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