79.1 Problem number 34

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

Optimal antiderivative \[ \frac {\arctan \left (\frac {\cosh \left (d x +c \right ) \sqrt {b}}{\sqrt {a -b}}\right )}{d \sqrt {a -b}\, \sqrt {b}} \]

command

integrate(sinh(d*x+c)/(a+b*sinh(d*x+c)**2),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 \[ \text {Timed out} \]_____________________________________________________