\[ \int \frac {\sinh ^4(c+d x)}{\left (a+b \tanh ^2(c+d x)\right )^3} \, dx \]
Optimal antiderivative \[ \frac {3 \left (a^{2}-10 a b +5 b^{2}\right ) x}{8 \left (a +b \right )^{5}}+\frac {3 \left (5 a^{2}-10 a b +b^{2}\right ) \arctan \left (\frac {\sqrt {b}\, \tanh \left (d x +c \right )}{\sqrt {a}}\right ) \sqrt {b}}{8 \left (a +b \right )^{5} d \sqrt {a}}-\frac {\left (5 a -3 b \right ) \cosh \left (d x +c \right ) \sinh \left (d x +c \right )}{8 \left (a +b \right )^{2} d \left (a +b \left (\tanh ^{2}\left (d x +c \right )\right )\right )^{2}}+\frac {\left (\cosh ^{3}\left (d x +c \right )\right ) \sinh \left (d x +c \right )}{4 \left (a +b \right ) d \left (a +b \left (\tanh ^{2}\left (d x +c \right )\right )\right )^{2}}+\frac {\left (7 a -5 b \right ) b \tanh \left (d x +c \right )}{8 \left (a +b \right )^{3} d \left (a +b \left (\tanh ^{2}\left (d x +c \right )\right )\right )^{2}}+\frac {3 \left (a -b \right ) b \tanh \left (d x +c \right )}{2 \left (a +b \right )^{4} d \left (a +b \left (\tanh ^{2}\left (d x +c \right )\right )\right )} \]
command
integrate(sinh(d*x+c)^4/(a+b*tanh(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 \[ \text {Timed out} \]