$\smallint \,\,\frac{{\sqrt {\tan \,\,x} }}{{\sin \,\,x\,\,\cos \,\,x}}\;\,\,dx = ... + c\,;\,\,x \ne \,\,\frac{{k\pi }}{2}\,\,{\rm{and}}\,\,\tan \,\,x > 0$

$\frac{1}{{2\,\sqrt {\tan \,\,x} }}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{\sqrt {\tan \,\,x} }}{{\sin \,\,x\,\,\cos \,\,x}}\;\,\,dx = ... + c\,;\,\,x \ne \,\,\frac{{k\pi }}{2}\,\,\mathrm{and}\,\,\tan \,\,x > 0

View answer and explanation

Correct option: C

2\,\sqrt {\tan \,\,x}

Option C (

2\sqrt {\tan \\,x}

) is correct because the integral of the given expression simplifies to

2\sqrt{\tan x} + c

after substitution.