Question

$\int \frac{1}{x\log x\log \left(\log x\right)}dx.$

• A. $\left[\log \left(\log x\right)\right].$
• B. $\log \left[\log \left(\log x\right)\right].$
• C. $\log \left[\log \left(\log x^2\right)\right].$
• D. $-\log \left[\log \left(\log x\right)\right].$

Answer 1

The correct option is B $\log \left[\log \left(\log x\right)\right].$

Let $I=\int \frac{1}{x\log x\log \left(\log x\right)}dx$
Put $\log \left(\log x\right)=t\Rightarrow \frac{1}{\log x}\frac{1}{x}dx=dt$
Therefore
$I=\int \frac{1}{t}dt=\log t=\log \left[\log \left(\log x\right)\right]$
Hence, option 'B' is correct.