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

Explanation

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

### Step 1: Express the linear term
We can express the linear term \( x + 1 \) in terms of the derivative of the quadratic \( x^2 - x + 1 \). We will write:

\[ x + 1 = a(2x - 1) + b \]
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