\[ \int \frac {\cos ^7(c+d x) \sin ^5(c+d x)}{a+a \sin (c+d x)} \, dx \]
Optimal antiderivative \[ \frac {\sin ^{6}\left (d x +c \right )}{6 a d}-\frac {\sin ^{7}\left (d x +c \right )}{7 a d}-\frac {\sin ^{8}\left (d x +c \right )}{4 a d}+\frac {2 \left (\sin ^{9}\left (d x +c \right )\right )}{9 a d}+\frac {\sin ^{10}\left (d x +c \right )}{10 a d}-\frac {\sin ^{11}\left (d x +c \right )}{11 a d} \]
command
integrate(cos(d*x+c)**7*sin(d*x+c)**5/(a+a*sin(d*x+c)),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 \[ \text {Timed out} \]_____________________________________________________