\[ \int \frac {1}{\left (a+b \text {sech}^2(c+d x)\right )^{7/2}} \, dx \]
Optimal antiderivative \[ \frac {\arctanh \left (\frac {\sqrt {a}\, \tanh \left (d x +c \right )}{\sqrt {a +b -b \left (\tanh ^{2}\left (d x +c \right )\right )}}\right )}{a^{\frac {7}{2}} d}-\frac {b \left (33 a^{2}+40 a b +15 b^{2}\right ) \tanh \left (d x +c \right )}{15 a^{3} \left (a +b \right )^{3} d \sqrt {a +b -b \left (\tanh ^{2}\left (d x +c \right )\right )}}-\frac {b \tanh \left (d x +c \right )}{5 a \left (a +b \right ) d \left (a +b -b \left (\tanh ^{2}\left (d x +c \right )\right )\right )^{\frac {5}{2}}}-\frac {b \left (9 a +5 b \right ) \tanh \left (d x +c \right )}{15 a^{2} \left (a +b \right )^{2} d \left (a +b -b \left (\tanh ^{2}\left (d x +c \right )\right )\right )^{\frac {3}{2}}} \]
command
integrate(1/(a+b*sech(d*x+c)^2)^(7/2),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 \[ \text {Timed out} \]