Question

Solve $\int \sqrt{2+\sin 3x}\cos 3xdx$

Answer 1

$I=\int \sqrt{2+\sin 3x}\cos 3xdx.$

Put $2+\sin 3x=t$

$\therefore 3\cos 3xdx=dt.$

$\therefore I=\frac{1}{3}\int \sqrt{t}dt$

$=\frac{1}{3}.\frac{2}{3}{t}^{3/2}+C$

$I=\frac{2}{9}{(2+\sin 3x)}^{3/2}+C$