\[ \int \frac {\coth ^{-1}(x)}{1-x^2} \, dx \]
Optimal antiderivative \[ \frac {\mathrm {arccoth}\left (x \right )^{2}}{2} \]
command
integrate(arccoth(x)/(-x^2+1),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{8} \, \log \left (\frac {x + 1}{x - 1}\right )^{2} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {\operatorname {arcoth}\left (x\right )}{x^{2} - 1}\,{d x} \]________________________________________________________________________________________