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