Evaluate: `intx^3\ (logx)^2\ dx`

Explanation

To evaluate the integral \( I = \int x^3 (\log x)^2 \, dx \), we will use integration by parts. Here’s a step-by-step solution:

### Step 1: Set up integration by parts
We will use the integration by parts formula:
\[ \int u \, dv = uv - \int v \, du \]
Let:
...