sinh(x) - cosh(x) - %i)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R \|a +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) - 2%i cosh(x) +--R + +--R - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression Complex Integer,...) +--E 307 + +--S 308 of 526 +m0458:= a0458-r0458 +--R +--R +--R (221) +--R - +--R +-+ +--------------+ +----------------+ +--R \|a \|%i csch(x) - 1 \|%i a csch(x) + a +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +--R (- sinh(x) - cosh(x) - %i)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--------------+ +----------------+ +--R \|a \|%i csch(x) - 1 \|%i a csch(x) + a +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +--------------+ +--R - 2a coth(x)atan(\|%i csch(x) - 1 ) +--R / +--R +--------------+ +----------------+ +--R \|%i csch(x) - 1 \|%i a csch(x) + a +--R Type: Expression Complex Integer +--E 308 + +--S 309 of 526 +d0458:= D(m0458,x) +--R +--R +--R (222) +--R 2 2 6 +--R (- 2a csch(x) + 2a coth(x) - 2a)sinh(x) +--R + +--R 2 2 +--R (- 12a cosh(x)csch(x) + 12a cosh(x)coth(x) - 12a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 2 2 +--R (- 30a cosh(x) - 2a)csch(x) + (30a cosh(x) + 2a)coth(x) +--R + +--R 2 +--R - 30a cosh(x) - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 40a cosh(x) - 8a cosh(x))csch(x) +--R + +--R 3 2 3 +--R (40a cosh(x) + 8a cosh(x))coth(x) - 40a cosh(x) - 8a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 30a cosh(x) - 12a cosh(x) + 12a)csch(x) +--R + +--R 4 2 2 4 +--R (30a cosh(x) + 12a cosh(x) - 12a)coth(x) - 30a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 12a cosh(x) - 8a cosh(x) + 24a cosh(x))csch(x) +--R + +--R 5 3 2 +--R (12a cosh(x) + 8a cosh(x) - 24a cosh(x))coth(x) +--R + +--R 5 3 +--R - 12a cosh(x) - 8a cosh(x) + 24a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 2a cosh(x) - 2a cosh(x) + 12a cosh(x) - 8a)csch(x) +--R + +--R 6 4 2 2 +--R (2a cosh(x) + 2a cosh(x) - 12a cosh(x) + 8a)coth(x) +--R + +--R 6 4 2 +--R - 2a cosh(x) - 2a cosh(x) + 12a cosh(x) - 8a +--R * +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 2 2 2 2 6 +--R (2%i a csch(x) - 2%i a coth(x) + 2%i a )sinh(x) +--R + +--R 2 2 2 2 2 +--R (12%i a cosh(x)csch(x) - 12%i a cosh(x)coth(x) + 12%i a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 2 2 +--R (30%i a cosh(x) - 2%i a )csch(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 30%i a cosh(x) + 2%i a )coth(x) + 30%i a cosh(x) - 2%i a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (40%i a cosh(x) - 8%i a cosh(x))csch(x) +--R + +--R 2 3 2 2 2 3 +--R (- 40%i a cosh(x) + 8%i a cosh(x))coth(x) + 40%i a cosh(x) +--R + +--R 2 +--R - 8%i a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (30%i a cosh(x) - 12%i a cosh(x) - 8%i a )csch(x) +--R + +--R 2 4 2 2 2 2 +--R (- 30%i a cosh(x) + 12%i a cosh(x) + 8%i a )coth(x) +--R + +--R 2 4 2 2 2 +--R 30%i a cosh(x) - 12%i a cosh(x) - 8%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (12%i a cosh(x) - 8%i a cosh(x) - 16%i a cosh(x))csch(x) +--R + +--R 2 5 2 3 2 2 +--R (- 12%i a cosh(x) + 8%i a cosh(x) + 16%i a cosh(x))coth(x) +--R + +--R 2 5 2 3 2 +--R 12%i a cosh(x) - 8%i a cosh(x) - 16%i a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (2%i a cosh(x) - 2%i a cosh(x) - 8%i a cosh(x) + 8%i a )csch(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 2%i a cosh(x) + 2%i a cosh(x) + 8%i a cosh(x) - 8%i a )coth(x) +--R + +--R 2 6 2 4 2 2 2 +--R 2%i a cosh(x) - 2%i a cosh(x) - 8%i a cosh(x) + 8%i a +--R * +--R +--------------+ +--R atan(\|%i csch(x) - 1 ) +--R + +--R 2 6 +--R (- 2a csch(x) - 2a)sinh(x) +--R + +--R 2 5 +--R ((- 12a cosh(x) + 6%i a)csch(x) - 12a cosh(x) + 6%i a)sinh(x) +--R + +--R 2 2 2 +--R (- 30a cosh(x) + 30%i a cosh(x) - a)csch(x) - 30a cosh(x) +--R + +--R 30%i a cosh(x) - a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 40a cosh(x) + 60%i a cosh(x) - 4a cosh(x) - 10%i a) +--R * +--R 2 +--R csch(x) +--R + +--R 3 2 +--R - 40a cosh(x) + 60%i a cosh(x) - 4a cosh(x) - 10%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R - 30a cosh(x) + 60%i a cosh(x) - 6a cosh(x) +--R + +--R - 30%i a cosh(x) + 8a +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R - 30a cosh(x) + 60%i a cosh(x) - 6a cosh(x) +--R + +--R - 30%i a cosh(x) + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R - 12a cosh(x) + 30%i a cosh(x) - 4a cosh(x) +--R + +--R 2 +--R - 30%i a cosh(x) + 16a cosh(x) + 4%i a +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 +--R - 12a cosh(x) + 30%i a cosh(x) - 4a cosh(x) +--R + +--R 2 +--R - 30%i a cosh(x) + 16a cosh(x) + 4%i a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 2a cosh(x) + 6%i a cosh(x) - a cosh(x) - 10%i a cosh(x) +--R + +--R 2 +--R 8a cosh(x) + 4%i a cosh(x) - 4a +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R - 2a cosh(x) + 6%i a cosh(x) - a cosh(x) - 10%i a cosh(x) +--R + +--R 2 +--R 8a cosh(x) + 4%i a cosh(x) - 4a +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (%i a csch(x) + %i a)sinh(x) +--R + +--R 2 5 +--R ((6%i a cosh(x) + 2a)csch(x) + 6%i a cosh(x) + 2a)sinh(x) +--R + +--R 2 2 +--R (15%i a cosh(x) + 10a cosh(x) - %i a)csch(x) +--R + +--R 2 +--R 15%i a cosh(x) + 10a cosh(x) - %i a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (20%i a cosh(x) + 20a cosh(x) - 4%i a cosh(x) - 8a)csch(x) +--R + +--R 3 2 +--R 20%i a cosh(x) + 20a cosh(x) - 4%i a cosh(x) - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 15%i a cosh(x) + 20a cosh(x) - 6%i a cosh(x) +--R + +--R - 24a cosh(x) - 6%i a +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R 15%i a cosh(x) + 20a cosh(x) - 6%i a cosh(x) - 24a cosh(x) +--R + +--R - 6%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R 6%i a cosh(x) + 10a cosh(x) - 4%i a cosh(x) +--R + +--R 2 +--R - 24a cosh(x) - 12%i a cosh(x) + 4a +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 2 +--R 6%i a cosh(x) + 10a cosh(x) - 4%i a cosh(x) - 24a cosh(x) +--R + +--R - 12%i a cosh(x) + 4a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R %i a cosh(x) + 2a cosh(x) - %i a cosh(x) - 8a cosh(x) +--R + +--R 2 +--R - 6%i a cosh(x) + 4a cosh(x) + 4%i a +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R %i a cosh(x) + 2a cosh(x) - %i a cosh(x) - 8a cosh(x) +--R + +--R 2 +--R - 6%i a cosh(x) + 4a cosh(x) + 4%i a +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +----------------+ +--R \|%i csch(x) - 1 \|%i a csch(x) + a +--R + +--R 2 2 6 +--R (- %i a coth(x) csch(x) - a coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (- 6%i a cosh(x)coth(x) csch(x) - 6a cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 +--R (- 15%i a cosh(x) - %i a)coth(x) csch(x) +--R + +--R 2 2 +--R (- 15a cosh(x) - a)coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 20%i a cosh(x) - 4%i a cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (- 20a cosh(x) - 4a cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 15%i a cosh(x) - 6%i a cosh(x) + 6%i a)coth(x) csch(x) +--R + +--R 4 2 2 +--R (- 15a cosh(x) - 6a cosh(x) + 6a)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 +--R (- 6%i a cosh(x) - 4%i a cosh(x) + 12%i a cosh(x)) +--R * +--R 2 +--R coth(x) csch(x) +--R + +--R 5 3 2 +--R (- 6a cosh(x) - 4a cosh(x) + 12a cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (- %i a cosh(x) - %i a cosh(x) + 6%i a cosh(x) - 4%i a) +--R * +--R 2 +--R coth(x) csch(x) +--R + +--R 6 4 2 2 +--R (- a cosh(x) - a cosh(x) + 6a cosh(x) - 4a)coth(x) +--R * +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 2 2 2 6 +--R (- a coth(x) csch(x) + %i a coth(x) )sinh(x) +--R + +--R 2 2 2 2 5 +--R (- 6a cosh(x)coth(x) csch(x) + 6%i a cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 2 2 +--R (- 15a cosh(x) + a )coth(x) csch(x) +--R + +--R 2 2 2 2 +--R (15%i a cosh(x) - %i a )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 20a cosh(x) + 4a cosh(x))coth(x) csch(x) +--R + +--R 2 3 2 2 +--R (20%i a cosh(x) - 4%i a cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 15a cosh(x) + 6a cosh(x) + 4a )coth(x) csch(x) +--R + +--R 2 4 2 2 2 2 +--R (15%i a cosh(x) - 6%i a cosh(x) - 4%i a )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (- 6a cosh(x) + 4a cosh(x) + 8a cosh(x))coth(x) csch(x) +--R + +--R 2 5 2 3 2 2 +--R (6%i a cosh(x) - 4%i a cosh(x) - 8%i a cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- a cosh(x) + a cosh(x) + 4a cosh(x) - 4a )coth(x) csch(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (%i a cosh(x) - %i a cosh(x) - 4%i a cosh(x) + 4%i a )coth(x) +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R / +--R 2 6 2 5 +--R (csch(x) + 1)sinh(x) + (6cosh(x)csch(x) + 6cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((15cosh(x) + 1)csch(x) + 15cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 3 +--R ((20cosh(x) + 4cosh(x))csch(x) + 20cosh(x) + 4cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (15cosh(x) + 6cosh(x) - 6)csch(x) + 15cosh(x) + 6cosh(x) +--R + +--R - 6 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (6cosh(x) + 4cosh(x) - 12cosh(x))csch(x) + 6cosh(x) +--R + +--R 3 +--R 4cosh(x) - 12cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (cosh(x) + cosh(x) - 6cosh(x) + 4)csch(x) + cosh(x) + cosh(x) +--R + +--R 2 +--R - 6cosh(x) + 4 +--R * +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- %i a csch(x) - %i a)sinh(x) +--R + +--R 2 5 +--R (- 6%i a cosh(x)csch(x) - 6%i a cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 15%i a cosh(x) + %i a)csch(x) - 15%i a cosh(x) + %i a)sinh(x) +--R + +--R 3 2 3 +--R (- 20%i a cosh(x) + 4%i a cosh(x))csch(x) - 20%i a cosh(x) +--R + +--R 4%i a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 15%i a cosh(x) + 6%i a cosh(x) + 4%i a)csch(x) +--R + +--R 4 2 +--R - 15%i a cosh(x) + 6%i a cosh(x) + 4%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 6%i a cosh(x) + 4%i a cosh(x) + 8%i a cosh(x))csch(x) +--R + +--R 5 3 +--R - 6%i a cosh(x) + 4%i a cosh(x) + 8%i a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- %i a cosh(x) + %i a cosh(x) + 4%i a cosh(x) - 4%i a)csch(x) +--R + +--R 6 4 2 +--R - %i a cosh(x) + %i a cosh(x) + 4%i a cosh(x) - 4%i a +--R * +--R +--------------+ +----------------+ +--R \|%i csch(x) - 1 \|%i a csch(x) + a +--R Type: Expression Complex Integer +--E 309 + +--S 310 of 526 +t0459:= (a-%i*a*csch(x))^(1/2) +--R +--R +--R +------------------+ +--R (223) \|- %i a csch(x) + a +--R Type: Expression Complex Integer +--E 310 + +--S 311 of 526 +r0459:= 2*a*atan((-1-%i*csch(x))^(1/2))*coth(x)/(-1-%i*csch(x))^(1/2)/(a-%i*a*csch(x))^(1/2) +--R +--R +--R +----------------+ +--R 2a coth(x)atan(\|- %i csch(x) - 1 ) +--R (224) ---------------------------------------- +--R +------------------+ +----------------+ +--R \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R Type: Expression Complex Integer +--E 311 + +--S 312 of 526 +a0459:= integrate(t0459,x) +--R +--R +--R (225) +--R +-+ +--R \|a +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +--R (sinh(x) + cosh(x) - %i)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|a +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression Complex Integer,...) +--E 312 + +--S 313 of 526 +m0459:= a0459-r0459 +--R +--R +--R (226) +--R +-+ +------------------+ +----------------+ +--R \|a \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +--R (sinh(x) + cosh(x) - %i)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +------------------+ +----------------+ +--R \|a \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +----------------+ +--R - 2a coth(x)atan(\|- %i csch(x) - 1 ) +--R / +--R +------------------+ +----------------+ +--R \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R Type: Expression Complex Integer +--E 313 + +--S 314 of 526 +d0459:= D(m0459,x) +--R +--R +--R (227) +--R 2 2 6 +--R (- 2a csch(x) + 2a coth(x) - 2a)sinh(x) +--R + +--R 2 2 +--R (- 12a cosh(x)csch(x) + 12a cosh(x)coth(x) - 12a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 2 2 +--R (- 30a cosh(x) - 2a)csch(x) + (30a cosh(x) + 2a)coth(x) +--R + +--R 2 +--R - 30a cosh(x) - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 40a cosh(x) - 8a cosh(x))csch(x) +--R + +--R 3 2 3 +--R (40a cosh(x) + 8a cosh(x))coth(x) - 40a cosh(x) - 8a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 30a cosh(x) - 12a cosh(x) + 12a)csch(x) +--R + +--R 4 2 2 4 +--R (30a cosh(x) + 12a cosh(x) - 12a)coth(x) - 30a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 12a