Evaluate the following integral: `int_0^2x\ sqrt(x+2)\ dx`

Explanation

To evaluate the integral \( \int_0^2 x \sqrt{x+2} \, dx \), we will use a substitution method.

### Step-by-Step Solution:

1. **Substitution**: Let \( u = x + 2 \). Then, we have:
\[ du = dx \quad \text{and} \quad x = u - 2 \]
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