Q. 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) $x/\log x$
Explanation
(c)
Put $\log x = t\ \Rightarrow \ \ \frac{1}{x}dx = dt$
$\therefore\int_{}^{}\frac{dx}{x\log x} = \int_{}^{}\frac{dt}{t} = \log t +$constant
$= \log{(\log x)} +$constant$= f(x) +$constant
$\therefore\ f(x) = \log{(\log x)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.