\[ \int \frac {\coth ^4(c+d x)}{\left (a+b \tanh ^2(c+d x)\right )^3} \, dx \]
Optimal antiderivative \[ \frac {x}{\left (a +b \right )^{3}}+\frac {b^{\frac {5}{2}} \left (63 a^{2}+90 a b +35 b^{2}\right ) \arctan \left (\frac {\sqrt {b}\, \tanh \left (d x +c \right )}{\sqrt {a}}\right )}{8 a^{\frac {9}{2}} \left (a +b \right )^{3} d}-\frac {\left (8 a^{3}-8 a^{2} b -55 a \,b^{2}-35 b^{3}\right ) \coth \left (d x +c \right )}{8 a^{4} \left (a +b \right )^{2} d}-\frac {\left (8 a^{2}+55 a b +35 b^{2}\right ) \left (\coth ^{3}\left (d x +c \right )\right )}{24 a^{3} \left (a +b \right )^{2} d}+\frac {b \left (\coth ^{3}\left (d x +c \right )\right )}{4 a \left (a +b \right ) d \left (a +b \left (\tanh ^{2}\left (d x +c \right )\right )\right )^{2}}+\frac {b \left (11 a +7 b \right ) \left (\coth ^{3}\left (d x +c \right )\right )}{8 a^{2} \left (a +b \right )^{2} d \left (a +b \left (\tanh ^{2}\left (d x +c \right )\right )\right )} \]
command
integrate(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \text {output too large to display} \]
Fricas 1.3.7 via sagemath 9.3 output \[ \text {Timed out} \]