cosh(x) - 8a cosh(x) + 24a cosh(x))csch(x) +--R + +--R 5 3 2 +--R (12a cosh(x) + 8a cosh(x) - 24a cosh(x))coth(x) +--R + +--R 5 3 +--R - 12a cosh(x) - 8a cosh(x) + 24a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 2a cosh(x) - 2a cosh(x) + 12a cosh(x) - 8a)csch(x) +--R + +--R 6 4 2 2 +--R (2a cosh(x) + 2a cosh(x) - 12a cosh(x) + 8a)coth(x) +--R + +--R 6 4 2 +--R - 2a cosh(x) - 2a cosh(x) + 12a cosh(x) - 8a +--R * +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 2 2 2 2 6 +--R (2%i a csch(x) - 2%i a coth(x) + 2%i a )sinh(x) +--R + +--R 2 2 2 2 2 +--R (12%i a cosh(x)csch(x) - 12%i a cosh(x)coth(x) + 12%i a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 2 2 +--R (30%i a cosh(x) - 2%i a )csch(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 30%i a cosh(x) + 2%i a )coth(x) + 30%i a cosh(x) - 2%i a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (40%i a cosh(x) - 8%i a cosh(x))csch(x) +--R + +--R 2 3 2 2 2 3 +--R (- 40%i a cosh(x) + 8%i a cosh(x))coth(x) + 40%i a cosh(x) +--R + +--R 2 +--R - 8%i a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (30%i a cosh(x) - 12%i a cosh(x) - 8%i a )csch(x) +--R + +--R 2 4 2 2 2 2 +--R (- 30%i a cosh(x) + 12%i a cosh(x) + 8%i a )coth(x) +--R + +--R 2 4 2 2 2 +--R 30%i a cosh(x) - 12%i a cosh(x) - 8%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (12%i a cosh(x) - 8%i a cosh(x) - 16%i a cosh(x))csch(x) +--R + +--R 2 5 2 3 2 2 +--R (- 12%i a cosh(x) + 8%i a cosh(x) + 16%i a cosh(x))coth(x) +--R + +--R 2 5 2 3 2 +--R 12%i a cosh(x) - 8%i a cosh(x) - 16%i a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (2%i a cosh(x) - 2%i a cosh(x) - 8%i a cosh(x) + 8%i a )csch(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 2%i a cosh(x) + 2%i a cosh(x) + 8%i a cosh(x) - 8%i a )coth(x) +--R + +--R 2 6 2 4 2 2 2 +--R 2%i a cosh(x) - 2%i a cosh(x) - 8%i a cosh(x) + 8%i a +--R * +--R +----------------+ +--R atan(\|- %i csch(x) - 1 ) +--R + +--R 2 6 +--R (2a csch(x) + 2a)sinh(x) +--R + +--R 2 5 +--R ((12a cosh(x) + 6%i a)csch(x) + 12a cosh(x) + 6%i a)sinh(x) +--R + +--R 2 2 2 +--R (30a cosh(x) + 30%i a cosh(x) + a)csch(x) + 30a cosh(x) +--R + +--R 30%i a cosh(x) + a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (40a cosh(x) + 60%i a cosh(x) + 4a cosh(x) - 10%i a) +--R * +--R 2 +--R csch(x) +--R + +--R 3 2 +--R 40a cosh(x) + 60%i a cosh(x) + 4a cosh(x) - 10%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 30a cosh(x) + 60%i a cosh(x) + 6a cosh(x) +--R + +--R - 30%i a cosh(x) - 8a +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R 30a cosh(x) + 60%i a cosh(x) + 6a cosh(x) - 30%i a cosh(x) +--R + +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R 12a cosh(x) + 30%i a cosh(x) + 4a cosh(x) +--R + +--R 2 +--R - 30%i a cosh(x) - 16a cosh(x) + 4%i a +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 +--R 12a cosh(x) + 30%i a cosh(x) + 4a cosh(x) +--R + +--R 2 +--R - 30%i a cosh(x) - 16a cosh(x) + 4%i a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R 2a cosh(x) + 6%i a cosh(x) + a cosh(x) - 10%i a cosh(x) +--R + +--R 2 +--R - 8a cosh(x) + 4%i a cosh(x) + 4a +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R 2a cosh(x) + 6%i a cosh(x) + a cosh(x) - 10%i a cosh(x) +--R + +--R 2 +--R - 8a cosh(x) + 4%i a cosh(x) + 4a +--R * +--R +------------------+ +--R \|- %i a csch(x) + a +--R + +--R 2 2 6 +--R (%i a coth(x) csch(x) - a coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (6%i a cosh(x)coth(x) csch(x) - 6a cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 +--R (15%i a cosh(x) + %i a)coth(x) csch(x) +--R + +--R 2 2 +--R (- 15a cosh(x) - a)coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (20%i a cosh(x) + 4%i a cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (- 20a cosh(x) - 4a cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (15%i a cosh(x) + 6%i a cosh(x) - 6%i a)coth(x) csch(x) +--R + +--R 4 2 2 +--R (- 15a cosh(x) - 6a cosh(x) + 6a)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (6%i a cosh(x) + 4%i a cosh(x) - 12%i a cosh(x))coth(x) +--R * +--R csch(x) +--R + +--R 5 3 2 +--R (- 6a cosh(x) - 4a cosh(x) + 12a cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (%i a cosh(x) + %i a cosh(x) - 6%i a cosh(x) + 4%i a) +--R * +--R 2 +--R coth(x) csch(x) +--R + +--R 6 4 2 2 +--R (- a cosh(x) - a cosh(x) + 6a cosh(x) - 4a)coth(x) +--R * +--R +-+ +--R \|a +--R * +--R +-----------------------------------------+ +--R +----------------+ | a +--R \|- %i csch(x) - 1 |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- %i a csch(x) - %i a)sinh(x) +--R + +--R 2 5 +--R ((- 6%i a cosh(x) + 2a)csch(x) - 6%i a cosh(x) + 2a)sinh(x) +--R + +--R 2 2 +--R (- 15%i a cosh(x) + 10a cosh(x) + %i a)csch(x) +--R + +--R 2 +--R - 15%i a cosh(x) + 10a cosh(x) + %i a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 20%i a cosh(x) + 20a cosh(x) + 4%i a cosh(x) - 8a) +--R * +--R 2 +--R csch(x) +--R + +--R 3 2 +--R - 20%i a cosh(x) + 20a cosh(x) + 4%i a cosh(x) - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R - 15%i a cosh(x) + 20a cosh(x) + 6%i a cosh(x) +--R + +--R - 24a cosh(x) + 6%i a +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R - 15%i a cosh(x) + 20a cosh(x) + 6%i a cosh(x) +--R + +--R - 24a cosh(x) + 6%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R - 6%i a cosh(x) + 10a cosh(x) + 4%i a cosh(x) +--R + +--R 2 +--R - 24a cosh(x) + 12%i a cosh(x) + 4a +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 +--R - 6%i a cosh(x) + 10a cosh(x) + 4%i a cosh(x) +--R + +--R 2 +--R - 24a cosh(x) + 12%i a cosh(x) + 4a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - %i a cosh(x) + 2a cosh(x) + %i a cosh(x) - 8a cosh(x) +--R + +--R 2 +--R 6%i a cosh(x) + 4a cosh(x) - 4%i a +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R - %i a cosh(x) + 2a cosh(x) + %i a cosh(x) - 8a cosh(x) +--R + +--R 2 +--R 6%i a cosh(x) + 4a cosh(x) - 4%i a +--R * +--R +-+ +------------------+ +--R \|a \|- %i a csch(x) + a +--R + +--R 2 2 2 2 6 +--R (a coth(x) csch(x) + %i a coth(x) )sinh(x) +--R + +--R 2 2 2 2 5 +--R (6a cosh(x)coth(x) csch(x) + 6%i a cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 2 2 +--R (15a cosh(x) - a )coth(x) csch(x) +--R + +--R 2 2 2 2 +--R (15%i a cosh(x) - %i a )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (20a cosh(x) - 4a cosh(x))coth(x) csch(x) +--R + +--R 2 3 2 2 +--R (20%i a cosh(x) - 4%i a cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (15a cosh(x) - 6a cosh(x) - 4a )coth(x) csch(x) +--R + +--R 2 4 2 2 2 2 +--R (15%i a cosh(x) - 6%i a cosh(x) - 4%i a )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (6a cosh(x) - 4a cosh(x) - 8a cosh(x))coth(x) csch(x) +--R + +--R 2 5 2 3 2 2 +--R (6%i a cosh(x) - 4%i a cosh(x) - 8%i a cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (a cosh(x) - a cosh(x) - 4a cosh(x) + 4a )coth(x) csch(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (%i a cosh(x) - %i a cosh(x) - 4%i a cosh(x) + 4%i a )coth(x) +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R / +--R 2 6 2 5 +--R (csch(x) + 1)sinh(x) + (6cosh(x)csch(x) + 6cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((15cosh(x) + 1)csch(x) + 15cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 3 +--R ((20cosh(x) + 4cosh(x))csch(x) + 20cosh(x) + 4cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R ((15cosh(x) + 6cosh(x) - 6)csch(x) + 15cosh(x) + 6cosh(x) - 6) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (6cosh(x) + 4cosh(x) - 12cosh(x))csch(x) + 6cosh(x) +--R + +--R 3 +--R 4cosh(x) - 12cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (cosh(x) + cosh(x) - 6cosh(x) + 4)csch(x) + cosh(x) + cosh(x) +--R + +--R 2 +--R - 6cosh(x) + 4 +--R * +--R +-+ +------------------+ +----------------+ +--R \|a \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- %i a csch(x) - %i a)sinh(x) +--R + +--R 2 5 +--R (- 6%i a cosh(x)csch(x) - 6%i a cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 15%i a cosh(x) + %i a)csch(x) - 15%i a cosh(x) + %i a)sinh(x) +--R + +--R 3 2 3 +--R (- 20%i a cosh(x) + 4%i a cosh(x))csch(x) - 20%i a cosh(x) +--R + +--R 4%i a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 15%i a cosh(x) + 6%i a cosh(x) + 4%i a)csch(x) +--R + +--R 4 2 +--R - 15%i a cosh(x) + 6%i a cosh(x) + 4%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 6%i a cosh(x) + 4%i a cosh(x) + 8%i a cosh(x))csch(x) +--R + +--R 5 3 +--R - 6%i a cosh(x) + 4%i a cosh(x) + 8%i a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- %i a cosh(x) + %i a cosh(x) + 4%i a cosh(x) - 4%i a)csch(x) +--R + +--R 6 4 2 +--R - %i a cosh(x) + %i a cosh(x) + 4%i a cosh(x) - 4%i a +--R * +--R +------------------+ +----------------+ +--R \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R Type: Expression Complex Integer +--E 314 + +--S 315 of 526 +t0460:= 1/(a+%i*a*csch(x))^(1/2) +--R +--R +--R 1 +--R (228) ------------------- +--R +----------------+ +--R \|%i a csch(x) + a +--R Type: Expression Complex Integer +--E 315 + +--S 316 of 526 +r0460:= -(2^(1/2)*atan(2^(1/2)*a^(1/2)/(-a+%i*a*csch(x))^(1/2))+2*atan((-a+%i*a*csch(x))^(1/2)/a^(1/2)))*(-a+%i*a*csch(x))^(1/2)*(a+%i*a*csch(x))^(1/2)*tanh(x)/a^(3/2) +--R +--R +--R (229) +--R +----------------+ +--R +----------------+ +----------------+ \|%i a csch(x) - a +--R - 2tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a atan(-------------------) +--R +-+ +--R \|a +--R + +--R - +--R +-+ +----------------+ +----------------+ +--R \|2 tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(-------------------) +--R +----------------+ +--R \|%i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression Complex Integer +--E 316 + +--S 317 of 526 +a0460:= integrate(t0460,x) +--R +--R +--R (230) +--R [ +--R - +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R - 2sinh(x) + (- 14cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (- 42cosh(x) - 72%i cosh(x) + 10)sinh(x) +--R + +--R 3 2 +--R (- 70cosh(x) - 180%i cosh(x) + 50cosh(x) + 24%i) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 +--R - 70cosh(x) - 240%i cosh(x) + 100cosh(x) +--R + +--R 96%i cosh(x) - 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 42cosh(x) - 180%i cosh(x) + 100cosh(x) +--R + +--R 2 +--R 144%i cosh(x) - 48cosh(x) - 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 14cosh(x) - 72%i cosh(x) + 50cosh(x) +--R + +--R 3 2 +--R 96%i cosh(x) - 48cosh(x) - 24%i cosh(x) + 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 +--R - 2cosh(x) - 12%i cosh(x) + 10cosh(x) +--R + +--R 4 3 2 +--R 24%i cosh(x) - 16cosh(x) - 12%i cosh(x) + 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) - 72%i cosh(x) + 20)sinh(x) +--R + +--R 3 2 +--R (- 140cosh(x) - 180%i cosh(x) + 100cosh(x) + 28%i) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) - 240%i cosh(x) + 200cosh(x) +--R + +--R 112%i cosh(x) - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 84cosh(x) - 180%i cosh(x) + 200cosh(x) +--R + +--R 2 +--R 168%i cosh(x) - 96cosh(x) - 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) - 72%i cosh(x) + 100cosh(x) +--R + +--R 3 2 +--R 112%i cosh(x) - 96cosh(x) - 48%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) - 12%i cosh(x) + 20cosh(x) + 28%i cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) - 24%i cosh(x) + 16cosh(x) + 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R - 3sinh(x) + (- 24cosh(x) + 4%i)sinh(x) +--R + +--R 2 6 +--R (- 84cosh(x) + 28%i cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (- 168cosh(x) + 84%i cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 +--R (- 210cosh(x) + 140%i cosh(x) - 60%i cosh(x) + 16) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 +--R - 168cosh(x) + 140%i cosh(x) - 120%i cosh(x) +--R + +--R 64cosh(x) + 24%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 +--R - 84cosh(x) + 84%i cosh(x) - 120%i cosh(x) +--R + +--R 2 +--R 96cosh(x) + 72%i cosh(x) - 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 +--R - 24cosh(x) + 28%i cosh(x) - 60%i cosh(x) +--R + +--R 3 2 +--R 64cosh(x) + 72%i cosh(x) - 40cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 5 4 +--R - 3cosh(x) + 4%i cosh(x) - 12%i cosh(x) + 16cosh(x) +--R + +--R 3 2 +--R 24%i cosh(x) - 20cosh(x) - 16%i cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) + 2%i a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) + 14%i a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 +--R - 112a cosh(x) + 42%i a