\[ \int (a+a \sin (e+f x))^{5/2} \tan ^2(e+f x) \, dx \]
Optimal antiderivative \[ \frac {9 \sec \left (f x +e \right ) \left (a +a \sin \left (f x +e \right )\right )^{\frac {5}{2}}}{5 f}-\frac {2 \sec \left (f x +e \right ) \left (a +a \sin \left (f x +e \right )\right )^{\frac {7}{2}}}{5 a f}+\frac {124 a^{3} \cos \left (f x +e \right )}{15 f \sqrt {a +a \sin \left (f x +e \right )}}+\frac {31 a^{2} \cos \left (f x +e \right ) \sqrt {a +a \sin \left (f x +e \right )}}{15 f} \]
command
integrate((a+a*sin(f*x+e))^(5/2)*tan(f*x+e)^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________