Function Expression :
\[f(x)=(x+1 )^2. e^{-2x} \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = +\infty \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- 2 \left(x + 1\right)^{2} e^{- 2 x} + \left(2 x + 2\right) e^{- 2 x} \]\[f^{\,\prime}(x)=2 x \left(- x - 1\right) e^{- 2 x} \]
\[ \]
Integral
\[F(x) = \frac{\left(- 2 x^{2} - 6 x - 5\right) e^{- 2 x}}{4} \]Sign Table
Variation Table
Plot
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