Question

Evaluate: $\int \frac{1}{xlogxlog\left(logx\right)}dx$

• A. $log\left(log\right(x\left)\right)+c$
• B. $log\left(log\right(log\left(\frac{1}{x}\right)\left)\right)+c$
• C. $log\left(log\right(log\left(x\right)\left)\right)+c$
• D. $log\left(log\right(\frac{1}{x}\left)\right)+c$

Answer 1

Answer: (C)

$log\left(log\right(log\left(x\right)\left)\right)+c$

Now,

$\int \frac{1}{xlogxlog\left(logx\right)}dx$

$\int \frac{d\left\{\log \right(\log x\left)\right\}}{\log \left(\log x\right)}dx$

$=\log \left\{\log \right(\log x\left)\right\}+c$ [ Where $c$ being integrating constant].