\[ \int \left (a+b \text {csch}^2(c+d x)\right )^{5/2} \, dx \]
Optimal antiderivative \[ \frac {a^{\frac {5}{2}} \arctanh \left (\frac {\coth \left (d x +c \right ) \sqrt {a}}{\sqrt {a -b +b \left (\coth ^{2}\left (d x +c \right )\right )}}\right )}{d}-\frac {b \coth \left (d x +c \right ) \left (a -b +b \left (\coth ^{2}\left (d x +c \right )\right )\right )^{\frac {3}{2}}}{4 d}-\frac {\left (15 a^{2}-10 a b +3 b^{2}\right ) \arctanh \left (\frac {\coth \left (d x +c \right ) \sqrt {b}}{\sqrt {a -b +b \left (\coth ^{2}\left (d x +c \right )\right )}}\right ) \sqrt {b}}{8 d}-\frac {\left (7 a -3 b \right ) b \coth \left (d x +c \right ) \sqrt {a -b +b \left (\coth ^{2}\left (d x +c \right )\right )}}{8 d} \]
command
integrate((a+b*csch(d*x+c)^2)^(5/2),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 \[ \text {Timed out} \]