77.1 Problem number 231

\[ \int \frac {\sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx \]

Optimal antiderivative \[ -\frac {a x}{b^{2}}+\frac {\cosh \left (d x +c \right )}{b d}-\frac {2 a^{2} \arctanh \left (\frac {b -a \tanh \left (\frac {d x}{2}+\frac {c}{2}\right )}{\sqrt {a^{2}+b^{2}}}\right )}{b^{2} d \sqrt {a^{2}+b^{2}}} \]

command

integrate(sinh(d*x+c)**2/(a+b*sinh(d*x+c)),x)

Sympy 1.10.1 under Python 3.10.4 output

\[ \text {output too large to display} \]

Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________