\[ \int \frac {a+b \cos ^2(x)}{c+d \sin (x)} \, dx \]
Optimal antiderivative \[ \frac {b c x}{d^{2}}+\frac {b \cos \left (x \right )}{d}+\frac {2 a \arctan \left (\frac {d +c \tan \left (\frac {x}{2}\right )}{\sqrt {c^{2}-d^{2}}}\right )}{\sqrt {c^{2}-d^{2}}}-\frac {2 b \arctan \left (\frac {d +c \tan \left (\frac {x}{2}\right )}{\sqrt {c^{2}-d^{2}}}\right ) \sqrt {c^{2}-d^{2}}}{d^{2}} \]
command
integrate((a+b*cos(x)**2)/(c+d*sin(x)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________