\[ \int \frac {\text {csch}^4(c+d x)}{\left (a+b \sinh ^2(c+d x)\right )^3} \, dx \]
Optimal antiderivative \[ \frac {b^{2} \left (48 a^{2}-80 a b +35 b^{2}\right ) \arctanh \left (\frac {\sqrt {a -b}\, \tanh \left (d x +c \right )}{\sqrt {a}}\right )}{8 a^{\frac {9}{2}} \left (a -b \right )^{\frac {5}{2}} d}+\frac {\left (8 a^{3}-4 a^{2} b -45 a \,b^{2}+35 b^{3}\right ) \coth \left (d x +c \right )}{8 a^{4} \left (a -b \right )^{2} d}-\frac {\left (8 a^{2}-52 a b +35 b^{2}\right ) \left (\coth ^{3}\left (d x +c \right )\right )}{24 a^{3} \left (a -b \right )^{2} d}-\frac {b \mathrm {csch}\left (d x +c \right )^{3} \mathrm {sech}\left (d x +c \right )^{3}}{4 a \left (a -b \right ) d \left (a -\left (a -b \right ) \left (\tanh ^{2}\left (d x +c \right )\right )\right )^{2}}-\frac {\left (10 a -7 b \right ) b \mathrm {csch}\left (d x +c \right )^{3} \mathrm {sech}\left (d x +c \right )}{8 a^{2} \left (a -b \right )^{2} d \left (a -\left (a -b \right ) \left (\tanh ^{2}\left (d x +c \right )\right )\right )} \]
command
integrate(csch(d*x+c)^4/(a+b*sinh(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 \[ \text {Timed out} \]