Question

Integrate the function $\sqrt{\sin 2x}\cos 2x$

Answer 1

Let $\sin 2x=t$
$\therefore 2\cos 2xdx=dt$
$\Rightarrow \int \sqrt{\sin 2x}\cos 2xdx=\frac{1}{2}\int \sqrt{t}dt$
$=\frac{1}{2}\left(\frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right)+C$
$=\frac{1}{3}{t}^{\frac{3}{2}}+C$
$=\frac{1}{3}(\sin 2x{)}^{\frac{3}{2}}+C$