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