Function Expression :
\[f(x)=\frac{1}{x+1}e^{\frac{1}{x+1}} \]Domain
\[\left]-\infty, -1\right[ \cup \left]-1, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = 0 \]\[\lim_{x \overset{<}{\rightarrow-1} }f(x) = 0 \]
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = +\infty \]
\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{e^{\frac{1}{x + 1}}}{\left(x + 1\right)^{2}} - \frac{e^{\frac{1}{x + 1}}}{\left(x + 1\right)^{3}} \]\[f^{\,\prime}(x)=\frac{\left(- x - 2\right) e^{\frac{1}{x + 1}}}{\left(x + 1\right)^{3}} \]
\[ \]
Integral
\[F(x) = - \operatorname{Ei}{\left(\frac{1}{x + 1} \right)} \]Sign Table
Variation Table
Plot
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