If ∫ (2x² + 5x + 9)/(√(x² + x + 1)) dx = x √(x² + x + 1) + α √(x² + x + 1) + β log e | x + 1/2 + √(x² + x + 1) | + C, where C is the constant of integration, then α + 2 β is equal to:

Unclassified (maths): JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q197

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumUnclassified (maths)

\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:

Your answerInteger or decimal