Practicing Success
Practicing Success
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$\int \frac{f(x) g'(x)-g(x) f'(x)}{f(x) . g(x)}\{\log g(x)-\log f(x)\} d x$ is equal to |
$\log _e\left\{\frac{g(x)}{f(x)}\right\}+C$ $\frac{1}{2}\left\{\log _e \frac{g(x)}{f(x)}\right\}^2+C$ $\frac{g(x)}{f(x)} \log _e \frac{g(x)}{f(x)}+C$ none of these |
$\frac{1}{2}\left\{\log _e \frac{g(x)}{f(x)}\right\}^2+C$ |
Let $I=\int \frac{f(x) g'(x)-g(x) f'(x)}{f(x) . g(x)}\{\log g(x)-\log f(x)\} d x$ $\Rightarrow I=\int \log \left\{\frac{g(x)}{f(x)}\right\} . d\left\{\log \frac{g(x)}{f(x)}\right\}=\frac{1}{2}\left\{\log _e \frac{g(x)}{f(x)}\right\}^2+C$ |
