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