If $$I=$$∫$$($$$$cot$$⁡x−$$tan$$⁡$$x)dx$$, then I equals

Correct option is 22log⁡|sin⁡x+cos⁡x+sin⁡2x|+C

Questions

$If I = \int (\sqrt{\cot x} - \sqrt{\tan x}) d x, then I equals$

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2log⁡(tan⁡x−cot⁡x)+C

2log⁡|sin⁡x+cos⁡x+sin⁡2x|+C

2log⁡|sin⁡x−cos⁡x+2sin⁡xcos⁡x|+C

2log⁡|sin⁡(x+π/4)+2sin⁡xcos⁡x|+C

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detailed solution

Correct option is B

I=∫cos⁡x−sin⁡xcos⁡xsin⁡xdx Put sin⁡x+cos⁡x=t, so that 2sin⁡xcos⁡x=t2−1∴I=2∫dtt2−1=2log⁡t+t2−1+C=2log⁡|sin⁡x+cos⁡x+sin⁡2x|+C

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If I=∫(cot⁡x−tan⁡x)dx, then I equals

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$If I = \int (\sqrt{\cot x} - \sqrt{\tan x}) d x, then I equals$