\[ \int \frac {\tan (e+f x)}{\left (a+b \sec ^2(e+f x)\right )^3} \, dx \]
Optimal antiderivative \[ \frac {b^{2}}{4 a^{3} f \left (b +a \left (\cos ^{2}\left (f x +e \right )\right )\right )^{2}}-\frac {b}{a^{3} f \left (b +a \left (\cos ^{2}\left (f x +e \right )\right )\right )}-\frac {\ln \left (b +a \left (\cos ^{2}\left (f x +e \right )\right )\right )}{2 a^{3} f} \]
command
integrate(tan(f*x+e)/(a+b*sec(f*x+e)^2)^3,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 \[ \text {Exception raised: NotImplementedError} \]_______________________________________________________