\[ \int \cos ^3(a+b x) \sqrt {\sin (2 a+2 b x)} \, dx \]
Optimal antiderivative \[ -\frac {5 \arcsin \! \left (\cos \! \left (b x +a \right )-\sin \! \left (b x +a \right )\right )}{32 b}-\frac {5 \ln \! \left (\cos \! \left (b x +a \right )+\sin \! \left (b x +a \right )+\sqrt {\sin }\left (2 b x +2 a \right )\right )}{32 b}+\frac {\cos \! \left (b x +a \right ) \left (\sin ^{\frac {3}{2}}\left (2 b x +2 a \right )\right )}{8 b}+\frac {5 \sin \! \left (b x +a \right ) \left (\sqrt {\sin }\left (2 b x +2 a \right )\right )}{16 b} \]
command
int(cos(b*x+a)^3*sin(2*b*x+2*a)^(1/2),x)
Maple 2022.1 output
hanged
Maple 2021.1 output
\[ \text {output too large to display} \]