$\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1+\sqrt{\cot x}} d x=$

• A

  $\frac{\pi}{4}$
• B

  $\frac{\pi}{2}$
• C

  $\frac{\pi}{6}$
• Correct answer
  D

  $\frac{\pi}{12}$

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