`int_(0)^(2) x sqrt(x+2) dx " (put x+2 " =t^(2)")"`

Explanation

To solve the integral \( \int_{0}^{2} x \sqrt{x+2} \, dx \) using the substitution \( x + 2 = t^2 \), we will follow these steps:

### Step 1: Substitution
Let \( x + 2 = t^2 \). Then, we can express \( x \) in terms of \( t \):
\[ x = t^2 - 2 \]

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