cosh(x) - 12a cosh(x) +--R + +--R - 6%i a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) + 70%i a cosh(x) - 30a cosh(x) +--R + +--R - 30%i a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) + 70%i a cosh(x) - 40a cosh(x) +--R + +--R 2 +--R - 60%i a cosh(x) + 64a cosh(x) + 12%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) + 42%i a cosh(x) - 30a cosh(x) +--R + +--R 3 2 +--R - 60%i a cosh(x) + 96a cosh(x) + 36%i a cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) + 14%i a cosh(x) - 12a cosh(x) +--R + +--R 4 3 2 +--R - 30%i a cosh(x) + 64a cosh(x) + 36%i a cosh(x) +--R + +--R - 24a cosh(x) - 8%i a +--R * +--R sinh(x) +--R + +--R 8 7 6 +--R - 2a cosh(x) + 2%i a cosh(x) - 2a cosh(x) +--R + +--R 5 4 3 +--R - 6%i a cosh(x) + 16a cosh(x) + 12%i a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) - 8%i a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) - 4%i)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) - 24%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) - 60%i cosh(x) + 20cosh(x) + 12%i)sinh(x) +--R + +--R 4 3 2 +--R 140cosh(x) - 80%i cosh(x) + 40cosh(x) +--R + +--R 48%i cosh(x) - 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R 84cosh(x) - 60%i cosh(x) + 40cosh(x) +--R + +--R 2 +--R 72%i cosh(x) - 72cosh(x) - 16%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R 28cosh(x) - 24%i cosh(x) + 20cosh(x) +--R + +--R 3 2 +--R 48%i cosh(x) - 72cosh(x) - 32%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 4cosh(x) - 4%i cosh(x) + 4cosh(x) + 12%i cosh(x) +--R + +--R 3 2 +--R - 24cosh(x) - 16%i cosh(x) + 16cosh(x) + 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R sinh(x) + (8cosh(x) - 4%i)sinh(x) +--R + +--R 2 6 +--R (28cosh(x) - 28%i cosh(x) - 4)sinh(x) +--R + +--R 3 2 5 +--R (56cosh(x) - 84%i cosh(x) - 24cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 +--R 70cosh(x) - 140%i cosh(x) - 60cosh(x) +--R + +--R 20%i cosh(x) + 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R 56cosh(x) - 140%i cosh(x) - 80cosh(x) +--R + +--R 2 +--R 40%i cosh(x) + 32cosh(x) + 16%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R 28cosh(x) - 84%i cosh(x) - 60cosh(x) +--R + +--R 3 2 +--R 40%i cosh(x) + 48cosh(x) + 48%i cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 8cosh(x) - 28%i cosh(x) - 24cosh(x) + 20%i cosh(x) +--R + +--R 3 2 +--R 32cosh(x) + 48%i cosh(x) - 24cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R cosh(x) - 4%i cosh(x) - 4cosh(x) + 4%i cosh(x) +--R + +--R 4 3 2 +--R 8cosh(x) + 16%i cosh(x) - 12cosh(x) - 16%i cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R / +--R +-+ +--R \|a +--R , +--R +--R - +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R 2%i |- \|a +--R \|a +--R * +--R atan +--R +-----------------------------------------+ +--R +-+ | a +--R %i\|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - %i a sinh(x) - %i a cosh(x) + a +--R / +--R +-+ +--R |2 +-+ +--R (a sinh(x) + a cosh(x)) |- \|a +--R \|a +--R / +--R +-+ +--R \|a +--R ] +--R Type: Union(List Expression Complex Integer,...) +--E 317 + +--S 318 of 526 +m0460a:= a0460.1-r0460 +--R +--R +--R (231) +--R - +--R a +--R * +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R a +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R a |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R - 2sinh(x) + (- 14cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (- 42cosh(x) - 72%i cosh(x) + 10)sinh(x) +--R + +--R 3 2 +--R (- 70cosh(x) - 180%i cosh(x) + 50cosh(x) + 24%i) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 +--R - 70cosh(x) - 240%i cosh(x) + 100cosh(x) +--R + +--R 96%i cosh(x) - 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 42cosh(x) - 180%i cosh(x) + 100cosh(x) +--R + +--R 2 +--R 144%i cosh(x) - 48cosh(x) - 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 14cosh(x) - 72%i cosh(x) + 50cosh(x) +--R + +--R 3 2 +--R 96%i cosh(x) - 48cosh(x) - 24%i cosh(x) + 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 2cosh(x) - 12%i cosh(x) + 10cosh(x) + 24%i cosh(x) +--R + +--R 3 2 +--R - 16cosh(x) - 12%i cosh(x) + 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) - 72%i cosh(x) + 20)sinh(x) +--R + +--R 3 2 4 +--R (- 140cosh(x) - 180%i cosh(x) + 100cosh(x) + 28%i)sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) - 240%i cosh(x) + 200cosh(x) +--R + +--R 112%i cosh(x) - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 84cosh(x) - 180%i cosh(x) + 200cosh(x) +--R + +--R 2 +--R 168%i cosh(x) - 96cosh(x) - 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) - 72%i cosh(x) + 100cosh(x) +--R + +--R 3 2 +--R 112%i cosh(x) - 96cosh(x) - 48%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) - 12%i cosh(x) + 20cosh(x) + 28%i cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) - 24%i cosh(x) + 16cosh(x) + 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R - 3sinh(x) + (- 24cosh(x) + 4%i)sinh(x) +--R + +--R 2 6 +--R (- 84cosh(x) + 28%i cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (- 168cosh(x) + 84%i cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 4 +--R (- 210cosh(x) + 140%i cosh(x) - 60%i cosh(x) + 16)sinh(x) +--R + +--R 5 4 2 +--R - 168cosh(x) + 140%i cosh(x) - 120%i cosh(x) +--R + +--R 64cosh(x) + 24%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 +--R - 84cosh(x) + 84%i cosh(x) - 120%i cosh(x) +--R + +--R 2 +--R 96cosh(x) + 72%i cosh(x) - 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 +--R - 24cosh(x) + 28%i cosh(x) - 60%i cosh(x) +--R + +--R 3 2 +--R 64cosh(x) + 72%i cosh(x) - 40cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 5 4 +--R - 3cosh(x) + 4%i cosh(x) - 12%i cosh(x) + 16cosh(x) +--R + +--R 3 2 +--R 24%i cosh(x) - 20cosh(x) - 16%i cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) + 2%i a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) + 14%i a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 +--R (- 112a cosh(x) + 42%i a cosh(x) - 12a cosh(x) - 6%i a) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) + 70%i a cosh(x) - 30a cosh(x) +--R + +--R - 30%i a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) + 70%i a cosh(x) - 40a cosh(x) +--R + +--R 2 +--R - 60%i a cosh(x) + 64a cosh(x) + 12%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) + 42%i a cosh(x) - 30a cosh(x) +--R + +--R 3 2 +--R - 60%i a cosh(x) + 96a cosh(x) + 36%i a cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) + 14%i a cosh(x) - 12a cosh(x) +--R + +--R 4 3 2 +--R - 30%i a cosh(x) + 64a cosh(x) + 36%i a cosh(x) +--R + +--R - 24a cosh(x) - 8%i a +--R * +--R sinh(x) +--R + +--R 8 7 6 +--R - 2a cosh(x) + 2%i a cosh(x) - 2a cosh(x) +--R + +--R 5 4 3 +--R - 6%i a cosh(x) + 16a cosh(x) + 12%i a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) - 8%i a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) - 4%i)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) - 24%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) - 60%i cosh(x) + 20cosh(x) + 12%i)sinh(x) +--R + +--R 4 3 2 +--R 140cosh(x) - 80%i cosh(x) + 40cosh(x) + 48%i cosh(x) +--R + +--R - 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 84cosh(x) - 60%i cosh(x) + 40cosh(x) + 72%i cosh(x) +--R + +--R - 72cosh(x) - 16%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) - 24%i cosh(x) + 20cosh(x) + 48%i cosh(x) +--R + +--R 2 +--R - 72cosh(x) - 32%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 4cosh(x) - 4%i cosh(x) + 4cosh(x) + 12%i cosh(x) +--R + +--R 3 2 +--R - 24cosh(x) - 16%i cosh(x) + 16cosh(x) + 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R sinh(x) + (8cosh(x) - 4%i)sinh(x) +--R + +--R 2 6 +--R (28cosh(x) - 28%i cosh(x) - 4)sinh(x) +--R + +--R 3 2 5 +--R (56cosh(x) - 84%i cosh(x) - 24cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 +--R 70cosh(x) - 140%i cosh(x) - 60cosh(x) + 20%i cosh(x) +--R + +--R 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) - 140%i cosh(x) - 80cosh(x) + 40%i cosh(x) +--R + +--R 32cosh(x) + 16%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) - 84%i cosh(x) - 60cosh(x) + 40%i cosh(x) +--R + +--R 2 +--R 48cosh(x) + 48%i cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 8cosh(x) - 28%i cosh(x) - 24cosh(x) + 20%i cosh(x) +--R + +--R 3 2 +--R 32cosh(x) + 48%i cosh(x) - 24cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R cosh(x) - 4%i cosh(x) - 4cosh(x) + 4%i cosh(x) +--R + +--R 4 3 2 +--R 8cosh(x) + 16%i cosh(x) - 12cosh(x) - 16%i cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R + +--R +----------------+ +--R +----------------+ +----------------+ \|%i a csch(x) - a +--R 2tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a atan(-------------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +----------------+ +----------------+ \|2 \|a +--R \|2 tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a atan(-------------------) +--R +----------------+ +--R \|%i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression Complex Integer +--E 318 + +--S 319 of 526 +--d0460a:= D(m0460a,x) +--E 319 + +--S 320 of 526 +m0460b:= a0460.2-r0460 +--R +--R +--R (232) +--R - +--R a +--R * +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R a +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +----------------+ +--R +----------------+ +----------------+ \|%i a csch(x) - a +--R 2tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a atan(-------------------) +--R +-+ +--R \|a +--R + +--R +-+ +--R |2 +-+ +--R 2%i a |- \|a +--R \|a +--R * +--R atan +--R +-----------------------------------------+ +--R +-+ | a +--R %i\|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - %i a sinh(x) - %i a cosh(x) + a +--R / +--R +-+ +--R |2 +-+ +--R (a sinh(x) + a cosh(x)) |- \|a +--R \|a +--R + +--R +-+ +-+ +--R +-+ +----------------+ +----------------+ \|2 \|a +--R \|2 tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a atan(-------------------) +--R +----------------+ +--R \|%i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression Complex Integer +--E 320 + +--S 321 of 526 +--d0460b:= D(m0460b,x) +--E 321 + +--S 322 of 526 +t0461:= 1/(a-%i*a*csch(x))^(1/2) +--R +--R +--R 1 +--R (233) --------------------- +--R +------------------+ +--R \|- %i a csch(x) + a +--R Type: Expression Complex Integer +--E 322 + +--S 323 of 526 +r0461:= -(2^(1/2)*atan(2^(1/2)*a^(1/2)/(-a-%i*a*csch(x))^(1/2))+2*atan((-a-%i*a*csch(x))^(1/2)/a^(1/2)))*(-a-%i*a*csch(x))^(1/2)*(a-%i*a*csch(x))^(1/2)*tanh(x)/a^(3/2) +--R +--R +--R (234) +--R - +--R +------------------+ +------------------+ +--R 2tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +------------------+ +--R \|- %i a csch(x) - a +--R atan(---------------------) +--R +-+ +--R \|a +--R + +--R - +--R +-+ +------------------+ +------------------+ +--R \|2 tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(---------------------) +--R +------------------+ +--R \|- %i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression Complex Integer +--E 323 + +--S 324 of 526 +a0461:= integrate(t0461,x) +--R +--R +--R (235) +--R [ +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R 2sinh(x) + (14cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (42cosh(x) - 72%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 +--R (70cosh(x) - 180%i cosh(x) - 50cosh(x) + 24%i) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 +--R 70cosh(x) - 240%i cosh(x) - 100cosh(x) +--R + +--R 96%i cosh(x) + 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R 42cosh(x) - 180%i cosh(x) - 100cosh(x) +--R + +--R 2 +--R 144%i cosh(x) + 48cosh(x) - 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R 14cosh(x) - 72%i cosh(x) - 50cosh(x) +--R + +--R 3 2 +--R 96%i cosh(x) + 48cosh(x) - 24%i cosh(x) - 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 2cosh(x) - 12%i cosh(x) - 10cosh(x) + 24%i cosh(x) +--R + +--R 3 2 +--R 16cosh(x) - 12%i cosh(x) - 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) + 12%i)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) + 72%i cosh(x) + 20)sinh(x) +--R + +--R 3 2 +--R (- 140cosh(x) + 180%i cosh(x) + 100cosh(x) - 28%i) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) + 240%i cosh(x) + 200cosh(x) +--R + +--R - 112%i cosh(x) - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 84cosh(x) + 180%i cosh(x) + 200cosh(x) +--R + +--R 2 +--R - 168%i cosh(x) - 96cosh(x) + 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) + 72%i cosh(x) + 100cosh(x) +--R + +--R 3 2 +--R - 