Evaluate: `int(x^2)/(sqrt(x+2))dx`

Explanation

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

### Step 1: Substitution
Let \( u = \sqrt{x + 2} \). Then, squaring both sides gives us:
\[ u^2 = x + 2 \implies x = u^2 - 2 \]
Next, we differentiate \( x \) with respect to \( u \) to find \( dx \):
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