Question

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

• A. $x\log \left(\log x\right)+c$
• B. $x\log x+c$
• C. $x+c$
• D. $None$

Answer 1

Answer: (A)

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

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

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

$=\log \left(\log x\right).x-\int \frac{1}{\log x}\times \frac{1}{x}\times xdx+\int \frac{dx}{\log x}$

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

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