Optimal. Leaf size=291 \[ \frac {a^3 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac {a^3 x}{2}+\frac {3 a^2 b \cosh ^5(c+d x)}{5 d}-\frac {2 a^2 b \cosh ^3(c+d x)}{d}+\frac {3 a^2 b \cosh (c+d x)}{d}+\frac {3 a b^2 \sinh ^7(c+d x) \cosh (c+d x)}{8 d}-\frac {7 a b^2 \sinh ^5(c+d x) \cosh (c+d x)}{16 d}+\frac {35 a b^2 \sinh ^3(c+d x) \cosh (c+d x)}{64 d}-\frac {105 a b^2 \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac {105}{128} a b^2 x+\frac {b^3 \cosh ^{11}(c+d x)}{11 d}-\frac {5 b^3 \cosh ^9(c+d x)}{9 d}+\frac {10 b^3 \cosh ^7(c+d x)}{7 d}-\frac {2 b^3 \cosh ^5(c+d x)}{d}+\frac {5 b^3 \cosh ^3(c+d x)}{3 d}-\frac {b^3 \cosh (c+d x)}{d} \]
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Rubi [A] time = 0.21, antiderivative size = 291, normalized size of antiderivative = 1.00, number of steps used = 13, number of rules used = 4, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.174, Rules used = {3220, 2635, 8, 2633} \[ \frac {3 a^2 b \cosh ^5(c+d x)}{5 d}-\frac {2 a^2 b \cosh ^3(c+d x)}{d}+\frac {3 a^2 b \cosh (c+d x)}{d}+\frac {a^3 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac {a^3 x}{2}+\frac {3 a b^2 \sinh ^7(c+d x) \cosh (c+d x)}{8 d}-\frac {7 a b^2 \sinh ^5(c+d x) \cosh (c+d x)}{16 d}+\frac {35 a b^2 \sinh ^3(c+d x) \cosh (c+d x)}{64 d}-\frac {105 a b^2 \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac {105}{128} a b^2 x+\frac {b^3 \cosh ^{11}(c+d x)}{11 d}-\frac {5 b^3 \cosh ^9(c+d x)}{9 d}+\frac {10 b^3 \cosh ^7(c+d x)}{7 d}-\frac {2 b^3 \cosh ^5(c+d x)}{d}+\frac {5 b^3 \cosh ^3(c+d x)}{3 d}-\frac {b^3 \cosh (c+d x)}{d} \]
Antiderivative was successfully verified.
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Rule 8
Rule 2633
Rule 2635
Rule 3220
Rubi steps
\begin {align*} \int \sinh ^2(c+d x) \left (a+b \sinh ^3(c+d x)\right )^3 \, dx &=-\int \left (-a^3 \sinh ^2(c+d x)-3 a^2 b \sinh ^5(c+d x)-3 a b^2 \sinh ^8(c+d x)-b^3 \sinh ^{11}(c+d x)\right ) \, dx\\ &=a^3 \int \sinh ^2(c+d x) \, dx+\left (3 a^2 b\right ) \int \sinh ^5(c+d x) \, dx+\left (3 a b^2\right ) \int \sinh ^8(c+d x) \, dx+b^3 \int \sinh ^{11}(c+d x) \, dx\\ &=\frac {a^3 \cosh (c+d x) \sinh (c+d x)}{2 d}+\frac {3 a b^2 \cosh (c+d x) \sinh ^7(c+d x)}{8 d}-\frac {1}{2} a^3 \int 1 \, dx-\frac {1}{8} \left (21 a b^2\right ) \int \sinh ^6(c+d x) \, dx+\frac {\left (3 a^2 b\right ) \operatorname {Subst}\left (\int \left (1-2 x^2+x^4\right ) \, dx,x,\cosh (c+d x)\right )}{d}-\frac {b^3 \operatorname {Subst}\left (\int \left (1-5 x^2+10 x^4-10 x^6+5 x^8-x^{10}\right ) \, dx,x,\cosh (c+d x)\right )}{d}\\ &=-\frac {a^3 x}{2}+\frac {3 a^2 b \cosh (c+d x)}{d}-\frac {b^3 \cosh (c+d x)}{d}-\frac {2 a^2 b \cosh ^3(c+d x)}{d}+\frac {5 b^3 \cosh ^3(c+d x)}{3 d}+\frac {3 a^2 b \cosh ^5(c+d x)}{5 d}-\frac {2 b^3 \cosh ^5(c+d x)}{d}+\frac {10 b^3 \cosh ^7(c+d x)}{7 d}-\frac {5 b^3 \cosh ^9(c+d x)}{9 d}+\frac {b^3 \cosh ^{11}(c+d x)}{11 d}+\frac {a^3 \cosh (c+d x) \sinh (c+d x)}{2 d}-\frac {7 a b^2 \cosh (c+d x) \sinh ^5(c+d x)}{16 d}+\frac {3 a b^2 \cosh (c+d x) \sinh ^7(c+d x)}{8 d}+\frac {1}{16} \left (35 a b^2\right ) \int \sinh ^4(c+d x) \, dx\\ &=-\frac {a^3 x}{2}+\frac {3 a^2 b \cosh (c+d x)}{d}-\frac {b^3 \cosh (c+d x)}{d}-\frac {2 a^2 b \cosh ^3(c+d x)}{d}+\frac {5 b^3 \cosh ^3(c+d x)}{3 d}+\frac {3 a^2 b \cosh ^5(c+d x)}{5 d}-\frac {2 b^3 \cosh ^5(c+d x)}{d}+\frac {10 b^3 \cosh ^7(c+d x)}{7 d}-\frac {5 b^3 \cosh ^9(c+d x)}{9 d}+\frac {b^3 \cosh ^{11}(c+d x)}{11 d}+\frac {a^3 \cosh (c+d x) \sinh (c+d x)}{2 d}+\frac {35 a b^2 \cosh (c+d x) \sinh ^3(c+d x)}{64 d}-\frac {7 a b^2 \cosh (c+d x) \sinh ^5(c+d x)}{16 d}+\frac {3 a b^2 \cosh (c+d x) \sinh ^7(c+d x)}{8 d}-\frac {1}{64} \left (105 a b^2\right ) \int \sinh ^2(c+d x) \, dx\\ &=-\frac {a^3 x}{2}+\frac {3 a^2 b \cosh (c+d x)}{d}-\frac {b^3 \cosh (c+d x)}{d}-\frac {2 a^2 b \cosh ^3(c+d x)}{d}+\frac {5 b^3 \cosh ^3(c+d x)}{3 d}+\frac {3 a^2 b \cosh ^5(c+d x)}{5 d}-\frac {2 b^3 \cosh ^5(c+d x)}{d}+\frac {10 b^3 \cosh ^7(c+d x)}{7 d}-\frac {5 b^3 \cosh ^9(c+d x)}{9 d}+\frac {b^3 \cosh ^{11}(c+d x)}{11 d}+\frac {a^3 \cosh (c+d x) \sinh (c+d x)}{2 d}-\frac {105 a b^2 \cosh (c+d x) \sinh (c+d x)}{128 d}+\frac {35 a b^2 \cosh (c+d x) \sinh ^3(c+d x)}{64 d}-\frac {7 a b^2 \cosh (c+d x) \sinh ^5(c+d x)}{16 d}+\frac {3 a b^2 \cosh (c+d x) \sinh ^7(c+d x)}{8 d}+\frac {1}{128} \left (105 a b^2\right ) \int 1 \, dx\\ &=-\frac {a^3 x}{2}+\frac {105}{128} a b^2 x+\frac {3 a^2 b \cosh (c+d x)}{d}-\frac {b^3 \cosh (c+d x)}{d}-\frac {2 a^2 b \cosh ^3(c+d x)}{d}+\frac {5 b^3 \cosh ^3(c+d x)}{3 d}+\frac {3 a^2 b \cosh ^5(c+d x)}{5 d}-\frac {2 b^3 \cosh ^5(c+d x)}{d}+\frac {10 b^3 \cosh ^7(c+d x)}{7 d}-\frac {5 b^3 \cosh ^9(c+d x)}{9 d}+\frac {b^3 \cosh ^{11}(c+d x)}{11 d}+\frac {a^3 \cosh (c+d x) \sinh (c+d x)}{2 d}-\frac {105 a b^2 \cosh (c+d x) \sinh (c+d x)}{128 d}+\frac {35 a b^2 \cosh (c+d x) \sinh ^3(c+d x)}{64 d}-\frac {7 a b^2 \cosh (c+d x) \sinh ^5(c+d x)}{16 d}+\frac {3 a b^2 \cosh (c+d x) \sinh ^7(c+d x)}{8 d}\\ \end {align*}
