`intxsqrt(x+2)dx`

Explanation

To solve the integral \( \int x \sqrt{x + 2} \, dx \), we will use a substitution method. Here’s a step-by-step solution:

### Step 1: Substitution
Let \( t = x + 2 \). Then, we differentiate to find \( dx \):
\[ dx = dt \]
Also, we can express \( x \) in terms of \( t \):
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