JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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\int \frac{\sin x-\cos x}{(\sin x+\cos x) \sqrt{\sin x \cos x+\sin ^2 x \cos ^2 x}} d x=

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Correct option: C

-\operatorname{Sec}^{-1}(\sin 2 x+1)+c

The correct answer is C (

-\operatorname{Sec}^{-1}(\sin 2 x+1)+c

) because the integral simplifies to a standard inverse secant form after appropriate trigonometric manipulations and substitution.

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