If \(\displaystyle \int \frac{2x^2 + 5x + 9}{\sqrt{x^2 + x + 1}} \, dx = x\sqrt{x^2 + x + 1} + \alpha \sqrt{x^2 + x + 1} + \beta \log_{e}\left| x + \frac{1}{2} + \sqrt{x^2 + x + 1} \right| + C \), where \( C \) is the constant of integration, then \( \alpha + 2\beta \) is equal to ____________.
