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