Question:
$\sqrt{\sin 2 x} \cos 2 x$
Solution:
Let $\sin 2 x=t$
$\therefore 2 \cos 2 x d x=d t$
$\Rightarrow \int \sqrt{\sin 2 x} \cos 2 x d x=\frac{1}{2} \int \sqrt{t} d t$
$=\frac{1}{2}\left(\frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right)+\mathrm{C}$
$=\frac{1}{3} t^{\frac{3}{2}}+\mathrm{C}$
$=\frac{1}{3}(\sin 2 x)^{\frac{3}{2}}+\mathrm{C}$
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