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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫cos⁡2x(cos⁡x+sin⁡x)2dx=\int \frac{\cos 2 x}{(\cos x+\sin x)^2} d x=
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Correct option: C
log⁡(cos⁡x+sin⁡x)+c\log (\cos x+\sin x)+c
Option C is correct because the integral simplifies to log⁡(cos⁡x+sin⁡x)+c\log(\cos x + \sin x) + c after using trigonometric identities and substitution.

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