Question

Integrate:
$\int \sin x\sqrt{1+\cos 2x}dx$

Answer 1

$\int sinx\sqrt{1+(2co{s}^{2}x-1)}dx=\int sinx\times \sqrt{2}cosxdx=\sqrt{2}\int sinxcosxdx=\left(\frac{\sqrt{2}}{2}\right)\int sin2xdx=\left(\frac{1}{\sqrt{2}}\right)[-(\frac{cos2x}{2}\left)\right]+C=\left(\frac{-cos2x}{2\sqrt{2}}\right)+C$