\[ \int \frac {\text {csch}^3(c+d x)}{\left (a+b \text {sech}^2(c+d x)\right )^3} \, dx \]
Optimal antiderivative \[ \frac {\left (a -5 b \right ) \arctanh \left (\cosh \left (d x +c \right )\right )}{2 \left (a +b \right )^{4} d}+\frac {\left (2 a -b \right ) b \cosh \left (d x +c \right )}{4 a \left (a +b \right )^{2} d \left (b +a \left (\cosh ^{2}\left (d x +c \right )\right )\right )^{2}}-\frac {\left (4 a^{2}-9 a b -b^{2}\right ) \cosh \left (d x +c \right )}{8 a \left (a +b \right )^{3} d \left (b +a \left (\cosh ^{2}\left (d x +c \right )\right )\right )}-\frac {\cosh \left (d x +c \right ) \left (\coth ^{2}\left (d x +c \right )\right )}{2 \left (a +b \right ) d \left (b +a \left (\cosh ^{2}\left (d x +c \right )\right )\right )^{2}}-\frac {\left (15 a^{2}-10 a b -b^{2}\right ) \arctan \left (\frac {\cosh \left (d x +c \right ) \sqrt {a}}{\sqrt {b}}\right ) \sqrt {b}}{8 a^{\frac {3}{2}} \left (a +b \right )^{4} d} \]
command
integrate(csch(d*x+c)^3/(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 \[ \text {Timed out} \]