$\smallint \,\,\frac{{\sec \,\,x\,\,{\rm{cosec}}\,\,x}}{{2\,\,\cot \,\,x - \,\,\sec x\,\,{\rm{cosec}}\,\,x}}\,\,dx$ is equal to

$\log \,\,|\sec \,\,x\,\, + \,\,\tan \,\,x| + \,\,c$

$\log \,\,|\sec \,\,x\,\, + \,\,{\rm{cosec}}\,\,x| + \,\,c$

$\log \,\,|\sec \,\,2x\,\, + \,\,{\rm{cosec}}\,\,2x| + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

\int \,\,\frac{{\sec \,\,x\,\,\mathrm{cosec}\,\,x}}{{2\,\,\cot \,\,x - \,\,\sec x\,\,\mathrm{cosec}\,\,x}}\,\,dx

is equal to

View answer and explanation

Correct option: C

\frac{1}{2}\,\,\log \,\,|\sec \,\,2x\,\, + \,\,\tan \,\,2x| + \,\,c

Option C is correct because the integral simplifies to the integral of sec(2x), which integrates to (1/2)log|sec(2x) + tan(2x)| + c.