\[ \int \frac {\text {sech}^7(c+d x)}{\left (a+b \tanh ^2(c+d x)\right )^2} \, dx \]
Optimal antiderivative \[ \frac {\left (4 a +5 b \right ) \arctan \! \left (\sinh \! \left (d x +c \right )\right )}{2 b^{3} d}-\frac {\left (4 a -b \right ) \left (a +b \right )^{\frac {3}{2}} \arctan \! \left (\frac {\sinh \left (d x +c \right ) \sqrt {a +b}}{\sqrt {a}}\right )}{2 a^{\frac {3}{2}} b^{3} d}+\frac {\left (a +b \right ) \left (2 a +b \right ) \sinh \! \left (d x +c \right )}{2 a \,b^{2} d \left (a +\left (a +b \right ) \left (\sinh ^{2}\left (d x +c \right )\right )\right )}-\frac {\mathrm {sech}\! \left (d x +c \right ) \tanh \! \left (d x +c \right )}{2 b d \left (a +\left (a +b \right ) \left (\sinh ^{2}\left (d x +c \right )\right )\right )} \]
command
integrate(sech(d*x+c)^7/(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
\[ \text {output too large to display} \]