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

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

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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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. Simplifying the expression inside the integral using trigonometric identities leads to the result.