\[ \int \frac {\text {csch}^2(c+d x)}{\left (a-b \sinh ^4(c+d x)\right )^3} \, dx \]
Optimal antiderivative \[ -\frac {\coth \left (d x +c \right )}{a^{3} d}-\frac {3 \arctanh \left (\frac {\sqrt {\sqrt {a}-\sqrt {b}}\, \tanh \left (d x +c \right )}{a^{\frac {1}{4}}}\right ) \sqrt {b}\, \left (20 a +15 b -34 \sqrt {a}\, \sqrt {b}\right )}{64 a^{\frac {13}{4}} d \left (\sqrt {a}-\sqrt {b}\right )^{\frac {5}{2}}}+\frac {3 \arctanh \left (\frac {\sqrt {\sqrt {a}+\sqrt {b}}\, \tanh \left (d x +c \right )}{a^{\frac {1}{4}}}\right ) \sqrt {b}\, \left (20 a +15 b +34 \sqrt {a}\, \sqrt {b}\right )}{64 a^{\frac {13}{4}} d \left (\sqrt {a}+\sqrt {b}\right )^{\frac {5}{2}}}+\frac {b^{2} \tanh \left (d x +c \right ) \left (a \left (a +3 b \right )-\left (a^{2}+6 a b +b^{2}\right ) \left (\tanh ^{2}\left (d x +c \right )\right )\right )}{8 a^{2} \left (a -b \right )^{3} d \left (a -2 a \left (\tanh ^{2}\left (d x +c \right )\right )+\left (a -b \right ) \left (\tanh ^{4}\left (d x +c \right )\right )\right )^{2}}+\frac {b \tanh \left (d x +c \right ) \left (\frac {2 a^{2} \left (9 a -17 b \right )}{\left (a -b \right )^{3}}-\frac {\left (18 a^{2}+15 a b -13 b^{2}\right ) \left (\tanh ^{2}\left (d x +c \right )\right )}{\left (a -b \right )^{2}}\right )}{32 a^{3} d \left (a -2 a \left (\tanh ^{2}\left (d x +c \right )\right )+\left (a -b \right ) \left (\tanh ^{4}\left (d x +c \right )\right )\right )} \]
command
integrate(csch(d*x+c)^2/(a-b*sinh(d*x+c)^4)^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 \[ \text {Timed out} \]