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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
If ∫(1−tan⁡3x)2dx=13[tan⁡3x+log⁡f(x)]+C\int(1-\tan 3 x)^2 d x=\frac{1}{3}[\tan 3 x+\log f(x)]+C then f(x)f(x) is given by
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Correct option: B
cos⁡23x\cos ^2 3 x
Option B (cos⁡23x\cos ^2 3 x) is correct because after expanding and integrating, the result matches the given form with f(x)=cos⁡23xf(x) = \cos^2 3x.

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