Evaluate: `intxlog(1+x)\ dx`

Explanation

To evaluate the integral \( I = \int x \log(1+x) \, dx \), we will use the method of integration by parts. The formula for integration by parts is given by:

\[ \int u \, dv = uv - \int v \, du \]

### Step 1: Choose \( u \) and \( dv \)

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