Function Expression :
\[f(x)=ln(e^x-1 )-(\frac{e^x}{e^x-1} ) \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{e^{2 x}}{\left(e^{x} - 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{e^{2 x}}{\left(1 - e^{x}\right)^{2}} \]
\[ \]
Integral
\[F(x) = x \log{\left(e^{x} - 1 \right)} - \int \frac{e^{x}}{e^{x} - 1}\, dx - \int \frac{x e^{x}}{e^{x} - 1}\, dx \]Sign Table
Variation Table
Plot
Elapsed Time: 0.0032 seconds