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Mathematica [A] time = 0.47, size = 194, normalized size = 0.67 \[ \frac {-27720 a \left (64 a^2-105 b^2\right ) (c+d x)+110880 a \left (8 a^2-21 b^2\right ) \sinh (2 (c+d x))-20790 b \left (77 b^2-320 a^2\right ) \cosh (c+d x)+34650 b \left (11 b^2-32 a^2\right ) \cosh (3 (c+d x))-2079 b \left (55 b^2-64 a^2\right ) \cosh (5 (c+d x))+582120 a b^2 \sinh (4 (c+d x))-110880 a b^2 \sinh (6 (c+d x))+10395 a b^2 \sinh (8 (c+d x))+27225 b^3 \cosh (7 (c+d x))-4235 b^3 \cosh (9 (c+d x))+315 b^3 \cosh (11 (c+d x))}{3548160 d} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.52, size = 568, normalized size = 1.95 \[ \frac {315 \, b^{3} \cosh \left (d x + c\right )^{11} + 3465 \, b^{3} \cosh \left (d x + c\right ) \sinh \left (d x + c\right )^{10} - 4235 \, b^{3} \cosh \left (d x + c\right )^{9} + 83160 \, a b^{2} \cosh \left (d x + c\right ) \sinh \left (d x + c\right )^{7} + 27225 \, b^{3} \cosh \left (d x + c\right )^{7} + 3465 \, {\left (15 \, b^{3} \cosh \left (d x + c\right )^{3} - 11 \, b^{3} \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{8} + 1155 \, {\left (126 \, b^{3} \cosh \left (d x + c\right )^{5} - 308 \, b^{3} \cosh \left (d x + c\right )^{3} + 165 \, b^{3} \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{6} + 2079 \, {\left (64 \, a^{2} b - 55 \, b^{3}\right )} \cosh \left (d x + c\right )^{5} + 83160 \, {\left (7 \, a b^{2} \cosh \left (d x + c\right )^{3} - 8 \, a b^{2} \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{5} + 3465 \, {\left (30 \, b^{3} \cosh \left (d x + c\right )^{7} - 154 \, b^{3} \cosh \left (d x + c\right )^{5} + 275 \, b^{3} \cosh \left (d x + c\right )^{3} + 3 \, {\left (64 \, a^{2} b - 55 \, b^{3}\right )} \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{4} - 34650 \, {\left (32 \, a^{2} b - 11 \, b^{3}\right )} \cosh \left (d x + c\right )^{3} + 27720 \, {\left (21 \, a b^{2} \cosh \left (d x + c\right )^{5} - 80 \, a b^{2} \cosh \left (d x + c\right )^{3} + 84 \, a b^{2} \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{3} - 27720 \, {\left (64 \, a^{3} - 105 \, a b^{2}\right )} d x + 3465 \, {\left (5 \, b^{3} \cosh \left (d x + c\right )^{9} - 44 \, b^{3} \cosh \left (d x + c\right )^{7} + 165 \, b^{3} \cosh \left (d x + c\right )^{5} + 6 \, {\left (64 \, a^{2} b - 55 \, b^{3}\right )} \cosh \left (d x + c\right )^{3} - 30 \, {\left (32 \, a^{2} b - 11 \, b^{3}\right )} \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )^{2} + 20790 \, {\left (320 \, a^{2} b - 77 \, b^{3}\right )} \cosh \left (d x + c\right ) + 27720 \, {\left (3 \, a b^{2} \cosh \left (d x + c\right )^{7} - 24 \, a b^{2} \cosh \left (d x + c\right )^{5} + 84 \, a b^{2} \cosh \left (d x + c\right )^{3} + 8 \, {\left (8 \, a^{3} - 21 \, a b^{2}\right )} \cosh \left (d x + c\right )\right )} \sinh \left (d x + c\right )}{3548160 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 