Evaluate: `intxcos^2x\ dx`

Explanation

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

### Step 1: Rewrite \( \cos^2 x \) using a trigonometric identity
We know that:
\[ \cos^2 x = \frac{1 + \cos 2x}{2} \]
Thus, we can rewrite the integral as:
...