112%i cosh(x) - 96cosh(x) + 48%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) + 12%i cosh(x) + 20cosh(x) - 28%i cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) + 24%i cosh(x) + 16cosh(x) - 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R 3sinh(x) + (24cosh(x) + 4%i)sinh(x) +--R + +--R 2 6 +--R (84cosh(x) + 28%i cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (168cosh(x) + 84%i cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 4 +--R (210cosh(x) + 140%i cosh(x) - 60%i cosh(x) - 16)sinh(x) +--R + +--R 5 4 2 +--R 168cosh(x) + 140%i cosh(x) - 120%i cosh(x) +--R + +--R - 64cosh(x) + 24%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 +--R 84cosh(x) + 84%i cosh(x) - 120%i cosh(x) +--R + +--R 2 +--R - 96cosh(x) + 72%i cosh(x) + 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 +--R 24cosh(x) + 28%i cosh(x) - 60%i cosh(x) +--R + +--R 3 2 +--R - 64cosh(x) + 72%i cosh(x) + 40cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 5 4 +--R 3cosh(x) + 4%i cosh(x) - 12%i cosh(x) - 16cosh(x) +--R + +--R 3 2 +--R 24%i cosh(x) + 20cosh(x) - 16%i cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) - 2%i a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) - 14%i a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 +--R - 112a cosh(x) - 42%i a cosh(x) - 12a cosh(x) +--R + +--R 6%i a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) - 70%i a cosh(x) - 30a cosh(x) +--R + +--R 30%i a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) - 70%i a cosh(x) - 40a cosh(x) +--R + +--R 2 +--R 60%i a cosh(x) + 64a cosh(x) - 12%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) - 42%i a cosh(x) - 30a cosh(x) +--R + +--R 3 2 +--R 60%i a cosh(x) + 96a cosh(x) - 36%i a cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) - 14%i a cosh(x) - 12a cosh(x) +--R + +--R 4 3 2 +--R 30%i a cosh(x) + 64a cosh(x) - 36%i a cosh(x) +--R + +--R - 24a cosh(x) + 8%i a +--R * +--R sinh(x) +--R + +--R 8 7 6 +--R - 2a cosh(x) - 2%i a cosh(x) - 2a cosh(x) +--R + +--R 5 4 3 +--R 6%i a cosh(x) + 16a cosh(x) - 12%i a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) + 8%i a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) + 4%i)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) + 24%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) + 60%i cosh(x) + 20cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 2 +--R 140cosh(x) + 80%i cosh(x) + 40cosh(x) +--R + +--R - 48%i cosh(x) - 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R 84cosh(x) + 60%i cosh(x) + 40cosh(x) +--R + +--R 2 +--R - 72%i cosh(x) - 72cosh(x) + 16%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R 28cosh(x) + 24%i cosh(x) + 20cosh(x) +--R + +--R 3 2 +--R - 48%i cosh(x) - 72cosh(x) + 32%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 4cosh(x) + 4%i cosh(x) + 4cosh(x) - 12%i cosh(x) +--R + +--R 3 2 +--R - 24cosh(x) + 16%i cosh(x) + 16cosh(x) - 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R - sinh(x) + (- 8cosh(x) - 4%i)sinh(x) +--R + +--R 2 6 +--R (- 28cosh(x) - 28%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 5 +--R (- 56cosh(x) - 84%i cosh(x) + 24cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 +--R - 70cosh(x) - 140%i cosh(x) + 60cosh(x) +--R + +--R 20%i cosh(x) - 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 56cosh(x) - 140%i cosh(x) + 80cosh(x) +--R + +--R 2 +--R 40%i cosh(x) - 32cosh(x) + 16%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) - 84%i cosh(x) + 60cosh(x) +--R + +--R 3 2 +--R 40%i cosh(x) - 48cosh(x) + 48%i cosh(x) + 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 8cosh(x) - 28%i cosh(x) + 24cosh(x) +--R + +--R 4 3 2 +--R 20%i cosh(x) - 32cosh(x) + 48%i cosh(x) + 24cosh(x) +--R + +--R - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R - cosh(x) - 4%i cosh(x) + 4cosh(x) + 4%i cosh(x) +--R + +--R 4 3 2 +--R - 8cosh(x) + 16%i cosh(x) + 12cosh(x) - 16%i cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R - +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R / +--R +-+ +--R \|a +--R , +--R +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R 2%i |- \|a +--R \|a +--R * +--R atan +--R +-----------------------------------------+ +--R +-+ | a +--R %i\|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R %i a sinh(x) + %i a cosh(x) + a +--R / +--R +-+ +--R |2 +-+ +--R (a sinh(x) + a cosh(x)) |- \|a +--R \|a +--R / +--R +-+ +--R \|a +--R ] +--R Type: Union(List Expression Complex Integer,...) +--E 324 + +--S 325 of 526 +m0461a:= a0461.1-r0461 +--R +--R +--R (236) +--R a +--R * +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R a |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R 2sinh(x) + (14cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (42cosh(x) - 72%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 4 +--R (70cosh(x) - 180%i cosh(x) - 50cosh(x) + 24%i)sinh(x) +--R + +--R 4 3 2 +--R 70cosh(x) - 240%i cosh(x) - 100cosh(x) +--R + +--R 96%i cosh(x) + 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R 42cosh(x) - 180%i cosh(x) - 100cosh(x) +--R + +--R 2 +--R 144%i cosh(x) + 48cosh(x) - 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R 14cosh(x) - 72%i cosh(x) - 50cosh(x) +--R + +--R 3 2 +--R 96%i cosh(x) + 48cosh(x) - 24%i cosh(x) - 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 2cosh(x) - 12%i cosh(x) - 10cosh(x) + 24%i cosh(x) +--R + +--R 3 2 +--R 16cosh(x) - 12%i cosh(x) - 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) + 12%i)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) + 72%i cosh(x) + 20)sinh(x) +--R + +--R 3 2 4 +--R (- 140cosh(x) + 180%i cosh(x) + 100cosh(x) - 28%i)sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) + 240%i cosh(x) + 200cosh(x) +--R + +--R - 112%i cosh(x) - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 84cosh(x) + 180%i cosh(x) + 200cosh(x) +--R + +--R 2 +--R - 168%i cosh(x) - 96cosh(x) + 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) + 72%i cosh(x) + 100cosh(x) +--R + +--R 3 2 +--R - 112%i cosh(x) - 96cosh(x) + 48%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) + 12%i cosh(x) + 20cosh(x) - 28%i cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) + 24%i cosh(x) + 16cosh(x) - 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R 3sinh(x) + (24cosh(x) + 4%i)sinh(x) +--R + +--R 2 6 +--R (84cosh(x) + 28%i cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (168cosh(x) + 84%i cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 4 +--R (210cosh(x) + 140%i cosh(x) - 60%i cosh(x) - 16)sinh(x) +--R + +--R 5 4 2 +--R 168cosh(x) + 140%i cosh(x) - 120%i cosh(x) +--R + +--R - 64cosh(x) + 24%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 2 +--R 84cosh(x) + 84%i cosh(x) - 120%i cosh(x) - 96cosh(x) +--R + +--R 72%i cosh(x) + 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 3 +--R 24cosh(x) + 28%i cosh(x) - 60%i cosh(x) - 64cosh(x) +--R + +--R 2 +--R 72%i cosh(x) + 40cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 5 4 +--R 3cosh(x) + 4%i cosh(x) - 12%i cosh(x) - 16cosh(x) +--R + +--R 3 2 +--R 24%i cosh(x) + 20cosh(x) - 16%i cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) - 2%i a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) - 14%i a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 +--R (- 112a cosh(x) - 42%i a cosh(x) - 12a cosh(x) + 6%i a) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) - 70%i a cosh(x) - 30a cosh(x) +--R + +--R 30%i a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) - 70%i a cosh(x) - 40a cosh(x) +--R + +--R 2 +--R 60%i a cosh(x) + 64a cosh(x) - 12%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) - 42%i a cosh(x) - 30a cosh(x) +--R + +--R 3 2 +--R 60%i a cosh(x) + 96a cosh(x) - 36%i a cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) - 14%i a cosh(x) - 12a cosh(x) +--R + +--R 4 3 2 +--R 30%i a cosh(x) + 64a cosh(x) - 36%i a cosh(x) +--R + +--R - 24a cosh(x) + 8%i a +--R * +--R sinh(x) +--R + +--R 8 7 6 +--R - 2a cosh(x) - 2%i a cosh(x) - 2a cosh(x) +--R + +--R 5 4 3 +--R 6%i a cosh(x) + 16a cosh(x) - 12%i a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) + 8%i a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) + 4%i)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) + 24%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) + 60%i cosh(x) + 20cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 2 +--R 140cosh(x) + 80%i cosh(x) + 40cosh(x) - 48%i cosh(x) +--R + +--R - 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 84cosh(x) + 60%i cosh(x) + 40cosh(x) - 72%i cosh(x) +--R + +--R - 72cosh(x) + 16%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) + 24%i cosh(x) + 20cosh(x) - 48%i cosh(x) +--R + +--R 2 +--R - 72cosh(x) + 32%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 4cosh(x) + 4%i cosh(x) + 4cosh(x) - 12%i cosh(x) +--R + +--R 3 2 +--R - 24cosh(x) + 16%i cosh(x) + 16cosh(x) - 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R - sinh(x) + (- 8cosh(x) - 4%i)sinh(x) +--R + +--R 2 6 +--R (- 28cosh(x) - 28%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 5 +--R (- 56cosh(x) - 84%i cosh(x) + 24cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 +--R - 70cosh(x) - 140%i cosh(x) + 60cosh(x) +--R + +--R 20%i cosh(x) - 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 56cosh(x) - 140%i cosh(x) + 80cosh(x) +--R + +--R 2 +--R 40%i cosh(x) - 32cosh(x) + 16%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) - 84%i cosh(x) + 60cosh(x) +--R + +--R 3 2 +--R 40%i cosh(x) - 48cosh(x) + 48%i cosh(x) + 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 8cosh(x) - 28%i cosh(x) + 24cosh(x) + 20%i cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) + 48%i cosh(x) + 24cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R - cosh(x) - 4%i cosh(x) + 4cosh(x) + 4%i cosh(x) +--R + +--R 4 3 2 +--R - 8cosh(x) + 16%i cosh(x) + 12cosh(x) - 16%i cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R - +--R a +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +------------------+ +------------------+ +--R 2tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +------------------+ +--R \|- %i a csch(x) - a +--R atan(---------------------) +--R +-+ +--R \|a +--R + +--R +-+ +------------------+ +------------------+ +--R \|2 tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(---------------------) +--R +------------------+ +--R \|- %i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression Complex Integer +--E 325 + +--S 326 of 526 +--d0461a:= D(m0461a,x) +--E 326 + +--S 327 of 526 +m0461b:= a0461.2-r0461 +--R +--R +--R (237) +--R a +--R * +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R a +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R 2%i a |- \|a +--R \|a +--R * +--R atan +--R +-----------------------------------------+ +--R +-+ | a +--R %i\|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R %i a sinh(x) + %i a cosh(x) + a +--R / +--R +-+ +--R |2 +-+ +--R (a sinh(x) + a cosh(x)) |- \|a +--R \|a +--R + +--R +------------------+ +------------------+ +--R 2tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +------------------+ +--R \|- %i a csch(x) - a +--R atan(---------------------) +--R +-+ +--R \|a +--R + +--R +-+ +------------------+ +------------------+ +--R \|2 tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(---------------------) +--R +------------------+ +--R \|- %i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression Complex Integer +--E 327 + +--S 328 of 526 +--d0461b:= D(m0461b,x) +--E 328 + +--S 329 of 526 +t0462:= 1/(3+5*%i*csch(x)) +--R +--R +--R %i +--R (238) - -------------- +--R 5csch(x) - 3%i +--R Type: Expression Complex Integer +--E 329 + +--S 330 of 526 +r0462:= 1/3*x+5/6*%i*atan(-3/4+5/4*%i*tanh(1/2*x)) +--R +--R +--R 5 5 1 3 1 +--R (239) - %i atan(- %i tanh(- x) - -) + - x +--R 6 4 2 4 3 +--R Type: Expression Complex Fraction Integer +--E 330 + +--S 331 of 526 +a0462:= integrate(t0462,x) +--R +--R +--R (240) +--R - 5log(3sinh(x) + 3cosh(x) + %i) + 5log(sinh(x) + cosh(x) + 3%i) + 4x +--R --------------------------------------------------------------------- +--R 12 +--R Type: Union(Expression Complex Integer,...) +--E 331 + +--S 332 of 526 +m0462:= a0462-r0462 +--R +--R +--R (241) +--R 5 5 +--R - -- log(3sinh(x) + 3cosh(x) + %i) + -- log(sinh(x) + cosh(x) + 3%i) +--R 12 12 +--R + +--R 5 5 1 3 +--R - - %i atan(- %i tanh(- x) - -) +--R 6 4 2 4 +--R Type: Expression