\[ \int \text {csch}(x) \log (\tanh (x)) \text {sech}(x) \, dx \]
Optimal antiderivative \[ \frac {\ln \left (\tanh \left (x \right )\right )^{2}}{2} \]
command
integrate(csch(x)*log(tanh(x))*sech(x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{2} \, \log \left (\frac {e^{\left (2 \, x\right )} - 1}{e^{\left (2 \, x\right )} + 1}\right )^{2} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \operatorname {csch}\left (x\right ) \log \left (\tanh \left (x\right )\right ) \operatorname {sech}\left (x\right )\,{d x} \]________________________________________________________________________________________