`intcos^4 2x\ dx`

Explanation

To solve the integral \(\int \cos^4(2x) \, dx\), we can follow these steps:

### Step 1: Rewrite the Integral
We start by rewriting \(\cos^4(2x)\) as \((\cos^2(2x))^2\).

\[ \int \cos^4(2x) \, dx = \int (\cos^2(2x))^2 \, dx \]
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