Question

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

Answer 1

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

$=\int \sqrt{{\cos }^{2}x+{\sin }^{2}x+2\sin x\cos x}dx$

$=\int \sqrt{(\cos x+\sin x{)}^2}dx$

$=\int \cos x+\sin xdx$

$=\sin x-\cos x+C$.