\[ \int \frac {a+b \coth ^{-1}(c+d x)}{(e+f x)^3} \, dx \]
Optimal antiderivative \[ \frac {b d}{2 \left (-c f +d e -f \right ) \left (-c f +d e +f \right ) \left (f x +e \right )}+\frac {-a -b \,\mathrm {arccoth}\left (d x +c \right )}{2 f \left (f x +e \right )^{2}}-\frac {b \,d^{2} \ln \left (-d x -c +1\right )}{4 f \left (-c f +d e +f \right )^{2}}+\frac {b \,d^{2} \ln \left (d x +c +1\right )}{4 f \left (-c f +d e -f \right )^{2}}-\frac {b \,d^{2} \left (-c f +d e \right ) \ln \left (f x +e \right )}{\left (-c f +d e +f \right )^{2} \left (d e -\left (1+c \right ) f \right )^{2}} \]
command
integrate((a+b*arccoth(d*x+c))/(f*x+e)^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \int \frac {b \operatorname {arcoth}\left (d x + c\right ) + a}{{\left (f x + e\right )}^{3}}\,{d x} \]_______________________________________________________