\[ \int \frac {\text {csch}^4(c+d x)}{\left (a+b \text {sech}^2(c+d x)\right )^3} \, dx \]
Optimal antiderivative \[ \frac {\left (a -2 b \right ) \coth \left (d x +c \right )}{\left (a +b \right )^{4} d}-\frac {\coth ^{3}\left (d x +c \right )}{3 \left (a +b \right )^{3} d}-\frac {5 \left (3 a -4 b \right ) \arctanh \left (\frac {\sqrt {b}\, \tanh \left (d x +c \right )}{\sqrt {a +b}}\right ) \sqrt {b}}{8 \left (a +b \right )^{\frac {9}{2}} d}-\frac {a b \tanh \left (d x +c \right )}{4 \left (a +b \right )^{3} d \left (a +b -b \left (\tanh ^{2}\left (d x +c \right )\right )\right )^{2}}-\frac {\left (7 a -4 b \right ) b \tanh \left (d x +c \right )}{8 \left (a +b \right )^{4} d \left (a +b -b \left (\tanh ^{2}\left (d x +c \right )\right )\right )} \]
command
integrate(csch(d*x+c)^4/(a+b*sech(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 \[ \text {Timed out} \]