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