79.2 Problem number 35

\[ \int \frac {1}{a+b \sinh ^2(c+d x)} \, dx \]

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

command

integrate(1/(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 \[ \text {Timed out} \]_____________________________________________________