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