\[ \int \frac {(c-c \sec (e+f x))^3}{(a+a \sec (e+f x))^2} \, dx \]
Optimal antiderivative \[ \frac {c^{3} x}{a^{2}}-\frac {c^{3} \arctanh \left (\sin \left (f x +e \right )\right )}{a^{2} f}-\frac {8 c^{3} \tan \left (f x +e \right )}{3 a^{2} f \left (1+\sec \left (f x +e \right )\right )^{2}}+\frac {4 c^{3} \tan \left (f x +e \right )}{3 a^{2} f \left (1+\sec \left (f x +e \right )\right )} \]
command
integrate((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {\frac {4 \, c^{3} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{3}}{a^{2}} + \frac {3 \, {\left (f x + e\right )} c^{3}}{a^{2}} - \frac {3 \, c^{3} \log \left ({\left | \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) + 1 \right |}\right )}{a^{2}} + \frac {3 \, c^{3} \log \left ({\left | \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) - 1 \right |}\right )}{a^{2}}}{3 \, f} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________