$\int \frac{1}{1+x+x^2} d x=$

• A

  $\frac{2}{\sqrt{3}} \log \left(\frac{2 x+1+\sqrt{3}}{2 x-1-\sqrt{3}}\right)+c$
• B

  $\frac{1}{\sqrt{3}} \log \left(\frac{2 x+1-\sqrt{3}}{2 x+1+\sqrt{3}}\right)+c$
• Correct answer
  C

  $\frac{2}{\sqrt{3}} \operatorname{Tan}^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c$
• D

  $\frac{2}{\sqrt{5}} \operatorname{Tan}^{-1}\left(\frac{2 \mathrm{x}+1}{\sqrt{5}}\right)+\mathrm{c}$

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