92.2 Problem number 4

\[ \int \frac {\text {csch}^2(2+3 x)}{2+\coth ^2(2+3 x)} \, dx \]

Optimal antiderivative \[ \frac {\arctan \left (\sqrt {2}\, \tanh \left (2+3 x \right )\right ) \sqrt {2}}{6} \]

command

integrate(csch(2+3*x)^2/(2+coth(2+3*x)^2),x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ \frac {1}{6} \, \sqrt {2} \arctan \left (\frac {1}{4} \, \sqrt {2} {\left (3 \, e^{\left (6 \, x + 4\right )} - 1\right )}\right ) \]

Giac 1.7.0 via sagemath 9.3 output

\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________