\[ \int \frac {\tanh ^5(e+f x)}{\sqrt {a+a \sinh ^2(e+f x)}} \, dx \]
Optimal antiderivative \[ -\frac {a^{2}}{5 f \left (a \left (\cosh ^{2}\left (f x +e \right )\right )\right )^{\frac {5}{2}}}+\frac {2 a}{3 f \left (a \left (\cosh ^{2}\left (f x +e \right )\right )\right )^{\frac {3}{2}}}-\frac {1}{f \sqrt {a \left (\cosh ^{2}\left (f x +e \right )\right )}} \]
command
integrate(tanh(f*x+e)^5/(a+a*sinh(f*x+e)^2)^(1/2),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
\[ -\frac {2 \, {\left (15 \, \sqrt {a} e^{\left (9 \, f x + 9 \, e\right )} + 20 \, \sqrt {a} e^{\left (7 \, f x + 7 \, e\right )} + 58 \, \sqrt {a} e^{\left (5 \, f x + 5 \, e\right )} + 20 \, \sqrt {a} e^{\left (3 \, f x + 3 \, e\right )} + 15 \, \sqrt {a} e^{\left (f x + e\right )}\right )}}{15 \, a f {\left (e^{\left (2 \, f x + 2 \, e\right )} + 1\right )}^{5}} \]