\[ \int \frac {\coth ^8(e+f x)}{\left (a+a \sinh ^2(e+f x)\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {\coth \! \left (f x +e \right ) \mathrm {csch}\! \left (f x +e \right )^{2}}{3 a f \sqrt {a \left (\cosh ^{2}\left (f x +e \right )\right )}}-\frac {2 \coth \! \left (f x +e \right ) \mathrm {csch}\! \left (f x +e \right )^{4}}{5 a f \sqrt {a \left (\cosh ^{2}\left (f x +e \right )\right )}}-\frac {\coth \! \left (f x +e \right ) \mathrm {csch}\! \left (f x +e \right )^{6}}{7 a f \sqrt {a \left (\cosh ^{2}\left (f x +e \right )\right )}} \]
command
integrate(coth(f*x+e)^8/(a+a*sinh(f*x+e)^2)^(3/2),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
\[ -\frac {8 \, {\left (35 \, \sqrt {a} e^{\left (11 \, f x + 11 \, e\right )} + 28 \, \sqrt {a} e^{\left (9 \, f x + 9 \, e\right )} + 114 \, \sqrt {a} e^{\left (7 \, f x + 7 \, e\right )} + 28 \, \sqrt {a} e^{\left (5 \, f x + 5 \, e\right )} + 35 \, \sqrt {a} e^{\left (3 \, f x + 3 \, e\right )}\right )}}{105 \, a^{2} f {\left (e^{\left (2 \, f x + 2 \, e\right )} - 1\right )}^{7}} \]