AP EAMCET · Maths · Indefinite Integration
\(\int \sqrt{\mathrm{x}^2+\mathrm{x}+1} \mathrm{dx}\)
- A \(\frac{(2 x+1)}{4} \sqrt{x^2+x+1}+\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c\)
- B \(\frac{x+1}{4} \sqrt{x^2+x+1}+\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c\)
- C \(\frac{x+1}{4} \sqrt{x^2+x+1}-\frac{3}{8} \operatorname{Sinh}^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c\)
- D \(\frac{(2 x+1)}{4} \sqrt{x^2+x+1}-\frac{3}{8} \operatorname{Sinh}^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c\)
Answer & Solution
Correct Answer
(A) \(\frac{(2 x+1)}{4} \sqrt{x^2+x+1}+\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c\)
Step-by-step Solution
Detailed explanation
\(\int \sqrt{x^2+x+1} dx = \int \sqrt{\left(x+\frac{1}{2}\right)^2 + \left(\frac{\sqrt{3}}{2}\right)^2} dx\)…
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