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Q.

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

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a

tan⁡xlog⁡cos⁡x+tan⁡x−x+C

b

tan⁡xlog⁡cos⁡x−tan⁡x+x2+C

c

tan⁡xlog⁡cos⁡x−cot⁡x+x+C

d

tan⁡xlog⁡cos⁡x+cot⁡x−x+C

answer is A.

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Detailed Solution

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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