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