\[ \int \frac {\text {csch}^3(c+d x)}{\left (a+b \sinh ^2(c+d x)\right )^3} \, dx \]
Optimal antiderivative \[ \frac {b^{\frac {3}{2}} \left (35 a^{2}-56 a b +24 b^{2}\right ) \arctan \left (\frac {\cosh \left (d x +c \right ) \sqrt {b}}{\sqrt {a -b}}\right )}{8 a^{4} \left (a -b \right )^{\frac {5}{2}} d}+\frac {\left (a +6 b \right ) \arctanh \left (\cosh \left (d x +c \right )\right )}{2 a^{4} d}-\frac {\left (2 a -3 b \right ) b \cosh \left (d x +c \right )}{4 a^{2} \left (a -b \right ) d \left (a -b +b \left (\cosh ^{2}\left (d x +c \right )\right )\right )^{2}}-\frac {\left (a -4 b \right ) \left (4 a -3 b \right ) b \cosh \left (d x +c \right )}{8 a^{3} \left (a -b \right )^{2} d \left (a -b +b \left (\cosh ^{2}\left (d x +c \right )\right )\right )}-\frac {\coth \left (d x +c \right ) \mathrm {csch}\left (d x +c \right )}{2 a d \left (a -b +b \left (\cosh ^{2}\left (d x +c \right )\right )\right )^{2}} \]
command
integrate(csch(d*x+c)^3/(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 \[ \text {Timed out} \]