\[ \int \frac {\text {sech}^5(c+d x)}{\left (a+b \tanh ^2(c+d x)\right )^2} \, dx \]
Optimal antiderivative \[ \frac {\arctan \! \left (\sinh \! \left (d x +c \right )\right )}{b^{2} d}+\frac {\left (a +b \right ) \sinh \! \left (d x +c \right )}{2 a b d \left (a +\left (a +b \right ) \left (\sinh ^{2}\left (d x +c \right )\right )\right )}-\frac {\left (2 a -b \right ) \arctan \! \left (\frac {\sinh \left (d x +c \right ) \sqrt {a +b}}{\sqrt {a}}\right ) \sqrt {a +b}}{2 a^{\frac {3}{2}} b^{2} d} \]
command
integrate(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2)^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {Exception raised: TypeError} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {output too large to display} \]