If \int {2 x^2+5 x+9}/{\sqrt{x^2+x+1}} \dx=x \sqrt{x^2+x+1}+\alpha \sqrt{x^2+x+1}+ , \beta \log _e{| x+\frac{1}{2}+\sqrt{x^2+x+1} |}+C where C is the constant of integration, then \alpha+2 \beta is equal to_____ [24 Jan 2025 Shift 2]

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