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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1
Integral of 1+2cot⁡x(cot⁡x+cosec⁡x)\sqrt{1+2 \cot x(\cot x+\operatorname{cosec} x)} w.r.t. xx, is
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Correct option: B
2ln⁡sin⁡x2+C2 \ln \sin \frac{x}{2}+C
Option B (2ln⁡sin⁡x2+C2 \ln \sin \frac{x}{2}+C) is correct because simplifying the expression inside the square root leads to an integral that can be directly evaluated to this result.

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