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