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