\[ \int \frac {1}{\left (a+b \text {sech}^2(c+d x)\right )^4} \, dx \]
Optimal antiderivative \[ \frac {x}{a^{4}}-\frac {\left (35 a^{3}+70 a^{2} b +56 a \,b^{2}+16 b^{3}\right ) \arctanh \left (\frac {\sqrt {b}\, \tanh \left (d x +c \right )}{\sqrt {a +b}}\right ) \sqrt {b}}{16 a^{4} \left (a +b \right )^{\frac {7}{2}} d}-\frac {b \tanh \left (d x +c \right )}{6 a \left (a +b \right ) d \left (a +b -b \left (\tanh ^{2}\left (d x +c \right )\right )\right )^{3}}-\frac {b \left (11 a +6 b \right ) \tanh \left (d x +c \right )}{24 a^{2} \left (a +b \right )^{2} d \left (a +b -b \left (\tanh ^{2}\left (d x +c \right )\right )\right )^{2}}-\frac {b \left (19 a^{2}+22 a b +8 b^{2}\right ) \tanh \left (d x +c \right )}{16 a^{3} \left (a +b \right )^{3} d \left (a +b -b \left (\tanh ^{2}\left (d x +c \right )\right )\right )} \]
command
integrate(1/(a+b*sech(d*x+c)^2)^4,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 \[ \text {Timed out} \]