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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫  dxx  (log⁡   x)  (log⁡  log⁡  x)  …  (log⁡  log⁡.... x)⏟8  times\int \,\,\frac{{dx}}{{x\,\,(\log \,\,\,x)\,\,(\log \,\,\log \,\,x)\,\, \ldots \,\,\underbrace {(\log \,\,\log ....\,x)}_{8\,\,\mathrm{times}}}} is equal to
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Correct option: C
(log⁡  log⁡  ....  x)⏟9  times  +  c\underbrace {(\log \,\,\log \,\,....\,\,x)}_{9\,\,\mathrm{times}}\,\, + \,\,c
Option C is correct because after repeated substitution, the integral simplifies to log(log...x) nine times + c.

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