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Integrate the function
$\sqrt{\sin 2 x} \cos 2 x$
$\sqrt{\sin 2 x} \cos 2 x$
Solution:
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Verified Answer
Put $\sin 2 x=t^2 \Rightarrow \cos 2 x d x=t d t$
$\begin{aligned}
&\therefore \int \sqrt{\sin 2 x} \cdot \cos 2 x d x=\int t \cdot t d t=\frac{t^3}{3}+C \\
&=\frac{(\sin 2 x)^{3 / 2}}{3}+C
\end{aligned}$
$\begin{aligned}
&\therefore \int \sqrt{\sin 2 x} \cdot \cos 2 x d x=\int t \cdot t d t=\frac{t^3}{3}+C \\
&=\frac{(\sin 2 x)^{3 / 2}}{3}+C
\end{aligned}$
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