Function Expression :
\[f(x)=2x+ln(1-\frac{1}{e^x} ) \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=2 + \frac{e^{- x}}{1 - 1 \cdot \frac{1}{e^{x}}} \]\[f^{\,\prime}(x)=\frac{2 e^{x} - 1}{e^{x} - 1} \]
\[ \]
Integral
\[F(x) = x \log{\left(1 - e^{- x} \right)} + \int \frac{x \left(2 e^{x} - 3\right)}{e^{x} - 1}\, dx \]Sign Table
Variation Table
Plot
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