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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫tan⁡(log⁡x)xdx=\int \frac{\tan (\log x)}{x} d x=
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Correct option: C
log⁡sec⁡(log⁡x)+c\log \sec (\log x)+c
Option C is correct because substituting t=log⁡xt = \log x transforms the integral to ∫tan⁡tdt\int \tan t dt, which equals log⁡∣sec⁡t∣+c=log⁡∣sec⁡(log⁡x)∣+c\log |\sec t| + c = \log |\sec(\log x)| + c.

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