∫log⁡(log⁡(log⁡x))xlog⁡xlog⁡(log⁡x)du=f(x)+C then f(x)=

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12loglogxlogx

12loglogx2

loglog(logx)2

12loglog(logx)2

answer is D.

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Detailed Solution

I=∫log(log(logx))xlogxlog(logx)dx Let log⁡(log⁡(log⁡x))=tI=1xlog⁡xlog⁡(log⁡x)dx=dtI=∫tdt=t22+C=(log⁡(log⁡(log⁡x)))22+C

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