Evaluate the following integral: `int_0^1log(1+x)dx`

Explanation

To evaluate the integral \( I = \int_0^1 \log(1+x) \, dx \), we can use integration by parts. Let's go through the steps one by one.

### Step 1: Set up the integration by parts
We choose:
- \( u = \log(1+x) \) (First function)
- \( dv = dx \) (Second function)

Now we need to find \( du \) and \( v \):
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