Question

If $\int \frac{dx}{x\log x}=f(x)+$ constant, then $f(x)$ is equal to

• A. $1/\log x$
• B. $\log x$
• C. $\log \log x$
• D. $x/\log x$

Answer 1

Answer: (C)

We have $\int dx/(x\log x)=f(x)+\text{constant}$ ..(i)
Let $\log x=t$
$\Rightarrow$ $\frac{1}{x}dx=dt$
$\therefore$ $\int \frac{dx}{x\log x}=\int \frac{dt}{t}=\log (t)+constant$
$=\log (\log x)+\text{constant}$
On comparing with Eq. (i), we get $f(x)=\log (\log x)$