Function Expression :
\[f(x)=\frac{1+xe^x}{x} \]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
\[f^{\,\prime}(x)=\frac{x e^{x} + e^{x}}{x} - \frac{x e^{x} + 1}{x^{2}} \]\[f^{\,\prime}(x)=e^{x} - \frac{1}{x^{2}} \]
\[f^{\,\prime}(x)=\frac{x^{2} e^{x} - 1}{x^{2}} \]
Integral
\[F(x) = e^{x} + \log{\left(x \right)} \]Sign Table
Variation Table
Plot
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