If ∫ (2 x^2+5 x+9)/(√(x^2+x+1)) d x=x √(x^2+x+1)+α √(x^2+x+1)+β log_e |x+1/2+√(x^2+x+1)|+ C, where C is the constant of integration, then α+2 β is…

If $\displaystyle \int \frac{2 x^2+5 x+9}{\sqrt{x^2+x+1}} \mathrm{~d} x=x \sqrt{x^2+x+1}+\alpha \sqrt{x^2+x+1}+\beta \log _{\mathrm{e}}\left|x+\frac{1}{2}+\sqrt{x^2+x+1}\right|+\mathrm{C}$, where $\displaystyle C$ is the constant of integration, then $\displaystyle \alpha+2 \beta$ is equal to $\displaystyle \_\_\_\_$.