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