\[ \int \frac {\coth ^{-1}(x)^2}{\left (1-x^2\right )^2} \, dx \]
Optimal antiderivative \[ \frac {x}{-4 x^{2}+4}-\frac {\mathrm {arccoth}\left (x \right )}{2 \left (-x^{2}+1\right )}+\frac {x \mathrm {arccoth}\left (x \right )^{2}}{-2 x^{2}+2}+\frac {\mathrm {arccoth}\left (x \right )^{3}}{6}+\frac {\arctanh \left (x \right )}{4} \]
command
integrate(arccoth(x)^2/(-x^2+1)^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {{\left (x - 1\right )} \log \left (\frac {x + 1}{x - 1}\right )^{2}}{16 \, {\left (x + 1\right )}} - \frac {{\left (x - 1\right )} \log \left (\frac {x + 1}{x - 1}\right )}{8 \, {\left (x + 1\right )}} - \frac {x - 1}{8 \, {\left (x + 1\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {\operatorname {arcoth}\left (x\right )^{2}}{{\left (x^{2} - 1\right )}^{2}}\,{d x} \]________________________________________________________________________________________