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