JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int \frac{2 x^2+5 x+9}{\sqrt{x^2+x+1}} \mathrm{~d} x=x \sqrt{x^2+x+1}+\alpha \sqrt{x^2+x+1}+\beta \log _e\left|x+\frac{1}{2}+\sqrt{x^2+x+1}\right|+\mathrm{C}\), where \(C\) is the constant of integration, then \(\alpha+2 \beta\) is equal to \(\qquad\) _______.
- A 12
- B 14
- C 16
- D 18
Answer & Solution
Correct Answer
(C) 16
Step-by-step Solution
Detailed explanation
\(2 \mathrm{x}^2+5 \mathrm{x}+9=\mathrm{A}\left(\mathrm{x}^2+\mathrm{x}+1\right)+\mathrm{B}(2 \mathrm{x}+1)+\mathrm{C} \) \( \mathrm{A}=2 \mathrm{~B}=\frac{3}{2} \mathrm{C}=\frac{11}{2} \)…
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