If $$I=$$∫log⁡$$($$$$cos$$⁡$$x)cos2$$⁡x, then I equals

Correct option is 1tan⁡xlog⁡cos⁡x+tan⁡x−x+C

Questions

$If I = \int \frac{\log (\cos x)}{\cos^{2} x}, then I equals$

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tan⁡xlog⁡cos⁡x+tan⁡x−x+C

tan⁡xlog⁡cos⁡x−tan⁡x+x2+C

tan⁡xlog⁡cos⁡x−cot⁡x+x+C

tan⁡xlog⁡cos⁡x+cot⁡x−x+C

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detailed solution

Correct option is A

I=∫sec2⁡xlog⁡cos⁡xdx=tan⁡xlog⁡cos⁡x−∫tanx(−tan⁡x)dx=tan⁡xlog⁡cos⁡x+tan⁡x−x+C

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If I=∫log⁡(cos⁡x)cos2⁡x, then I equals

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$If I = \int \frac{\log (\cos x)}{\cos^{2} x}, then I equals$