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