What is $\int x^{2} \cdot e^{- x}$ $intx^2*e^-x$ ? Please explain?

Question

1154 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-14T19:28:36

$\int x^{2} e^{- x} d x = - (x^{2} + 2 x + 2) e^{- x} + C$ $int x^2 e^(-x) dx = -(x^2+2x+2) e^(-x) + C$

$\frac{d}{d x} e^{- x} = - e^{- x}$ $d/(dx) e^(-x) = -e^(-x)$

$d/(dx) (u*v) = uv' + u'v$

So:

$d/(dx) x^2 e^(-x) = -x^2 e^(-x) + 2x e^(-x)$

$d/(dx) 2x e^(-x) = -2x e^(-x) + 2 e^(-x)$

So:

$d/(dx) (-(x^2+2x+2) e^(-x) + C)$

$= (x^2+2x+2) e^(-x) - (2x+2) e^(-x)$

$= x^2 e^(-x)$

What is intx^2*e^-x∫x2⋅e−xintx^2*e^-x? Please explain?