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