$\smallint \,\,\cos \,\,\left[ {2\,\,{{\cot }^{ - 1}}\,\,\sqrt {\frac{{1\,\, - \,\,x}}{{1\,\, + \,\,x}}} } \right]\,\,dx$ is equal to

$\frac{1}{2}\,\,\sin \,\,\left[ {2\,\,{{\cot }^{ - 1}}\,\,\sqrt {\frac{{1\,\, - \,\,x}}{{1\,\, + \,\,x}}} } \right]\,\, + \,\,c$

$\frac{1}{2}\,\,x\,\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\cos \,\,\left[ {2\,\,{{\cot }^{ - 1}}\,\,\sqrt {\frac{{1\,\, - \,\,x}}{{1\,\, + \,\,x}}} } \right]\,\,dx

is equal to

View answer and explanation

Correct option: C

- \,\,\frac{1}{2}\,\,{x^2}\,\, + \,\,c

Option C (

- \frac{1}{2}\\ {x^2}\\ + \\ c

) is correct because the expression inside the cosine simplifies to -x, and the integral of -x is -x²/2 + c.