Evaluate: `intsin^4 2x\ dx`

Explanation

To evaluate the integral \( I = \int \sin^4(2x) \, dx \), we will follow these steps:

### Step 1: Rewrite the Integral
We start by rewriting \( \sin^4(2x) \) using the identity \( \sin^2(2x) = 1 - \cos^2(2x) \):
\[ \sin^4(2x) = \sin^2(2x) \cdot \sin^2(2x) = \sin^2(2x)(1 - \cos^2(2x)) \]
Thus, we can express the integral as:
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