Evaluate: `int(x+2)\ sqrt(x^2+x+1)\ dx`

Explanation

To evaluate the integral \( I = \int (x + 2) \sqrt{x^2 + x + 1} \, dx \), we can follow these steps:

### Step 1: Express the Linear Term
We start by expressing the linear term \( x + 2 \) in terms of the derivative of the quadratic \( x^2 + x + 1 \). We can write:
\[ x + 2 = a(2x + 1) + b \]
where \( a \) and \( b \) are constants we need to determine.
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