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