Complex Fraction Integer +--E 332 + +--S 333 of 526 +d0462:= D(m0462,x) +--R +--R +--R (242) +--R 1 2 2 1 2 1 1 2 +--R (- sinh(x) + - cosh(x)sinh(x) + - cosh(x) - -)tanh(- x) +--R 3 3 3 3 2 +--R + +--R 4 4 1 1 2 2 +--R (- sinh(x) + - cosh(x))tanh(- x) - - sinh(x) - - cosh(x)sinh(x) +--R 3 3 2 3 3 +--R + +--R 1 2 1 +--R - - cosh(x) + - +--R 3 3 +--R / +--R 2 10 2 10 +--R (sinh(x) + (2cosh(x) + -- %i)sinh(x) + cosh(x) + -- %i cosh(x) - 1) +--R 3 3 +--R * +--R 1 2 +--R tanh(- x) +--R 2 +--R + +--R 6 2 12 6 2 +--R - %i sinh(x) + (-- %i cosh(x) - 4)sinh(x) + - %i cosh(x) - 4cosh(x) +--R 5 5 5 +--R + +--R 6 +--R - - %i +--R 5 +--R * +--R 1 +--R tanh(- x) +--R 2 +--R + +--R 2 10 2 10 +--R - sinh(x) + (- 2cosh(x) - -- %i)sinh(x) - cosh(x) - -- %i cosh(x) + 1 +--R 3 3 +--R Type: Expression Complex Fraction Integer +--E 333 + +--S 334 of 526 +t0463:= 1/(a+b*csch(x)) +--R +--R +--R 1 +--R (243) ------------- +--R b csch(x) + a +--R Type: Expression Integer +--E 334 + +--S 335 of 526 +r0463:= x/a+2*b*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a/(a^2+b^2)^(1/2) +--R +--R +--R x +--R b tanh(-) - a +-------+ +--R 2 | 2 2 +--R - 2b atanh(-------------) + x\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (244) --------------------------------------- +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression Integer +--E 335 + +--S 336 of 526 +a0463:= integrate(t0463,x) +--R +--R +--R (245) +--R 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 x\|b + a +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Union(Expression Integer,...) +--E 336 + +--S 337 of 526 +m0463:= a0463-r0463 +--R +--R +--R (246) +--R 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 2 +--R 2b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression Integer +--E 337 + +--S 338 of 526 +d0463:= D(m0463,x) +--R +--R +--R (247) +--R 2 2 x 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b)tanh(-) +--R 2 +--R + +--R x 2 +--R (4b sinh(x) + 4b cosh(x))tanh(-) - b sinh(x) - 2b cosh(x)sinh(x) +--R 2 +--R + +--R 2 +--R - b cosh(x) + b +--R / +--R 2 2 2 +--R a b sinh(x) + (2a b cosh(x) + 2b )sinh(x) + a b cosh(x) +--R + +--R 2 +--R 2b cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 2 +--R - 2a sinh(x) + (- 4a cosh(x) - 4a b)sinh(x) - 2a cosh(x) +--R + +--R 2 +--R - 4a b cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 2 2 +--R - a b sinh(x) + (- 2a b cosh(x) - 2b )sinh(x) - a b cosh(x) +--R + +--R 2 +--R - 2b cosh(x) + a b +--R Type: Expression Integer +--E 338 + +--S 339 of 526 +t0464:= 1/(a+b*csch(x))^2 +--R +--R +--R 1 +--R (248) ------------------------------ +--R 2 2 2 +--R b csch(x) + 2a b csch(x) + a +--R Type: Expression Integer +--E 339 + +--S 340 of 526 +r0464:= x/a^2-2*b^3*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^2/(a^2+b^2)^(3/2)+4*b*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^2/(a^2+b^2)^(1/2)-b^2*cosh(x)/a/(a^2+b^2)/(b+a*sinh(x)) +--R +--R +--R (249) +--R x +--R b tanh(-) - a +--R 3 3 4 2 2 2 +--R ((- 2a b - 4a b)sinh(x) - 2b - 4a b )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 3 2 3 2 | 2 2 +--R ((a b + a )x sinh(x) - a b cosh(x) + (b + a b)x)\|b + a +--R / +--R +-------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b + a )sinh(x) + a b + a b)\|b + a +--R Type: Expression Integer +--E 340 + +--S 341 of 526 +a0464:= integrate(t0464,x) +--R +--R +--R (250) +--R 3 3 2 3 3 4 2 2 +--R (a b + 2a b)sinh(x) + ((2a b + 4a b)cosh(x) + 2b + 4a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (a b + 2a b)cosh(x) + (2b + 4a b )cosh(x) - a b - 2a 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 3 2 +--R (a b + a )x sinh(x) +--R + +--R 2 3 3 2 3 +--R ((2a b + 2a )x cosh(x) + (2b + 2a b)x + 2b )sinh(x) +--R + +--R 2 3 2 3 2 3 2 3 +--R (a b + a )x cosh(x) + ((2b + 2a b)x + 2b )cosh(x) + (- a b - a )x +--R + +--R 2 +--R - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 2 5 2 3 2 5 2 3 4 +--R (a b + a )sinh(x) + ((2a b + 2a )cosh(x) + 2a b + 2a b)sinh(x) +--R + +--R 3 2 5 2 2 3 4 3 2 5 +--R (a b + a )cosh(x) + (2a b + 2a b)cosh(x) - a b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression Integer,...) +--E 341 + +--S 342 of 526 +m0464:= a0464-r0464 +--R +--R +--R (251) +--R 2 3 4 3 +--R (a b + 2a b)sinh(x) +--R + +--R 2 3 4 4 3 2 2 +--R ((2a b + 4a b)cosh(x) + 3a b + 6a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 2 3 +--R (a b + 2a b)cosh(x) + (4a b + 8a b )cosh(x) + 2b + 3a b +--R + +--R 4 +--R - 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 5 2 3 4 3 2 +--R (a b + 2a b )cosh(x) + (2b + 4a b )cosh(x) - a b - 2a 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 3 4 3 +--R (2a b + 4a b)sinh(x) +--R + +--R 2 3 4 4 3 2 2 +--R ((4a b + 8a b)cosh(x) + 6a b + 12a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 2 3 +--R (2a b + 4a b)cosh(x) + (8a b + 16a b )cosh(x) + 4b + 6a b +--R + +--R 4 +--R - 4a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 5 2 3 4 3 2 +--R (2a b + 4a b )cosh(x) + (4b + 8a b )cosh(x) - 2a b - 4a b +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 3 2 +--R (a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 2 3 4 2 2 2 2 3 +--R (2a b cosh(x) + 4a b cosh(x) + 2b - 2a b )sinh(x) + a b cosh(x) +--R + +--R 3 2 4 2 2 3 +--R 2a b cosh(x) + (2b - a b )cosh(x) - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 2 6 3 4 2 6 3 3 5 2 +--R (a b + a )sinh(x) + ((2a b + 2a )cosh(x) + 3a b + 3a b)sinh(x) +--R + +--R 4 2 6 2 3 3 5 2 4 4 2 6 +--R ((a b + a )cosh(x) + (4a b + 4a b)cosh(x) + 2a b + a b - a ) +--R * +--R sinh(x) +--R + +--R 3 3 5 2 2 4 4 2 3 3 5 +--R (a b + a b)cosh(x) + (2a b + 2a b )cosh(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression Integer +--E 342 + +--S 343 of 526 +d0464:= D(m0464,x) +--R +--R +--R (252) +--R 3 3 5 6 +--R (2a b + 2a b)sinh(x) +--R + +--R 3 3 5 2 4 4 2 5 +--R ((8a b + 8a b)cosh(x) + 7a b + 8a b )sinh(x) +--R + +--R 3 3 5 2 2 4 4 2 5 +--R (11a b + 12a b)cosh(x) + (24a b + 28a b )cosh(x) + 9a b +--R + +--R 3 3 5 +--R 10a b - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 4 2 2 +--R (4a b + 8a b)cosh(x) + (26a b + 36a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (24a b + 32a b - 8a b)cosh(x) + 4b + 2a b - 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 5 4 2 4 4 2 3 +--R (- 4a b + 2a b)cosh(x) + (4a b + 20a b )cosh(x) +--R + +--R 5 3 3 5 2 6 2 4 4 2 +--R (18a b + 38a b - 4a b)cosh(x) + (8b + 12a b - 20a b )cosh(x) +--R + +--R 5 3 3 5 +--R - 2a b - 10a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 4 4 2 4 3 3 3 +--R - 4a b cosh(x) + (- 9a b + 4a b )cosh(x) + 20a b cosh(x) +--R + +--R 6 2 4 4 2 2 3 3 2 4 4 2 +--R (4b + 18a b - 8a b )cosh(x) - 16a b cosh(x) - a b + 4a b +--R * +--R sinh(x) +--R + +--R 3 3 6 2 4 5 5 3 3 4 +--R - a b cosh(x) - 4a b cosh(x) + (- 3a b + 4a b )cosh(x) +--R + +--R 2 4 3 5 3 3 2 2 4 5 3 3 +--R 8a b cosh(x) + (2a b - 5a b )cosh(x) - 4a b cosh(x) + a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 6 4 2 3 3 5 5 +--R - 2a b sinh(x) + (- 8a b cosh(x) - 2a b + 8a b)sinh(x) +--R + +--R 4 2 2 3 3 5 2 4 4 2 +--R (- 10a b cosh(x) + (- 8a b + 24a b)cosh(x) + 8a b + 28a b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 2 2 4 4 2 5 +--R (- 4a b + 24a b)cosh(x) + (24a b + 72a b )cosh(x) + 16a b +--R + +--R 3 3 5 +--R 28a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 4 3 3 5 3 +--R 10a b cosh(x) + (16a b + 8a b)cosh(x) +--R + +--R 2 4 4 2 2 5 3 3 5 6 +--R (32a b + 56a b )cosh(x) + (40a b + 64a b - 8a b)cosh(x) + 8b +--R + +--R 4 2 +--R - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 5 3 3 4 2 4 4 2 3 +--R 8a b cosh(x) + 22a b cosh(x) + (24a b + 8a b )cosh(x) +--R + +--R 5 3 3 2 6 2 4 4 2 +--R (32a b + 36a b )cosh(x) + (16b + 8a b - 16a b )cosh(x) +--R + +--R 5 3 3 +--R - 8a b - 10a b +--R * +--R sinh(x) +--R + +--R 4 2 6 3 3 5 2 4 4 2 4 +--R 2a b cosh(x) + 8a b cosh(x) + (8a b - 4a b )cosh(x) +--R + +--R 5 3 6 2 4 4 2 2 +--R 8a b cosh(x) + (8b + 8a b + 2a b )cosh(x) +--R + +--R 5 3 3 +--R (- 8a b - 8a b )cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 5 6 +--R (- 2a b - 2a b)sinh(x) +--R + +--R 3 3 5 2 4 4 2 5 +--R ((- 8a b - 8a b)cosh(x) - 7a b - 8a b )sinh(x) +--R + +--R 3 3 5 2 2 4 4 2 5 +--R (- 11a b - 12a b)cosh(x) + (- 24a b - 28a b )cosh(x) - 9a b +--R + +--R 3 3 5 +--R - 10a b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 4 2 2 +--R (- 4a b - 8a b)cosh(x) + (- 26a b - 36a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (- 24a b - 32a b + 8a b)cosh(x) - 4b - 2a b + 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 5 4 2 4 4 2 3 +--R (4a b - 2a b)cosh(x) + (- 4a b - 20a b )cosh(x) +--R + +--R 5 3 3 5 2 6 2 4 4 2 +--R (- 18a b - 38a b + 4a b)cosh(x) + (- 8b - 12a b + 20a b )cosh(x) +--R + +--R 5 3 3 5 +--R 2a b + 10a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 4 4 2 4 3 3 3 +--R 4a b cosh(x) + (9a b - 4a b )cosh(x) - 20a b cosh(x) +--R + +--R 6 2 4 4 2 2 3 3 2 4 4 2 +--R (- 4b - 18a b + 8a b )cosh(x) + 16a b cosh(x) + a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 6 2 4 5 5 3 3 4 2 4 3 +--R a b cosh(x) + 4a b cosh(x) + (3a b - 4a b )cosh(x) - 8a b cosh(x) +--R + +--R 5 3 3 2 2 4 5 3 3 +--R (- 2a b + 5a b )cosh(x) + 4a b cosh(x) - a b - 2a b +--R / +--R 5 3 7 6 +--R (a b + a b)sinh(x) +--R + +--R 5 3 7 4 4 6 2 5 +--R ((4a b + 4a b)cosh(x) + 6a b + 6a b )sinh(x) +--R + +--R 5 3 7 2 4 4 6 2 3 5 +--R (6a b + 6a b)cosh(x) + (20a b + 20a b )cosh(x) + 13a b +--R + +--R 5 3 7 +--R 11a b - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 7 3 4 4 6 2 2 +--R (4a b + 4a b)cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 3 5 5 3 7 2 6 4 4 6 2 +--R (36a b + 32a b - 4a b)cosh(x) + 12a b + 4a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 7 4 4 4 6 2 3 +--R (a b + a b)cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 3 5 5 3 7 2 +--R (34a b + 32a b - 2a b)cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 7 +--R (28a b + 16a b - 12a b )cosh(x) + 4a b - 6a b - 9a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (2a b + 2a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (20a b + 16a b - 4a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 6 2 +--R (8a b - 4a b - 12a b )cosh(x) - 4a b - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 4 2 6 4 4 3 +--R (a b + a b )cosh(x) + (4a b + 4a b )cosh(x) +--R + +--R 7 3 5 5 3 2 2 6 4 4 3 5 +--R (4a b + 2a b - 2a b )cosh(x) + (- 4a b - 4a b )cosh(x) + a b +--R + +--R 5 3 +--R a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 2 8 6 +--R (- 2a b - 2a )sinh(x) +--R + +--R 6 2 8 5 3 7 5 +--R ((- 8a b - 8a )cosh(x) - 12a b - 12a b)sinh(x) +--R + +--R 6 2 8 2 5 3 7 4 4 +--R (- 12a b - 12a )cosh(x) + (- 40a b - 40a b)cosh(x) - 26a b +--R + +--R 6 2 8 +--R - 22a b + 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 8 3 5 3 7 2 +--R (- 8a b - 8a )cosh(x) + (- 48a b - 48a b)cosh(x) +--R + +--R 4 4 6 2 8 3 5 5 3 7 +--R (- 72a b - 64a b + 8a )cosh(x) - 24a b - 8a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 8 4 5 3 7 3 +--R (- 2a b - 2a )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 4 4 6 2 8 2 +--R (- 68a b - 64a b + 4a )cosh(x) +--R + +--R 3 5 5 3 7 2 6 4 4 6 2 8 +--R (- 56a b - 32a b + 24a b)cosh(x) - 8a b + 12a b + 18a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 7 4 4 4 6 2 3 +--R (- 4a b - 4a b)cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 3 5 5 3 7 2 +--R (- 40a b - 32a b + 8a b)cosh(x) +--R + +--R 2 6 4 4 6 2 3 5 5 3 7 +--R (- 16a b + 8a b + 24a b )cosh(x) + 8a b + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (- 2a b - 2a b )cosh(x) + (- 8a b - 8a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 3 5 5 3 4 4 +--R (- 8a b - 4a b + 4a b )cosh(x) + (8a b + 8a b )cosh(x) - 2a b +--R + +--R 6 2 +--R - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 3 7 6 +--R (- a b - a b)sinh(x) +--R + +--R 5 3 7 4 4 6 2 5 +--R ((- 4a b - 4a b)cosh(x) - 6a b - 6a b )sinh(x) +--R + +--R 5 3 7 2 4 4 6 2 3 5 +--R (- 6a b - 6a b)cosh(x) + (- 20a b - 20a b )cosh(x) - 13a b +--R + +--R 5 3 7 +--R - 11a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 7 3 4 4 6 2 2 +--R (- 4a b - 4a b)cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 3 5 5 3 7 2 6 4 4 6 2 +--R (- 36a b - 32a b + 4a b)cosh(x) - 12a b - 4a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 7 4 4 4 6 2 3 +--R (- a b - a b)cosh(x) + (- 12a b - 12a b )cosh(x) +--R + +--R 3 5 5 3 7 2 +--R (- 34a b - 32a