$\int \sqrt{\mathrm{x}^2+\mathrm{x}+1} \mathrm{dx}$

• Correct answer
  A

  $\frac{(2 x+1)}{4} \sqrt{x^2+x+1}+\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c$
• 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

  $\frac{(2 x+1)}{4} \sqrt{x^2+x+1}-\frac{3}{8} \operatorname{Sinh}^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c$

Hence, the correct answer is option: 'A'.