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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1
If ∫1−5sin⁡2xcos⁡5xsin⁡2xdx=f(x)cos⁡5x+C\int \frac{1-5 \sin ^2 x}{\cos ^5 x \sin ^2 x} d x=\frac{f(x)}{\cos ^5 x}+C, then f(x)f(x) is
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Correct option: D
cot⁡x\cot x
Option D (cot⁡x\cot x) is correct because by rewriting the integrand and integrating, f(x)f(x) is found to be cot⁡x\cot x.

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