\[ \int \sin ^2(a+b x) \sin ^{\frac {7}{2}}(2 a+2 b x) \, dx \]
Optimal antiderivative \[ -\frac {5 \sqrt {\frac {1}{2}+\frac {\sin \left (2 b x +2 a \right )}{2}}\, \EllipticF \left (\cos \left (a +\frac {\pi }{4}+b x \right ), \sqrt {2}\right )}{42 \sin \left (a +\frac {\pi }{4}+b x \right ) b}-\frac {\cos \left (2 b x +2 a \right ) \left (\sin ^{\frac {5}{2}}\left (2 b x +2 a \right )\right )}{14 b}-\frac {\sin ^{\frac {9}{2}}\left (2 b x +2 a \right )}{18 b}-\frac {5 \cos \left (2 b x +2 a \right ) \left (\sqrt {\sin }\left (2 b x +2 a \right )\right )}{42 b} \]
command
int(sin(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(\text {Expression too large to display}\) | \(519395265\) |
Maple 2021.1 output
\[ \int \left (\sin ^{2}\left (b x +a \right )\right ) \left (\sin ^{\frac {7}{2}}\left (2 b x +2 a \right )\right )\, dx \]________________________________________________________________________________________