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