b + 2a b)cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 7 +--R (- 28a b - 16a b + 12a b )cosh(x) - 4a b + 6a b + 9a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (- 2a b - 2a b )cosh(x) + (- 12a b - 12a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 20a b - 16a b + 4a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 6 2 +--R (- 8a b + 4a b + 12a b )cosh(x) + 4a b + 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 4 2 6 4 4 3 +--R (- a b - a b )cosh(x) + (- 4a b - 4a b )cosh(x) +--R + +--R 7 3 5 5 3 2 2 6 4 4 3 5 5 3 +--R (- 4a b - 2a b + 2a b )cosh(x) + (4a b + 4a b )cosh(x) - a b - a b +--R Type: Expression Integer +--E 343 + +--S 344 of 526 +t0465:= 1/(a+b*csch(x))^3 +--R +--R +--R 1 +--R (253) ---------------------------------------------- +--R 3 3 2 2 2 3 +--R b csch(x) + 3a b csch(x) + 3a b csch(x) + a +--R Type: Expression Integer +--E 344 + +--S 345 of 526 +r0465:= x/a^3-b^3*(a^2-2*b^2)*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^3/(a^2+b^2)^(5/2)-6*b^3*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^3/(a^2+b^2)^(3/2)+6*b*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^3/(a^2+b^2)^(1/2)+1/2*b^3*cosh(x)/a^2/(a^2+b^2)/(b+a*sinh(x))^2+3/2*b^4*cosh(x)/a^2/(a^2+b^2)^2/(b+a*sinh(x))-3*b^2*cosh(x)/a^2/(a^2+b^2)/(b+a*sinh(x)) +--R +--R +--R (254) +--R 2 5 4 3 6 2 +--R (- 4a b - 10a b - 12a b)sinh(x) +--R + +--R 6 3 4 5 2 7 2 5 4 3 +--R (- 8a b - 20a b - 24a b )sinh(x) - 4b - 10a b - 12a b +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 4 4 2 6 2 +--R (2a b + 4a b + 2a )x sinh(x) +--R + +--R 2 4 4 2 5 3 3 5 +--R ((- 3a b - 6a b )cosh(x) + (4a b + 8a b + 4a b)x)sinh(x) +--R + +--R 5 3 3 6 2 4 4 2 +--R (- 2a b - 5a b )cosh(x) + (2b + 4a b + 2a b )x +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 4 7 2 9 2 4 5 6 3 8 3 6 +--R (2a b + 4a b + 2a )sinh(x) + (4a b + 8a b + 4a b)sinh(x) + 2a b +--R + +--R 5 4 7 2 +--R 4a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression Integer +--E 345 + +--S 346 of 526 +a0465:= integrate(t0465,x) +--R +--R +--R (255) +--R 2 5 4 3 6 4 +--R (2a b + 5a b + 6a b)sinh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 3 +--R ((8a b + 20a b + 24a b)cosh(x) + 8a b + 20a b + 24a b )sinh(x) +--R + +--R 2 5 4 3 6 2 +--R (12a b + 30a b + 36a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 5 4 3 6 +--R (24a b + 60a b + 72a b )cosh(x) + 8b + 16a b + 14a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 3 6 3 +--R (8a b + 20a b + 24a b)cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (24a b + 60a b + 72a b )cosh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 +--R (16b + 32a b + 28a b - 24a b)cosh(x) - 8a b - 20a b - 24a b +--R * +--R sinh(x) +--R + +--R 2 5 4 3 6 4 6 3 4 5 2 3 +--R (2a b + 5a b + 6a b)cosh(x) + (8a b + 20a b + 24a b )cosh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (8b + 16a b + 14a b - 12a b)cosh(x) +--R + +--R 6 3 4 5 2 2 5 4 3 6 +--R (- 8a b - 20a b - 24a b )cosh(x) + 2a b + 5a b + 6a 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 4 4 2 6 4 +--R (2a b + 4a b + 2a )x sinh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (8a b + 16a b + 8a )x cosh(x) + (8a b + 16a b + 8a b)x +--R + +--R 5 3 3 +--R 8a b + 14a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 2 6 2 +--R (12a b + 24a b + 12a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((24a b + 48a b + 24a b)x + 24a b + 42a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R (8b + 12a b - 4a )x + 12b + 18a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 +--R (8a b + 16a b + 8a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 2 +--R ((24a b + 48a b + 24a b)x + 24a b + 42a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R ((16b + 24a b - 8a )x + 24b + 36a b - 24a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R (- 8a b - 16a b - 8a b)x - 16a b - 34a b +--R * +--R sinh(x) +--R + +--R 2 4 4 2 6 4 +--R (2a b + 4a b + 2a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 3 +--R ((8a b + 16a b + 8a b)x + 8a b + 14a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 2 +--R ((8b + 12a b - 4a )x + 12b + 18a b - 12a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((- 8a b - 16a b - 8a b)x - 16a b - 34a b )cosh(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (2a b + 4a b + 2a )x + 6a b + 12a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 4 7 2 9 4 +--R (2a b + 4a b + 2a )sinh(x) +--R + +--R 5 4 7 2 9 4 5 6 3 8 3 +--R ((8a b + 16a b + 8a )cosh(x) + 8a b + 16a b + 8a b)sinh(x) +--R + +--R 5 4 7 2 9 2 4 5 6 3 8 +--R (12a b + 24a b + 12a )cosh(x) + (24a b + 48a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 9 +--R 8a b + 12a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 7 2 9 3 4 5 6 3 8 2 +--R (8a b + 16a b + 8a )cosh(x) + (24a b + 48a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 9 4 5 6 3 8 +--R (16a b + 24a b - 8a )cosh(x) - 8a b - 16a b - 8a b +--R * +--R sinh(x) +--R + +--R 5 4 7 2 9 4 4 5 6 3 8 3 +--R (2a b + 4a b + 2a )cosh(x) + (8a b + 16a b + 8a b)cosh(x) +--R + +--R 3 6 5 4 9 2 4 5 6 3 8 +--R (8a b + 12a b - 4a )cosh(x) + (- 8a b - 16a b - 8a b)cosh(x) +--R + +--R 5 4 7 2 9 +--R 2a b + 4a b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression Integer,...) +--E 346 + +--S 347 of 526 +m0465:= a0465-r0465 +--R +--R +--R (256) +--R 4 5 6 3 8 6 +--R (2a b + 5a b + 6a b)sinh(x) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 5 +--R ((8a b + 20a b + 24a b)cosh(x) + 12a b + 30a b + 36a b )sinh(x) +--R + +--R 4 5 6 3 8 2 +--R (12a b + 30a b + 36a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 +--R (40a b + 100a b + 120a b )cosh(x) + 26a b + 61a b + 68a b +--R + +--R 8 +--R - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (8a b + 20a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (48a b + 120a b + 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 8 3 6 +--R (72a b + 172a b + 196a b - 24a b)cosh(x) + 24a b + 44a b +--R + +--R 5 4 7 2 +--R 32a b - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (2a b + 5a b + 6a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (24a b + 60a b + 72a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (68a b + 166a b + 194a b - 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 4 5 +--R (56a b + 116a b + 108a b - 72a b )cosh(x) + 8b - 24a b +--R + +--R 6 3 8 +--R - 55a b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (4a b + 10a b + 12a b )cosh(x) +--R + +--R 2 7 4 5 6 3 3 +--R (24a b + 60a b + 72a b )cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (40a b + 92a b + 100a b - 24a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 +--R (16b + 16a b - 12a b - 72a b )cosh(x) - 8a b - 16a b +--R + +--R 5 4 7 2 +--R - 14a b + 12a b +--R * +--R sinh(x) +--R + +--R 2 7 4 5 6 3 4 8 3 6 5 4 3 +--R (2a b + 5a b + 6a b )cosh(x) + (8a b + 20a b + 24a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 2 +--R (8b + 16a b + 14a b - 12a b )cosh(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 +--R (- 8a b - 20a b - 24a b )cosh(x) + 2a b + 5a b + 6a 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 4 5 6 3 8 6 +--R (4a b + 10a b + 12a b)sinh(x) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 5 +--R ((16a b + 40a b + 48a b)cosh(x) + 24a b + 60a b + 72a b )sinh(x) +--R + +--R 4 5 6 3 8 2 +--R (24a b + 60a b + 72a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 +--R (80a b + 200a b + 240a b )cosh(x) + 52a b + 122a b + 136a b +--R + +--R 8 +--R - 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (16a b + 40a b + 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (96a b + 240a b + 288a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 8 3 6 +--R (144a b + 344a b + 392a b - 48a b)cosh(x) + 48a b + 88a b +--R + +--R 5 4 7 2 +--R 64a b - 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (4a b + 10a b + 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (48a b + 120a b + 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (136a b + 332a b + 388a b - 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 4 5 +--R (112a b + 232a b + 216a b - 144a b )cosh(x) + 16b - 48a b +--R + +--R 6 3 8 +--R - 110a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (8a b + 20a b + 24a b )cosh(x) +--R + +--R 2 7 4 5 6 3 3 +--R (48a b + 120a b + 144a b )cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (80a b + 184a b + 200a b - 48a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 +--R (32b + 32a b - 24a b - 144a b )cosh(x) - 16a b - 32a b +--R + +--R 5 4 7 2 +--R - 28a b + 24a b +--R * +--R sinh(x) +--R + +--R 2 7 4 5 6 3 4 +--R (4a b + 10a b + 12a b )cosh(x) +--R + +--R 8 3 6 5 4 3 +--R (16a b + 40a b + 48a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 2 +--R (16b + 32a b + 28a b - 24a b )cosh(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 +--R (- 16a b - 40a b - 48a b )cosh(x) + 4a b + 10a b + 12a b +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 4 6 2 3 5 5 3 5 +--R ((3a b + 6a b )cosh(x) + 8a b + 14a b )sinh(x) +--R + +--R 4 4 6 2 2 3 5 5 3 2 6 +--R (12a b + 24a b )cosh(x) + (38a b + 71a b )cosh(x) + 28a b +--R + +--R 4 4 6 2 +--R 46a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 4 6 2 3 3 5 5 3 2 +--R (18a b + 36a b )cosh(x) + (68a b + 134a b )cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 +--R (92a b + 158a b - 36a b )cosh(x) + 32a b + 34a b - 58a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (12a b + 24a b )cosh(x) + (56a b + 116a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (108a b + 198a b - 36a b )cosh(x) +--R + +--R 7 3 5 5 3 8 2 6 4 4 +--R (80a b + 102a b - 116a b )cosh(x) + 12b - 14a b - 74a b +--R + +--R 6 2 +--R 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 5 3 5 5 3 4 +--R (3a b + 6a b )cosh(x) + (20a b + 44a b )cosh(x) +--R + +--R 2 6 4 4 6 2 3 +--R (52a b + 106a b - 12a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (64a b + 98a b - 68a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 7 3 5 5 3 +--R (24b - 4a b - 109a b + 6a b )cosh(x) - 16a b - 22a b + 24a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 5 2 6 4 4 4 +--R (2a b + 5a b )cosh(x) + (8a b + 20a b )cosh(x) +--R + +--R 7 3 5 5 3 3 8 2 6 4 4 2 +--R (16a b + 30a b - 10a b )cosh(x) + (12b + 10a b - 32a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 +--R (- 16a b - 32a b + 5a b )cosh(x) + 6a b + 12a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 7 4 9 2 11 6 +--R (2a b + 4a b + 2a )sinh(x) +--R + +--R 7 4 9 2 11 6 5 8 3 10 5 +--R ((8a b + 16a b + 8a )cosh(x) + 12a b + 24a b + 12a b)sinh(x) +--R + +--R 7 4 9 2 11 2 +--R (12a b + 24a b + 12a )cosh(x) +--R + +--R 6 5 8 3 10 5 6 7 4 9 2 11 +--R (40a b + 80a b + 40a b)cosh(x) + 26a b + 48a b + 18a b - 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 7 4 9 2 11 3 +--R (8a b + 16a b + 8a )cosh(x) +--R + +--R 6 5 8 3 10 2 +--R (48a b + 96a b + 48a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 4 7 6 5 8 3 +--R (72a b + 136a b + 56a b - 8a )cosh(x) + 24a b + 32a b - 8a b +--R + +--R 10 +--R - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 4 9 2 11 4 6 5 8 3 10 3 +--R (2a b + 4a b + 2a )cosh(x) + (24a b + 48a b + 24a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 2 +--R (68a b + 132a b + 60a b - 4a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 3 8 5 6 7 4 +--R (56a b + 88a b + 8a b - 24a b)cosh(x) + 8a b - 4a b - 30a b +--R + +--R 9 2 11 +--R - 16a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 8 3 10 4 +--R (4a b + 8a b + 4a b)cosh(x) +--R + +--R 5 6 7 4 9 2 3 +--R (24a b + 48a b + 24a b )cosh(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (40a b + 72a b + 24a b - 8a b)cosh(x) +--R + +--R 3 8 5 6 7 4 9 2 4 7 6 5 10 +--R (16a b + 8a b - 32a b - 24a b )cosh(x) - 8a b - 12a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 6 7 4 9 2 4 4 7 6 5 8 3 3 +--R (2a b + 4a b + 2a b )cosh(x) + (8a b + 16a b + 8a b )cosh(x) +--R + +--R 3 8 5 6 9 2 2 4 7 6 5 8 3 +--R (8a b + 12a b - 4a b )cosh(x) + (- 8a b - 16a b - 8a b )cosh(x) +--R + +--R 5 6 7 4 9 2 +--R 2a b + 4a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression Integer +--E 347 + +--S 348 of 526 +d0465:= D(m0465,x) +--R +--R +--R (257) +--R 5 5 7 3 9 9 +--R (5a b + 11a b + 6a b)sinh(x) +--R + +--R 5 5 7 3 9 4 6 6 4 8 2 8 +--R ((30a b + 66a b + 36a b)cosh(x) + 29a b + 68a b + 42a b )sinh(x) +--R + +--R 5 5 7 3 9 2 +--R (72a b + 159a b + 90a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 