\[ \int \frac {1}{\left (1-x^2\right ) \coth ^{-1}(x)} \, dx \]
Optimal antiderivative \[ \ln \left (\mathrm {arccoth}\left (x \right )\right ) \]
command
integrate(1/(-x^2+1)/arccoth(x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \log \left ({\left | \log \left (\frac {x + 1}{x - 1}\right ) \right |}\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {1}{{\left (x^{2} - 1\right )} \operatorname {arcoth}\left (x\right )}\,{d x} \]________________________________________________________________________________________