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