7 5 5 7 3 +--R (156a b + 366a b + 228a b )cosh(x) + 74a b + 173a b + 105a b +--R + +--R 9 +--R - 18a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 7 3 9 3 +--R (82a b + 184a b + 120a b)cosh(x) +--R + +--R 4 6 6 4 8 2 2 +--R (326a b + 770a b + 510a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 8 4 6 +--R (342a b + 816a b + 528a b - 72a b)cosh(x) + 98a b + 208a b +--R + +--R 6 4 8 2 +--R 92a b - 102a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 7 3 9 4 +--R (30a b + 75a b + 90a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 +--R (304a b + 736a b + 600a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (594a b + 1467a b + 1098a b - 108a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 9 3 7 +--R (384a b + 870a b + 504a b - 360a b )cosh(x) + 64a b + 94a b +--R + +--R 5 5 7 3 9 +--R - 33a b - 213a b + 18a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (- 30a b - 54a b + 36a b)cosh(x) +--R + +--R 4 6 6 4 8 2 4 +--R (60a b + 180a b + 390a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (430a b + 1144a b + 1212a b - 72a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (546a b + 1368a b + 1134a b - 468a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 10 +--R (216a b + 402a b + 102a b - 678a b + 36a b)cosh(x) + 16b +--R + +--R 2 8 4 6 6 4 8 2 +--R - 14a b - 84a b - 186a b + 78a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 7 3 9 6 +--R (- 40a b - 79a b + 6a b)cosh(x) +--R + +--R 4 6 6 4 8 2 5 +--R (- 116a b - 242a b + 132a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 4 +--R (30a b + 171a b + 753a b - 18a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (304a b + 924a b + 1316a b - 264a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (256a b + 628a b + 570a b - 789a b + 18a b)cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 9 +--R (48b + 24a b - 120a b - 594a b + 132a b )cosh(x) - 16a b +--R + +--R 3 7 5 5 7 3 9 +--R - 22a b - 53a b + 115a b - 6a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 7 3 7 +--R (- 18a b - 36a b )cosh(x) +--R + +--R 4 6 6 4 8 2 6 +--R (- 94a b - 214a b + 18a b )cosh(x) +--R + +--R 3 7 5 5 7 3 5 +--R (- 126a b - 288a b + 252a b )cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (6a b + 144a b + 804a b - 54a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (112a b + 412a b + 774a b - 396a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (48b + 108a b + 90a b - 654a b + 54a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 +--R (- 24a b - 54a b - 228a b + 180a b )cosh(x) + 6a b + 4a b +--R + +--R 6 4 8 2 +--R 64a b - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 7 3 8 4 6 6 4 7 +--R (- 3a b - 6a b )cosh(x) + (- 24a b - 60a b )cosh(x) +--R + +--R 3 7 5 5 7 3 6 +--R (- 58a b - 163a b + 36a b )cosh(x) +--R + +--R 2 8 4 6 6 4 5 +--R (- 48a b - 114a b + 228a b )cosh(x) +--R + +--R 3 7 5 5 7 3 4 +--R (78a b + 411a b - 72a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 3 +--R (16b + 88a b + 204a b - 276a b )cosh(x) +--R + +--R 3 7 5 5 7 3 2 +--R (- 18a b - 249a b + 60a b )cosh(x) +--R + +--R 4 6 6 4 3 7 5 5 7 3 +--R (- 18a b + 108a b )cosh(x) - 2a b + 4a b - 18a b +--R * +--R sinh(x) +--R + +--R 4 6 6 4 8 3 7 5 5 7 +--R (- a b - 4a b )cosh(x) + (- 6a b - 24a b )cosh(x) +--R + +--R 2 8 4 6 6 4 6 +--R (- 10a b - 40a b + 18a b )cosh(x) +--R + +--R 9 3 7 5 5 5 +--R (- 8a b - 14a b + 72a b )cosh(x) +--R + +--R 2 8 4 6 6 4 4 +--R (18a b + 78a b - 30a b )cosh(x) +--R + +--R 9 3 7 5 5 3 +--R (8a b + 14a b - 72a b )cosh(x) +--R + +--R 2 8 4 6 6 4 2 3 7 5 5 2 8 +--R (- 6a b - 32a b + 22a b )cosh(x) + (6a b + 24a b )cosh(x) - 2a b +--R + +--R 4 6 6 4 +--R - 5a b - 6a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 4 8 2 9 +--R (- 6a b - 12a b )sinh(x) +--R + +--R 6 4 8 2 5 5 7 3 9 8 +--R ((- 36a b - 72a b )cosh(x) - 22a b - 46a b + 24a b)sinh(x) +--R + +--R 6 4 8 2 2 +--R (- 84a b - 168a b )cosh(x) +--R + +--R 5 5 7 3 9 4 6 6 4 8 2 +--R (- 120a b - 252a b + 120a b)cosh(x) - 16a b - 28a b + 156a b +--R * +--R 7 +--R sinh(x) +--R + +--R 6 4 8 2 3 +--R (- 84a b - 168a b )cosh(x) +--R + +--R 5 5 7 3 9 2 +--R (- 232a b - 490a b + 240a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 7 5 5 +--R (- 60a b - 120a b + 696a b )cosh(x) + 56a b + 130a b +--R + +--R 7 3 9 +--R 362a b - 48a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 7 3 9 3 +--R (- 128a b - 272a b + 240a b)cosh(x) +--R + +--R 6 4 8 2 2 +--R (- 36a b + 1188a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 8 +--R (288a b + 612a b + 1440a b - 144a b)cosh(x) + 136a b +--R + +--R 4 6 6 4 8 2 +--R 244a b + 300a b - 228a b +--R * +--R 5 +--R sinh(x) +--R + +--R 6 4 8 2 5 5 5 7 3 9 4 +--R (84a b + 168a b )cosh(x) + (180a b + 390a b + 120a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 +--R (292a b + 544a b + 912a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (648a b + 1254a b + 2052a b - 144a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 9 +--R (552a b + 984a b + 1092a b - 600a b )cosh(x) + 112a b +--R + +--R 3 7 5 5 7 3 9 +--R 88a b - 90a b - 378a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 4 8 2 6 5 5 7 3 9 5 +--R (84a b + 168a b )cosh(x) + (328a b + 724a b + 24a b)cosh(x) +--R + +--R 4 6 6 4 8 2 4 +--R (528a b + 1116a b + 228a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (800a b + 1480a b + 1112a b - 48a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (880a b + 1528a b + 1308a b - 480a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 10 +--R (384a b + 384a b - 144a b - 876a b + 24a b)cosh(x) + 32b +--R + +--R 2 8 4 6 6 4 8 2 +--R - 80a b - 232a b - 204a b + 84a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 8 2 7 5 5 7 3 6 +--R (36a b + 72a b )cosh(x) + (200a b + 458a b )cosh(x) +--R + +--R 4 6 6 4 8 2 5 +--R (396a b + 936a b - 72a b )cosh(x) +--R + +--R 3 7 5 5 7 3 4 +--R (552a b + 1086a b - 6a b )cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (688a b + 1168a b + 468a b - 72a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (480a b + 576a b - 36a b - 546a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 9 +--R (96b - 144a b - 540a b - 480a b + 72a b )cosh(x) - 48a b +--R + +--R 3 7 5 5 7 3 +--R - 48a b + 46a b + 94a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 4 8 2 8 5 5 7 3 7 +--R (6a b + 12a b )cosh(x) + (48a b + 120a b )cosh(x) +--R + +--R 4 6 6 4 8 2 6 +--R (128a b + 356a b - 36a b )cosh(x) +--R + +--R 3 7 5 5 7 3 5 +--R (192a b + 468a b - 168a b )cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (264a b + 468a b - 120a b + 36a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (256a b + 352a b - 24a b - 24a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (96b - 48a b - 360a b - 276a b - 12a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 +--R (- 96a b - 144a b - 12a b + 72a b )cosh(x) + 24a b + 52a b +--R + +--R 6 4 +--R 34a b +--R * +--R sinh(x) +--R + +--R 5 5 7 3 8 4 6 6 4 7 +--R (2a b + 8a b )cosh(x) + (12a b + 48a b )cosh(x) +--R + +--R 3 7 5 5 7 3 6 +--R (24a b + 90a b - 24a b )cosh(x) +--R + +--R 2 8 4 6 6 4 5 +--R (40a b + 88a b - 72a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 4 +--R (48a b + 72a b - 42a b + 24a b )cosh(x) +--R + +--R 10 2 8 4 6 3 +--R (32b + 16a b - 52a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (- 48a b - 96a b - 50a b - 8a b )cosh(x) +--R + +--R 2 8 4 6 6 4 +--R (24a b + 48a b + 24a b )cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 5 7 3 9 9 +--R (- 5a b - 11a b - 6a b)sinh(x) +--R + +--R 5 5 7 3 9 4 6 6 4 8 2 8 +--R ((- 30a b - 66a b - 36a b)cosh(x) - 29a b - 68a b - 42a b )sinh(x) +--R + +--R 5 5 7 3 9 2 +--R (- 72a b - 159a b - 90a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 7 5 5 7 3 +--R (- 156a b - 366a b - 228a b )cosh(x) - 74a b - 173a b - 105a b +--R + +--R 9 +--R 18a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 7 3 9 3 +--R (- 82a b - 184a b - 120a b)cosh(x) +--R + +--R 4 6 6 4 8 2 2 +--R (- 326a b - 770a b - 510a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 8 4 6 +--R (- 342a b - 816a b - 528a b + 72a b)cosh(x) - 98a b - 208a b +--R + +--R 6 4 8 2 +--R - 92a b + 102a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 7 3 9 4 +--R (- 30a b - 75a b - 90a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 +--R (- 304a b - 736a b - 600a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (- 594a b - 1467a b - 1098a b + 108a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 9 3 7 +--R (- 384a b - 870a b - 504a b + 360a b )cosh(x) - 64a b - 94a b +--R + +--R 5 5 7 3 9 +--R 33a b + 213a b - 18a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (30a b + 54a b - 36a b)cosh(x) +--R + +--R 4 6 6 4 8 2 4 +--R (- 60a b - 180a b - 390a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (- 430a b - 1144a b - 1212a b + 72a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (- 546a b - 1368a b - 1134a b + 468a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 10 +--R (- 216a b - 402a b - 102a b + 678a b - 36a b)cosh(x) - 16b +--R + +--R 2 8 4 6 6 4 8 2 +--R 14a b + 84a b + 186a b - 78a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 7 3 9 6 +--R (40a b + 79a b - 6a b)cosh(x) +--R + +--R 4 6 6 4 8 2 5 +--R (116a b + 242a b - 132a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 4 +--R (- 30a b - 171a b - 753a b + 18a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 304a b - 924a b - 1316a b + 264a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 256a b - 628a b - 570a b + 789a b - 18a b)cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 9 +--R (- 48b - 24a b + 120a b + 594a b - 132a b )cosh(x) + 16a b +--R + +--R 3 7 5 5 7 3 9 +--R 22a b + 53a b - 115a b + 6a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 7 3 7 4 6 6 4 8 2 6 +--R (18a b + 36a b )cosh(x) + (94a b + 214a b - 18a b )cosh(x) +--R + +--R 3 7 5 5 7 3 5 +--R (126a b + 288a b - 252a b )cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (- 6a b - 144a b - 804a b + 54a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (- 112a b - 412a b - 774a b + 396a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (- 48b - 108a b - 90a b + 654a b - 54a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 6 4 +--R (24a b + 54a b + 228a b - 180a b )cosh(x) - 6a b - 4a b - 64a b +--R + +--R 8 2 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 7 3 8 4 6 6 4 7 +--R (3a b + 6a b )cosh(x) + (24a b + 60a b )cosh(x) +--R + +--R 3 7 5 5 7 3 6 +--R (58a b + 163a b - 36a b )cosh(x) +--R + +--R 2 8 4 6 6 4 5 +--R (48a b + 114a b - 228a b )cosh(x) +--R + +--R 3 7 5 5 7 3 4 +--R (- 78a b - 411a b + 72a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 3 +--R (- 16b - 88a b - 204a b + 276a b )cosh(x) +--R + +--R 3 7 5 5 7 3 2 4 6 6 4 +--R (18a b + 249a b - 60a b )cosh(x) + (18a b - 108a b )cosh(x) +--R + +--R 3 7 5 5 7 3 +--R 2a b - 4a b + 18a b +--R * +--R sinh(x) +--R + +--R 4 6 6 4 8 3 7 5 5 7 +--R (a b + 4a b )cosh(x) + (6a b + 24a b )cosh(x) +--R + +--R 2 8 4 6 6 4 6 9 3 7 5 5 5 +--R (10a b + 40a b - 18a b )cosh(x) + (8a b + 14a b - 72a b )cosh(x) +--R + +--R 2 8 4 6 6 4 4 +--R (- 18a b - 78a b + 30a b )cosh(x) +--R + +--R 9 3 7 5 5 3 2 8 4 6 6 4 2 +--R (- 8a b - 14a b + 72a b )cosh(x) + (6a b + 32a b - 22a b )cosh(x) +--R + +--R 3 7 5 5 2 8 4 6 6 4 +--R (- 6a b - 24a b )cosh(x) + 2a b + 5a b + 6a b +--R / +--R 8 5 10 3 12 9 +--R (2a b + 4a b + 2a b)sinh(x) +--R + +--R 8 5 10 3 12 7 6 9 4 11 2 +--R ((12a b + 24a b + 12a b)cosh(x) + 18a b + 36a b + 18a b ) +--R * +--R 8 +--R sinh(x) +--R + +--R 8 5 10 3 12 2 +--R (30a b + 60a b + 30a b)cosh(x) +--R + +--R 7 6 9 4 11 2 6 7 8 5 10 3 +--R (96a b + 192a b + 96a b )cosh(x) + 66a b + 126a b + 54a b +--R + +--R 12 +--R - 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 8 5 10 3 12 3 +--R (40a b + 80a b + 40a b)cosh(x) +--R + +--R 7 6 9 4 11 2 2 +--R (210a b + 420a b + 210a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 5 8 +--R (312a b + 600a b + 264a b - 24a b)cosh(x) + 126a b +--R + +--R 7 6 9 4 11 2 +--R 210a b + 42a b - 42a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 10 3 12 4 +--R (30a b + 60a b + 30a b)cosh(x) +--R + +--R 7 6 9 4 11 2 3 +--R (240a b + 480a b + 240a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 2 +--R (594a b + 1152a b + 522a b - 36a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 4 9 +--R (528a b + 912a b + 240a b - 144a b )cosh(x) + 132a b +--R + +--R 6 