\[ \int \sqrt {a-a \sin ^2(e+f x)} \tan ^3(e+f x) \, dx \]
Optimal antiderivative \[ \frac {a}{f \sqrt {a \left (\cos ^{2}\left (f x +e \right )\right )}}+\frac {\sqrt {a \left (\cos ^{2}\left (f x +e \right )\right )}}{f} \]
command
integrate((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {4 \, \sqrt {a} \mathrm {sgn}\left (\tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{4} - 1\right )}{{\left (\tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{4} - 1\right )} f} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________