Question

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

• A. $\log x\left[\log \right(\log x)-1]+c$
• B. $x\left[\log \right(\log x)+1]+c$
• C. $\log x\left[\log \right(\log x)+1]+c$
• D. $x\left[\log \right(\log x)-1]+c$

Answer 1

Answer: (A)

$\log x\left[\log \right(\log x)-1]+c$

$\int \frac{log\left(logx\right)}{x}dx$
$=log\left(logx\right)\left(logx\right)-\int \left(\frac{1}{logx}\frac{1}{x}logx\right)dx$
$=log\left(logx\right)\left[logx\right]-logx+c$
$=logx\left[log\right(logx)-1]+c$