Standard algebraic and irrational integralsHard

Integral of Algebraic Radical Function

If $\int {\,\frac{{2{x^2} + 5x + 9}}{{\sqrt {{x^2} + x + 1} }}dx}$ $= x\sqrt {{x^2} + x + 1} + \alpha \sqrt {{x^2} + x + 1} +$ $\beta {\log _e}\left| {x + \frac{1}{2} + \sqrt {{x^2} + x + 1} } \right| + C$ where C is the constant of integration, then α + 2β is equal to ___

Ask about this question