Function Expression :
\[f(x)=(x-1 ).ln(x ) \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\log{\left(x \right)} + \frac{x - 1}{x} \]\[f^{\,\prime}(x)=\log{\left(x \right)} + 1 - \frac{1}{x} \]
\[f^{\,\prime}(x)=\frac{x \log{\left(x \right)} + x - 1}{x} \]
Integral
\[F(x) = \frac{x^{2} \log{\left(x \right)}}{2} - \frac{x^{2}}{4} - x \log{\left(x \right)} + x \]Sign Table
Variation Table
Plot
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