# Weird Trigonometric Integral

## Homework Statement

I need to calculate the integral:
$$\int_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}\mathrm{d}x$$

## The Attempt at a Solution

There is a tip: "try substituting $$y=\frac{\pi}{2}-x$$. I tried it and didn't get anywhere. I also tried several trigonometric identities.