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

Explanation

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

### Step 1: Express the linear term as a combination of the derivative of the quadratic and a constant
We start by expressing \( x + 1 \) in terms of the derivative of the quadratic \( 1 - x - x^2 \). The derivative of the quadratic is:
\[ \frac{d}{dx}(1 - x - x^2) = -1 - 2x \]
So, we can write:
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