Function Expression :
\[f(x)=e^x-ln(e^x-1 ) \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=e^{x} - \frac{e^{x}}{e^{x} - 1} \]\[f^{\,\prime}(x)=\frac{\left(e^{x} - 2\right) e^{x}}{e^{x} - 1} \]
\[ \]
Integral
\[F(x) = - x \log{\left(e^{x} - 1 \right)} + \int \frac{\left(x + e^{x} - 1\right) e^{x}}{e^{x} - 1}\, dx \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0058 seconds