\[ \int \cos ^3(a+b x) (c \sin (a+b x))^m \, dx \]
Optimal antiderivative \[ \frac {\left (c \sin \left (b x +a \right )\right )^{1+m}}{b c \left (1+m \right )}-\frac {\left (c \sin \left (b x +a \right )\right )^{3+m}}{b \,c^{3} \left (3+m \right )} \]
command
int(cos(b*x+a)^3*(c*sin(b*x+a))^m,x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(1318\) |
Maple 2021.1 output
\[ \int \left (\cos ^{3}\left (b x +a \right )\right ) \left (c \sin \left (b x +a \right )\right )^{m}\, dx \]________________________________________________________________________________________