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