Integrate the functions`(4x+2)sqrt(x^2+x+1)`

Explanation

To solve the integral \( \int (4x + 2) \sqrt{x^2 + x + 1} \, dx \), we can follow these steps:

### Step 1: Substitution
Let \( t = x^2 + x + 1 \). Then, we differentiate \( t \) with respect to \( x \):
\[ \frac{dt}{dx} = 2x + 1 \implies dt = (2x + 1) \, dx \]

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