52.1 Problem number 25

\[ \int \frac {\sin ^3(x)}{a+b \cos (x)} \, dx \]

Optimal antiderivative \[ -\frac {a \cos \left (x \right )}{b^{2}}+\frac {\cos ^{2}\left (x \right )}{2 b}+\frac {\left (a^{2}-b^{2}\right ) \ln \left (a +b \cos \left (x \right )\right )}{b^{3}} \]

command

integrate(sin(x)**3/(a+b*cos(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 \[ \text {Timed out} \]_____________________________________________________