\[ \int \frac {1}{\left (a+b \text {csch}^2(c+d x)\right )^4} \, dx \]
Optimal antiderivative \[ \frac {x}{a^{4}}+\frac {b \coth \left (d x +c \right )}{6 a \left (a -b \right ) d \left (a -b +b \left (\coth ^{2}\left (d x +c \right )\right )\right )^{3}}+\frac {\left (11 a -6 b \right ) b \coth \left (d x +c \right )}{24 a^{2} \left (a -b \right )^{2} d \left (a -b +b \left (\coth ^{2}\left (d x +c \right )\right )\right )^{2}}+\frac {b \left (19 a^{2}-22 a b +8 b^{2}\right ) \coth \left (d x +c \right )}{16 a^{3} \left (a -b \right )^{3} d \left (a -b +b \left (\coth ^{2}\left (d x +c \right )\right )\right )}-\frac {\left (35 a^{3}-70 a^{2} b +56 a \,b^{2}-16 b^{3}\right ) \arctan \left (\frac {\sqrt {a -b}\, \tanh \left (d x +c \right )}{\sqrt {b}}\right ) \sqrt {b}}{16 a^{4} \left (a -b \right )^{\frac {7}{2}} d} \]
command
integrate(1/(a+b*csch(d*x+c)^2)^4,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 \[ \text {Timed out} \]