\[ \int \frac {\text {sech}^4(c+d x)}{\left (a+b \sinh ^2(c+d x)\right )^3} \, dx \]
Optimal antiderivative \[ \frac {b^{2} \left (48 a^{2}-16 a b +3 b^{2}\right ) \arctanh \left (\frac {\sqrt {a -b}\, \tanh \left (d x +c \right )}{\sqrt {a}}\right )}{8 a^{\frac {5}{2}} \left (a -b \right )^{\frac {9}{2}} d}+\frac {\left (a -4 b \right ) \tanh \left (d x +c \right )}{\left (a -b \right )^{4} d}-\frac {\tanh ^{3}\left (d x +c \right )}{3 \left (a -b \right )^{3} d}+\frac {b^{4} \tanh \left (d x +c \right )}{4 a \left (a -b \right )^{4} d \left (a -\left (a -b \right ) \left (\tanh ^{2}\left (d x +c \right )\right )\right )^{2}}-\frac {\left (16 a -3 b \right ) b^{3} \tanh \left (d x +c \right )}{8 a^{2} \left (a -b \right )^{4} d \left (a -\left (a -b \right ) \left (\tanh ^{2}\left (d x +c \right )\right )\right )} \]
command
integrate(sech(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 \[ \text {Timed out} \]