Evaluate: `intx^2cos2x\ dx`

Explanation

To evaluate the integral \( I = \int x^2 \cos(2x) \, dx \), we will use the method of integration by parts.

### Step-by-Step Solution

1. **Identify the Functions**:
We will use the integration by parts formula:
\[
\int u \, dv = uv - \int v \, du
...