Evaluate: `intcos^3 3x\ dx`

Explanation

To evaluate the integral \( \int \cos^3(3x) \, dx \), we can follow these steps:

### Step 1: Use the identity for \( \cos^3(x) \)
We can express \( \cos^3(3x) \) in terms of \( \cos(3x) \) and \( \cos(9x) \) using the identity:
\[ \cos^3(x) = \frac{1}{4} \left(3\cos(x) + \cos(3x)\right) \]
Thus, we have:
...