7 8 5 10 3 12 +--R 150a b - 90a b - 102a b + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 10 3 12 5 +--R (12a b + 24a b + 12a b)cosh(x) +--R + +--R 7 6 9 4 11 2 4 +--R (150a b + 300a b + 150a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 3 +--R (576a b + 1128a b + 528a b - 24a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (870a b + 1560a b + 510a b - 180a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R (492a b + 648a b - 168a b - 312a b + 12a b)cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R 72a b - 6a b - 198a b - 90a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 10 3 12 6 +--R (2a b + 4a b + 2a b)cosh(x) +--R + +--R 7 6 9 4 11 2 5 +--R (48a b + 96a b + 48a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 4 +--R (294a b + 582a b + 282a b - 6a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (704a b + 1312a b + 512a b - 96a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (696a b + 1044a b + 6a b - 336a b + 6a b)cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (240a b + 96a b - 480a b - 288a b + 48a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R 16a b - 64a b - 122a b + 10a b + 50a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 9 4 11 2 6 +--R (6a b + 12a b + 6a b )cosh(x) +--R + +--R 6 7 8 5 10 3 5 +--R (72a b + 144a b + 72a b )cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (282a b + 546a b + 246a b - 18a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (456a b + 768a b + 168a b - 144a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (288a b + 252a b - 342a b - 288a b + 18a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 3 10 +--R (48a b - 120a b - 312a b - 72a b + 72a b )cosh(x) - 24a b +--R + +--R 5 8 7 6 9 4 11 2 +--R - 6a b + 54a b + 30a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 7 8 5 10 3 6 +--R (6a b + 12a b + 6a b )cosh(x) +--R + +--R 5 8 7 6 9 4 5 +--R (48a b + 96a b + 48a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (132a b + 246a b + 96a b - 18a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (144a b + 192a b - 48a b - 96a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (48a b - 48a b - 222a b - 108a b + 18a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 4 9 6 7 +--R (- 48a b - 48a b + 48a b + 48a b )cosh(x) + 12a b + 18a b +--R + +--R 10 3 +--R - 6a b +--R * +--R sinh(x) +--R + +--R 5 8 7 6 9 4 6 4 9 6 7 8 5 5 +--R (2a b + 4a b + 2a b )cosh(x) + (12a b + 24a b + 12a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (24a b + 42a b + 12a b - 6a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 3 +--R (16a b + 8a b - 32a b - 24a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 2 +--R (- 24a b - 42a b - 12a b + 6a b )cosh(x) +--R + +--R 4 9 6 7 8 5 5 8 7 6 9 4 +--R (12a b + 24a b + 12a b )cosh(x) - 2a b - 4a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 9 4 11 2 13 9 +--R (- 4a b - 8a b - 4a )sinh(x) +--R + +--R 9 4 11 2 13 8 5 10 3 12 +--R ((- 24a b - 48a b - 24a )cosh(x) - 36a b - 72a b - 36a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 9 4 11 2 13 2 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 8 5 10 3 12 7 6 9 4 +--R (- 192a b - 384a b - 192a b)cosh(x) - 132a b - 252a b +--R + +--R 11 2 13 +--R - 108a b + 12a +--R * +--R 7 +--R sinh(x) +--R + +--R 9 4 11 2 13 3 +--R (- 80a b - 160a b - 80a )cosh(x) +--R + +--R 8 5 10 3 12 2 +--R (- 420a b - 840a b - 420a b)cosh(x) +--R + +--R 7 6 9 4 11 2 13 6 7 +--R (- 624a b - 1200a b - 528a b + 48a )cosh(x) - 252a b +--R + +--R 8 5 10 3 12 +--R - 420a b - 84a b + 84a b +--R * +--R 6 +--R sinh(x) +--R + +--R 9 4 11 2 13 4 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 8 5 10 3 12 3 +--R (- 480a b - 960a b - 480a b)cosh(x) +--R + +--R 7 6 9 4 11 2 13 2 +--R (- 1188a b - 2304a b - 1044a b + 72a )cosh(x) +--R + +--R 6 7 8 5 10 3 12 5 8 +--R (- 1056a b - 1824a b - 480a b + 288a b)cosh(x) - 264a b +--R + +--R 7 6 9 4 11 2 13 +--R - 300a b + 180a b + 204a b - 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 9 4 11 2 13 5 +--R (- 24a b - 48a b - 24a )cosh(x) +--R + +--R 8 5 10 3 12 4 +--R (- 300a b - 600a b - 300a b)cosh(x) +--R + +--R 7 6 9 4 11 2 13 3 +--R (- 1152a b - 2256a b - 1056a b + 48a )cosh(x) +--R + +--R 6 7 8 5 10 3 12 2 +--R (- 1740a b - 3120a b - 1020a b + 360a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 13 +--R (- 984a b - 1296a b + 336a b + 624a b - 24a )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R - 144a b + 12a b + 396a b + 180a b - 60a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 4 11 2 13 6 +--R (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 8 5 10 3 12 5 +--R (- 96a b - 192a b - 96a b)cosh(x) +--R + +--R 7 6 9 4 11 2 13 4 +--R (- 588a b - 1164a b - 564a b + 12a )cosh(x) +--R + +--R 6 7 8 5 10 3 12 3 +--R (- 1408a b - 2624a b - 1024a b + 192a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 13 2 +--R (- 1392a b - 2088a b - 12a b + 672a b - 12a )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R (- 480a b - 192a b + 960a b + 576a b - 96a b)cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 13 +--R - 32a b + 128a b + 244a b - 20a b - 100a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 8 5 10 3 12 6 +--R (- 12a b - 24a b - 12a b)cosh(x) +--R + +--R 7 6 9 4 11 2 5 +--R (- 144a b - 288a b - 144a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 4 +--R (- 564a b - 1092a b - 492a b + 36a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (- 912a b - 1536a b - 336a b + 288a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 576a b - 504a b + 684a b + 576a b - 36a b)cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (- 96a b + 240a b + 624a b + 144a b - 144a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R 48a b + 12a b - 108a b - 60a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 9 4 11 2 6 +--R (- 12a b - 24a b - 12a b )cosh(x) +--R + +--R 6 7 8 5 10 3 5 +--R (- 96a b - 192a b - 96a b )cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (- 264a b - 492a b - 192a b + 36a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 288a b - 384a b + 96a b + 192a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 96a b + 96a b + 444a b + 216a b - 36a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 5 8 7 6 +--R (96a b + 96a b - 96a b - 96a b )cosh(x) - 24a b - 36a b +--R + +--R 11 2 +--R 12a b +--R * +--R sinh(x) +--R + +--R 6 7 8 5 10 3 6 +--R (- 4a b - 8a b - 4a b )cosh(x) +--R + +--R 5 8 7 6 9 4 5 +--R (- 24a b - 48a b - 24a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (- 48a b - 84a b - 24a b + 12a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 32a b - 16a b + 64a b + 48a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 2 +--R (48a b + 84a b + 24a b - 12a b )cosh(x) +--R + +--R 5 8 7 6 9 4 6 7 8 5 10 3 +--R (- 24a b - 48a b - 24a b )cosh(x) + 4a b + 8a b + 4a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 8 5 10 3 12 9 +--R (- 2a b - 4a b - 2a b)sinh(x) +--R + +--R 8 5 10 3 12 7 6 9 4 11 2 +--R ((- 12a b - 24a b - 12a b)cosh(x) - 18a b - 36a b - 18a b ) +--R * +--R 8 +--R sinh(x) +--R + +--R 8 5 10 3 12 2 +--R (- 30a b - 60a b - 30a b)cosh(x) +--R + +--R 7 6 9 4 11 2 6 7 8 5 10 3 +--R (- 96a b - 192a b - 96a b )cosh(x) - 66a b - 126a b - 54a b +--R + +--R 12 +--R 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 8 5 10 3 12 3 +--R (- 40a b - 80a b - 40a b)cosh(x) +--R + +--R 7 6 9 4 11 2 2 +--R (- 210a b - 420a b - 210a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 5 8 7 6 +--R (- 312a b - 600a b - 264a b + 24a b)cosh(x) - 126a b - 210a b +--R + +--R 9 4 11 2 +--R - 42a b + 42a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 10 3 12 4 +--R (- 30a b - 60a b - 30a b)cosh(x) +--R + +--R 7 6 9 4 11 2 3 +--R (- 240a b - 480a b - 240a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 2 +--R (- 594a b - 1152a b - 522a b + 36a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 4 9 6 7 +--R (- 528a b - 912a b - 240a b + 144a b )cosh(x) - 132a b - 150a b +--R + +--R 8 5 10 3 12 +--R 90a b + 102a b - 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 10 3 12 5 +--R (- 12a b - 24a b - 12a b)cosh(x) +--R + +--R 7 6 9 4 11 2 4 +--R (- 150a b - 300a b - 150a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 3 +--R (- 576a b - 1128a b - 528a b + 24a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 870a b - 1560a b - 510a b + 180a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 3 10 +--R (- 492a b - 648a b + 168a b + 312a b - 12a b)cosh(x) - 72a b +--R + +--R 5 8 7 6 9 4 11 2 +--R 6a b + 198a b + 90a b - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 10 3 12 6 +--R (- 2a b - 4a b - 2a b)cosh(x) +--R + +--R 7 6 9 4 11 2 5 +--R (- 48a b - 96a b - 48a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 4 +--R (- 294a b - 582a b - 282a b + 6a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (- 704a b - 1312a b - 512a b + 96a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 696a b - 1044a b - 6a b + 336a b - 6a b)cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 11 +--R (- 240a b - 96a b + 480a b + 288a b - 48a b )cosh(x) - 16a b +--R + +--R 4 9 6 7 8 5 10 3 12 +--R 64a b + 122a b - 10a b - 50a b + 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 9 4 11 2 6 +--R (- 6a b - 12a b - 6a b )cosh(x) +--R + +--R 6 7 8 5 10 3 5 +--R (- 72a b - 144a b - 72a b )cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (- 282a b - 546a b - 246a b + 18a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 456a b - 768a b - 168a b + 144a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 288a b - 252a b + 342a b + 288a b - 18a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 3 10 +--R (- 48a b + 120a b + 312a b + 72a b - 72a b )cosh(x) + 24a b +--R + +--R 5 8 7 6 9 4 11 2 +--R 6a b - 54a b - 30a b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 7 8 5 10 3 6 +--R (- 6a b - 12a b - 6a b )cosh(x) +--R + +--R 5 8 7 6 9 4 5 +--R (- 48a b - 96a b - 48a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (- 132a b - 246a b - 96a b + 18a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 144a b - 192a b + 48a b + 96a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 48a b + 48a b + 222a b + 108a b - 18a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 4 9 6 7 10 3 +--R (48a b + 48a b - 48a b - 48a b )cosh(x) - 12a b - 18a b + 6a b +--R * +--R sinh(x) +--R + +--R 5 8 7 6 9 4 6 4 9 6 7 8 5 5 +--R (- 2a b - 4a b - 2a b )cosh(x) + (- 12a b - 24a b - 12a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (- 24a b - 42a b - 12a b + 6a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 3 +--R (- 16a b - 8a b + 32a b + 24a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 2 +--R (24a b + 42a b + 12a b - 6a b )cosh(x) +--R + +--R 4 9 6 7 8 5 5 8 7 6 9 4 +--R (- 12a b - 24a b - 12a b )cosh(x) + 2a b + 4a b + 2a b +--R Type: Expression Integer +--E 348 + +--S 349 of 526 +t0466:= 1/(a+b*csch(x)^2) +--R +--R +--R 1 +--R (258) -------------- +--R 2 +--R b csch(x) + a +--R Type: Expression Integer +--E 349 + +--S 350 of 526 +r0466:= x/a-b^(1/2)*atan((a-b)^(1/2)*tanh(x)/b^(1/2))/a/(a-b)^(1/2) +--R +--R +--R +-------+ +--R +-+ tanh(x)\|- b + a +-------+ +--R - \|b atan(-----------------) + x\|- b + a +--R +-+ +--R \|b +--R (259) ------------------------------------------- +--R +-------+ +--R a\|- b + a +--R Type: Expression Integer +--E 350 + +--S 351 of 526 +a0466:= integrate(t0466,x) +--R +--R +--R (260) +--R [ +--R +-----+ +--R | b +--R |----- +--R \|b - a +--R * +--R log +--R 2 2 2 +--R (4a b - 4a )sinh(x) + (8a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b - 4a )cosh(x) + 8b - 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b - a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b - 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b - 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b - 2a )cosh(x) + 8b - 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b - 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b - 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b - 2a)cosh(x) + a +--R + +--R 2x +--R / +--R 2a +--R , +--R +-------+ +--R | b +--R +-------+ (2b - 2a) |- ----- +--R | b \| b - a +--R - |- ----- atan(----------------------------------------------------) + x +--R \| b - a 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b - a +--R --------------------------------------------------------------------------] +--R