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Indefinite Integrals question

2025 · 24 Jan · Shift 2 · Q47

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JEE Main
Mathematics
Indefinite Integrals
2025 · 24 Jan · Shift 2 · Q47

Indefinite Integrals question

2025 · 24 Jan · Shift 2 · Q47

JEE MainMathematicsIndefinite IntegralsNumerical+4 / −1

If

\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

C

is the constant of integration, then

\alpha+2 \beta

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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