$\smallint \left( {\sqrt {\tan \,\,x} \,\, + \,\,\sqrt {\cot \,\,x} } \right)dx$ is equal to

$\sqrt 2 \,\,{\tan ^{ - 1}}\,(\sin \,\,x\,\, - \,\,\cos \,\,x)\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \left( {\sqrt {\tan \,\,x} \,\, + \,\,\sqrt {\cot \,\,x} } \right)dx

is equal to

View answer and explanation

Correct option: A

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

Option A is correct because the integral simplifies to a form that can be solved using a trigonometric substitution, resulting in the given arcsine function.

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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