431, normalized size = 1.48 \[ \frac {b^{3} e^{\left (11 \, d x + 11 \, c\right )}}{22528 \, d} - \frac {11 \, b^{3} e^{\left (9 \, d x + 9 \, c\right )}}{18432 \, d} + \frac {3 \, a b^{2} e^{\left (8 \, d x + 8 \, c\right )}}{2048 \, d} + \frac {55 \, b^{3} e^{\left (7 \, d x + 7 \, c\right )}}{14336 \, d} - \frac {a b^{2} e^{\left (6 \, d x + 6 \, c\right )}}{64 \, d} + \frac {21 \, a b^{2} e^{\left (4 \, d x + 4 \, c\right )}}{256 \, d} - \frac {21 \, a b^{2} e^{\left (-4 \, d x - 4 \, c\right )}}{256 \, d} + \frac {a b^{2} e^{\left (-6 \, d x - 6 \, c\right )}}{64 \, d} + \frac {55 \, b^{3} e^{\left (-7 \, d x - 7 \, c\right )}}{14336 \, d} - \frac {3 \, a b^{2} e^{\left (-8 \, d x - 8 \, c\right )}}{2048 \, d} - \frac {11 \, b^{3} e^{\left (-9 \, d x - 9 \, c\right )}}{18432 \, d} + \frac {b^{3} e^{\left (-11 \, d x - 11 \, c\right )}}{22528 \, d} - \frac {1}{128} \, {\left (64 \, a^{3} - 105 \, a b^{2}\right )} x + \frac {3 \, {\left (64 \, a^{2} b - 55 \, b^{3}\right )} e^{\left (5 \, d x + 5 \, c\right )}}{10240 \, d} - \frac {5 \, {\left (32 \, a^{2} b - 11 \, b^{3}\right )} e^{\left (3 \, d x + 3 \, c\right )}}{1024 \, d} + \frac {{\left (8 \, a^{3} - 21 \, a b^{2}\right )} e^{\left (2 \, d x + 2 \, c\right )}}{64 \, d} + \frac {3 \, {\left (320 \, a^{2} b - 77 \, b^{3}\right )} e^{\left (d x + c\right )}}{1024 \, d} + \frac {3 \, {\left (320 \, a^{2} b - 77 \, b^{3}\right )} e^{\left (-d x - c\right )}}{1024 \, d} - \frac {{\left (8 \, a^{3} - 21 \, a b^{2}\right )} e^{\left (-2 \, d x - 2 \, c\right )}}{64 \, d} - \frac {5 \, {\left (32 \, a^{2} b - 11 \, b^{3}\right )} e^{\left (-3 \, d x - 3 \, c\right )}}{1024 \, d} + \frac {3 \, {\left (64 \, a^{2} b - 55 \, b^{3}\right )} e^{\left (-5 \, d x - 5 \, c\right )}}{10240 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 188, normalized size = 0.65 \[ \frac {b^{3} \left (-\frac {256}{693}+\frac {\left (\sinh ^{10}\left (d x +c \right )\right )}{11}-\frac {10 \left (\sinh ^{8}\left (d x +c \right )\right )}{99}+\frac {80 \left (\sinh ^{6}\left (d x +c \right )\right )}{693}-\frac {32 \left (\sinh ^{4}\left (d x +c \right )\right )}{231}+\frac {128 \left (\sinh ^{2}\left (d x +c \right )\right )}{693}\right ) \cosh \left (d x +c \right )+3 a \,b^{2} \left (\left (\frac {\left (\sinh ^{7}\left (d x +c \right )\right )}{8}-\frac {7 \left (\sinh ^{5}\left (d x +c \right )\right )}{48}+\frac {35 \left (\sinh ^{3}\left (d x +c \right )\right )}{192}-\frac {35 \sinh \left (d x +c \right )}{128}\right ) \cosh \left (d x +c \right )+\frac {35 d x}{128}+\frac {35 c}{128}\right )+3 a^{2} b \left (\frac {8}{15}+\frac {\left (\sinh ^{4}\left (d x +c \right )\right )}{5}-\frac {4 \left (\sinh ^{2}\left (d x +c \right )\right )}{15}\right ) \cosh \left (d x +c \right )+a^{3} \left (\frac {\cosh \left (d x +c \right ) \sinh \left (d x +c \right )}{2}-\frac {d x}{2}-\frac {c}{2}\right )}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 387, normalized size = 1.33 \[ -\frac {1}{8} \, a^{3} {\left (4 \, x - \frac {e^{\left (2 \, d x + 2 \, c\right )}}{d} + \frac {e^{\left (-2 \, d x - 2 \, c\right )}}{d}\right )} - \frac {1}{1419264} \, b^{3} {\left (\frac {{\left (847 \, e^{\left (-2 \, d x - 2 \, c\right )} - 5445 \, e^{\left (-4 \, d x - 4 \, c\right )} + 22869 \, e^{\left (-6 \, d x - 6 \, c\right )} - 76230 \, e^{\left (-8 \, d x - 8 \, c\right )} + 320166 \, e^{\left (-10 \, d x - 10 \, c\right )} - 63\right )} e^{\left (11 \, d x + 11 \, c\right )}}{d} + \frac {320166 \, e^{\left (-d x - c\right )} - 76230 \, e^{\left (-3 \, d x - 3 \, c\right )} + 22869 \, e^{\left (-5 \, d x - 5 \, c\right )} - 5445 \, e^{\left (-7 \, d x - 7 \, c\right )} + 847 \, e^{\left (-9 \, d x - 9 \, c\right )} - 63 \, e^{\left (-11 \, d x - 11 \, c\right )}}{d}\right )} - \frac {1}{2048} \, a b^{2} {\left (\frac {{\left (32 \, e^{\left (-2 \, d x - 2 \, c\right )} - 168 \, e^{\left (-4 \, d x - 4 \, c\right )} + 672 \, e^{\left (-6 \, d x - 6 \, c\right )} - 3\right )} e^{\left (8 \, d x + 8 \, c\right )}}{d} - \frac {1680 \, {\left (d x + c\right )}}{d} - \frac {672 \, e^{\left (-2 \, d x - 2 \, c\right )} - 168 \, e^{\left (-4 \, d x - 4 \, c\right )} + 32 \, e^{\left (-6 \, d x - 6 \, c\right )} - 3 \, e^{\left (-8 \, d x - 8 \, c\right )}}{d}\right )} + \frac {1}{160} \, a^{2} b {\left (\frac {3 \, e^{\left (5 \, d x + 5 \, c\right )}}{d} - \frac {25 \, e^{\left (3 \, d x + 3 \, c\right )}}{d} + \frac {150 \, e^{\left (d x + c\right )}}{d} + \frac {150 \, e^{\left (-d x - c\right )}}{d} - \frac {25 \, e^{\left (-3 \, d x - 3 \, c\right )}}{d} + \frac {3 \, e^{\left (-5 \, d x - 5 \, c\right )}}{d}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.09, size = 231, normalized size = 0.79 \[ \frac {\frac {\mathrm {sinh}\left (c+d\,x\right )\,a^3\,\mathrm {cosh}\left (c+d\,x\right )}{2}-\frac {d\,x\,a^3}{2}+\frac {3\,a^2\,b\,{\mathrm {cosh}\left (c+d\,x\right )}^5}{5}-2\,a^2\,b\,{\mathrm {cosh}\left (c+d\,x\right )}^3+3\,a^2\,b\,\mathrm {cosh}\left (c+d\,x\right )+\frac {3\,\mathrm {sinh}\left (c+d\,x\right )\,a\,b^2\,{\mathrm {cosh}\left (c+d\,x\right )}^7}{8}-\frac {25\,\mathrm {sinh}\left (c+d\,x\right )\,a\,b^2\,{\mathrm {cosh}\left (c+d\,x\right )}^5}{16}+\frac {163\,\mathrm {sinh}\left (c+d\,x\right )\,a\,b^2\,{\mathrm {cosh}\left (c+d\,x\right )}^3}{64}-\frac {279\,\mathrm {sinh}\left (c+d\,x\right )\,a\,b^2\,\mathrm {cosh}\left (c+d\,x\right )}{128}+\frac {105\,d\,x\,a\,b^2}{128}+\frac {b^3\,{\mathrm {cosh}\left (c+d\,x\right )}^{11}}{11}-\frac {5\,b^3\,{\mathrm {cosh}\left (c+d\,x\right )}^9}{9}+\frac {10\,b^3\,{\mathrm {cosh}\left (c+d\,x\right )}^7}{7}-2\,b^3\,{\mathrm {cosh}\left (c+d\,x\right )}^5+\frac {5\,b^3\,{\mathrm {cosh}\left (c+d\,x\right )}^3}{3}-b^3\,\mathrm {cosh}\left (c+d\,x\right )}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 33.47, size = 498, normalized size = 1.71 \[ \begin {cases} \frac {a^{3} x \sinh ^{2}{\left (c + d x \right )}}{2} - \frac {a^{3} x \cosh ^{2}{\left (c + d x \right )}}{2} + \frac {a^{3} \sinh {\left (c + d x \right )} \cosh {\left (c + d x \right )}}{2 d} + \frac {3 a^{2} b \sinh ^{4}{\left (c + d x \right )} \cosh {\left (c + d x \right )}}{d} - \frac {4 a^{2} b \sinh ^{2}{\left (c + d x \right )} \cosh ^{3}{\left (c + d x \right )}}{d} + \frac {8 a^{2} b \cosh ^{5}{\left (c + d x \right )}}{5 d} + \frac {105 a b^{2} x \sinh ^{8}{\left (c + d x \right )}}{128} - \frac {105 a b^{2} x \sinh ^{6}{\left (c + d x \right )} \cosh ^{2}{\left (c + d x \right )}}{32} + \frac {315 a b^{2} x \sinh ^{4}{\left (c + d x \right )} \cosh ^{4}{\left (c + d x \right )}}{64} - \frac {105 a b^{2} x \sinh ^{2}{\left (c + d x \right )} \cosh ^{6}{\left (c + d x \right )}}{32} + \frac {105 a b^{2} x \cosh ^{8}{\left (c + d x \right )}}{128} + \frac {279 a b^{2} \sinh ^{7}{\left (c + d x \right )} \cosh {\left (c + d x \right )}}{128 d} - \frac {511 a b^{2} \sinh ^{5}{\left (c + d x \right )} \cosh ^{3}{\left (c + d x \right )}}{128 d} + \frac {385 a b^{2} \sinh ^{3}{\left (c + d x \right )} \cosh ^{5}{\left (c + d x \right )}}{128 d} - \frac {105 a b^{2} \sinh {\left (c + d x \right )} \cosh ^{7}{\left (c + d x \right )}}{128 d} + \frac {b^{3} \sinh ^{10}{\left (c + d x \right )} \cosh {\left (c + d x \right )}}{d} - \frac {10 b^{3} \sinh ^{8}{\left (c + d x \right )} \cosh ^{3}{\left (c + d x \right )}}{3 d} + \frac {16 b^{3} \sinh ^{6}{\left (c + d x \right )} \cosh ^{5}{\left (c + d x \right )}}{3 d} - \frac {32 b^{3} \sinh ^{4}{\left (c + d x \right )} \cosh ^{7}{\left (c + d x \right )}}{7 d} + \frac {128 b^{3} \sinh ^{2}{\left (c + d x \right )} \cosh ^{9}{\left (c + d x \right )}}{63 d} - \frac {256 b^{3} \cosh ^{11}{\left (c + d x \right )}}{693 d} & \text {for}\: d \neq 0 \\x \left (a + b \sinh ^{3}{\relax (c )}\right )^{3} \sinh ^{2}{\relax (c )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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