Q. $\int_{}^{}{\frac{f^{'}(x)}{f(x)\log{\lbrack f(x)\rbrack}}dx}$ is equal to
A) $\frac{f(x)}{\log{f(x)}} + c$
B) $f(x).\log{f(x)} + c$
C) $\log{\lbrack\log{f(x)}\rbrack} + c$
D) $\frac{1}{\log{\lbrack\log{f(x)}\rbrack}} + c$
Explanation
(c)
Let $I = \int_{}^{}\frac{f^{'}(x)}{f(x)\log{f(x)}}dx$
Put $\log{f(x)} = t\ \Rightarrow \ \ \frac{f^{'}(x)}{f(x)}dx = dt$
$\therefore\ I = \int_{}^{}\frac{1}{t}\ dt = \log t + c$
$= \log{\log{f(x)}} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.