\[ \int \frac {\coth ^{-1}(\tanh (a+b x))^3}{x^2} \, dx \]
Optimal antiderivative \[ -3 b^{2} x \left (b x -\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )\right )+\frac {3 b \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{2}}{2}-\frac {\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{3}}{x}+3 b \left (b x -\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )\right )^{2} \ln \left (x \right ) \]
command
integrate(arccoth(tanh(b*x+a))^3/x^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{2} \, b^{3} x^{2} - \frac {3}{2} \, {\left (-i \, \pi b^{2} - 2 \, a b^{2}\right )} x - \frac {3}{4} \, {\left (\pi ^{2} b - 4 i \, \pi a b - 4 \, a^{2} b\right )} \log \left (x\right ) - \frac {-i \, \pi ^{3} - 6 \, \pi ^{2} a + 12 i \, \pi a^{2} + 8 \, a^{3}}{8 \, x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {\operatorname {arcoth}\left (\tanh \left (b x + a\right )\right )^{3}}{x^{2}}\,{d x} \]________________________________________________________________________________________