5.3 Problem number 179

$$\int \frac{{\cos }^3(a+bx)}{\sqrt{\sin (2a+2bx)}}dx$$

Optimal antiderivative $$-\frac{3\arcsin (\cos (bx+a)-\sin (bx+a))}{8b}+\frac{3\ln (\cos (bx+a)+\sin (bx+a)+\sqrt{\sin }(2bx+2a))}{8b}+\frac{\cos (bx+a)\left(\sqrt{\sin }(2bx+2a)\right)}{4b}$$

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

$$\text{output too large to display}$$