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