Function Expression :
\[f(x)=x(1-e^{2x} )+3 \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -\infty \]\[\lim_{x \rightarrow+\infty}f(x) = -\infty \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- 2 x e^{2 x} - e^{2 x} + 1 \]\[ \]
Integral
\[F(x) = \frac{x^{2}}{2} + 3 x + \frac{\left(1 - 2 x\right) e^{2 x}}{4} \]Sign Table
Variation Table
Plot
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