I would like to know if there is some way to calculate exactly
$$\int_{0}^{\pi/2} \frac{\cos^3 x}{\sqrt {\sin x}(1+\sin^3 x)}\,dx$$
The numerical value is 1,52069
I would like to know if there is some way to calculate exactly
$$\int_{0}^{\pi/2} \frac{\cos^3 x}{\sqrt {\sin x}(1+\sin^3 x)}\,dx$$
The numerical value is 1,52069