Question

$\int_{}^{}\frac{dx}{x(\log x)(\log{\log x})...\underset{8times}{\overset{(\log{{log...}x})}{︸}}}$ is equal to –

• A. $\underset{8times}{\overset{(\log{{log...}x})}{︸}} + C$
• B. $\underset{7times}{\overset{(\log{{log...}x})}{︸}} + C$
• C. $\underset{9times}{\overset{(\log{{log...}x})}{︸}} + C$
• D. None of these

Answer 1

Answer: (C)

$\underset{9times}{\overset{(\log{{log...}x})}{︸}} + C$

Answer 2

put $\underset{8times}{\overset{\log{{log...}x}}{︸}}$ = t

= = dt

I = $\int \frac { \mathrm { dt } } { \mathrm { t } }$ = log t + C = log $\underset{8times}{\overset{(\log{{log...}x})}{︸}}$ + C