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

$\int(\sqrt{\tan x}+\sqrt{\cot x}) d x=$
  1. $\sqrt{2} \operatorname{Tan}^{-1}\left(\frac{\tan x+1}{\sqrt{\tan x}}\right)+c$
  2. $\sqrt{2} \operatorname{Tan}^{-1}\left(\frac{\tan x-1}{\sqrt{2 \tan x}}\right)+c$
  3. $\frac{1}{\sqrt{2}} \operatorname{Tan}^{-1}\left(\frac{\tan x+1}{\sqrt{2} \tan x}\right)+c$
  4. $\frac{1}{\sqrt{2}} \operatorname{Tan}^{-1}\left(\frac{\sqrt{\tan x}-1}{\sqrt{2} \tan x}\right)+c$

Solution

No solution. Refer to answer key.

Asked in: AP EAMCET 2017 (24 Apr Shift 1)

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