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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
The value of 2∫sin⁡xsin⁡(x−π4)dx\sqrt{2} \int \frac{\sin x}{\sin \left(x-\frac{\pi}{4}\right)} d x, is
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Correct option: A
x+log⁡∣sin⁡(x−π4)∣+Cx+\log \left|\sin \left(x-\frac{\pi}{4}\right)\right|+C
Option A (x+log⁡∣sin⁡(x−π4)∣+Cx+\log \left|\sin \left(x-\frac{\pi}{4}\right)\right|+C) is correct because after applying trigonometric identities and integrating, the result matches this option.

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