Evaluate: `intcos^4x\ dx`

Explanation

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

### Step 1: Rewrite \( \cos^4 x \)
We can express \( \cos^4 x \) as \( (\cos^2 x)^2 \). Using the identity for \( \cos^2 x \):
\[ \cos^2 x = \frac{1 + \cos 2x}{2} \]
we can substitute this into our expression:
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