Evaluate the integrals`int_0^2xsqrt(x+2)`

Explanation

To evaluate the integral \(\int_0^2 x \sqrt{x + 2} \, dx\), we will use the substitution method. Here’s the step-by-step solution:

### Step 1: Substitution
Let’s make the substitution:
\[ t = x + 2 \]
Then, differentiating both sides with respect to \(x\):
...