JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

The integral

\int \sqrt{1+2 \cot x(\operatorname{cosec} x+\cot x)} d x

\left(0 < x < \frac{\pi}{2}\right)

is equal to:
(where

\mathrm{C}

is a constant of integration)

View answer and explanation

Correct option: A

2 \log \left|\sin \frac{x}{2}\right|+C

Option A (

2 \log \left|\sin \frac{{x}}{{2}}\right|+C

) is correct because simplifying the integrand leads to an expression that can be directly integrated to obtain the given result.

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