`intcos^(3)x" " dx=`

Explanation

To solve the integral \( \int \cos^3 x \, dx \), we can use the trigonometric identity for \( \cos 3x \). Here's the step-by-step solution:

### Step 1: Use the trigonometric identity
We know that:
\[ \cos 3x = 4 \cos^3 x - 3 \cos x \]
From this, we can express \( \cos^3 x \) in terms of \( \cos 3x \):
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