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$If \int \tan x \tan 2 x \tan 3 x d x = - A \log | \cos 3 x | - B \log | \cos 2 x | + \log | \cos x | + c$

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A=-13, B= -12

A=-13, B= 12

A=13, B= -12

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Correct option is C

Solution. tan⁡3x=tan⁡2x+tan⁡x1−tan⁡2xtan⁡x∴ tan⁡3xtan⁡2xtan⁡x=tan⁡3x−tan⁡2x−tan⁡x∴ ∫(tan⁡3x−tan⁡2x−tan⁡x)dx =−13log⁡|cos⁡3x|+12log⁡|cos⁡2x|+log⁡|cos⁡x|+c

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If∫tan⁡xtan⁡2xtan⁡3xdx=-Alog⁡|cos⁡3x|-Blog⁡|cos⁡2x|+log⁡|cos⁡x|+c

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$If \int \tan x \tan 2 x \tan 3 x d x = - A \log | \cos 3 x | - B \log | \cos 2 x | + \log | \cos x | + c$