$\int(\sqrt{\tan x}+\sqrt{\cot x}) d x=$

• A

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

  $\operatorname{Tan}^{-1}\left(\frac{\tan x-2}{2 \sqrt{\tan x}}\right)+c$
• Correct answer
  C

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

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

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