\int \sqrt{x^2+x+1} \dx [AP EAPCET 22 May 2025 S2]

Correct Answer is : (2x+1)4√x2+x+1+38sinh−1(2x+1√3)+c

\frac{(2 {\x}+1)}{4} \sqrt{ {\x}^2+ {\x}+1}+\frac{3}{8} {\sinh} ^{-1} ( {2 {\x}+1}/{\sqrt{3}}) + {\c}

\frac{x+1}{4} \sqrt{x^2+x+1}+\frac{3}{8} {\Sinh}^{-1} ( {2 x+1}/{\sqrt{3}}) +c

\frac{x+1}{4} \sqrt{x^2+x+1}-\frac{3}{8} {\Sinh}^{-1} ( {2 x+1}/{\sqrt{3}}) +c

\frac{(2 x+1)}{4} \sqrt{x^2+x+1}-\frac{3}{8} {\Sinh}^{-1} ( {2 x+1}/{\sqrt{3}}) +c

Indefinite Integration

Section: Mathematics

Question : 33 of 89

Marks: +1, -0

∫√x2+x+1‌dx

[AP EAPCET 22 May 2025 S2]

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