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

$\sqrt{2} \sin ^{-1}(\sin \mathrm{x}+\cos \mathrm{x})+\mathrm{C}$

$\sqrt{2} \cos ^{-1}(\sin x-\cos x)+C$

$\sqrt{2} \cos ^{-1}(\sin x+\cos x)+C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

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

, then I equals:

View answer and explanation

Correct option: C

\sqrt{2} \sin ^{-1}(\sin x-\cos x)+C

Option C (

\sqrt{2} \sin ^{-1}(\sin x-\cos x)+C

) is correct because after substituting and integrating, the result matches this option.

Practice All Chapter MCQs →

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{C}

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