Function Expression :
\[f(x)=x+\frac{4e^x}{1+e^x} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = +\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=1 + \frac{4 e^{x}}{e^{x} + 1} - \frac{4 e^{2 x}}{\left(e^{x} + 1\right)^{2}} \]\[f^{\,\prime}(x)=\frac{e^{2 x} + 6 e^{x} + 1}{e^{2 x} + 2 e^{x} + 1} \]
\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} + 4 \log{\left(e^{x} + 1 \right)} \]Sign Table
Variation Table
Plot
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