Function Expression :
\[f(x)=2x+ln(4(e^x-1 ) ) \]Domain
\[\left]0, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=2 + \frac{e^{x}}{e^{x} - 1} \]\[f^{\,\prime}(x)=\frac{3 e^{x} - 2}{e^{x} - 1} \]
\[ \]
Integral
\[F(x) = x \log{\left(4 e^{x} - 4 \right)} + \int \frac{x \left(e^{x} - 2\right)}{e^{x} - 1}\, dx \]Sign Table
Variation Table
Plot
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