Function Expression :
\[f(x)=(\frac{x-1}{x} ).ln x \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{\log{\left(x \right)}}{x} - \frac{\left(x - 1\right) \log{\left(x \right)}}{x^{2}} + \frac{x - 1}{x^{2}} \]\[f^{\,\prime}(x)=\frac{x + \log{\left(x \right)} - 1}{x^{2}} \]
\[ \]
Integral
\[F(x) = x \log{\left(x \right)} - x - \frac{\log{\left(x \right)}^{2}}{2} \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0299 seconds