Answer
\begin{aligned}
\int \sin ^{4} 2 x \cos 2 x d x =\frac{1}{10} \sin ^{5} 2 x+C
\end{aligned}
Work Step by Step
Given $$\begin{equation}
\int \sin ^{4} 2 x \cos 2 x d x
\end{equation}$$
So, we have
\begin{aligned}
I&=\int \sin ^{4} 2 x \cos 2 x d x\\
&=\frac{1}{2} \int \sin ^{4} 2 x \cos 2 x \cdot 2 d x\\
&=\frac{1}{10} \sin ^{5} 2 x+C
\end{aligned}
