$\int \frac{f(x) g'(x)-g(x) f'(x)}{f(x) . g(x)}\{\log g(x)-\log f(x)\} d x$ is equal to
Answer & explanation
Correct answer: option 2
Let
$I=\int \frac{f(x) g'(x)-g(x) f'(x)}{f(x) . g(x)}\{\log g(x)-\log f(x)\} d x$
$\Rightarrow I=\int \log \left\{\frac{g(x)}{f(x)}\right\} . d\left\{\log \frac{g(x)}{f(x)}\right\}=\frac{1}{2}\left\{\log _e \frac{g(x)}{f(x)}\right\}^2+C$