What is the integral of (x^2e^{-x}) ?

The integral of (x^2e^{-x}) is -e^{-x}x^2+2(-e^{-x}x-e^{-x})+C

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integral of (x^2e^{-x})

\int (x^{2} e^{- x}) d x

- e^{- x} x^{2} + 2 (- e^{- x} x - e^{- x}) + C

Solution steps

\int x^{2} e^{- x} d x

Apply Integration By Parts

= - e^{- x} x^{2} - \int - 2 e^{- x} x d x

\int - 2 e^{- x} x d x = - 2 (- e^{- x} x - e^{- x})

= - e^{- x} x^{2} - (- 2 (- e^{- x} x - e^{- x}))

Simplify

= - e^{- x} x^{2} + 2 (- e^{- x} x - e^{- x})

Add a constant to the solution

= - e^{- x} x^{2} + 2 (- e^{- x} x - e^{- x}) + C

\frac{d}{d x} (4 x + 6)

\int_{- \infty}^{0} \frac{1}{2 - 7 x} d x

d er i v a t i v e x^{5} ln (x)

\int_{1}^{x} 1 + 9 t d t

n \to \infty lim (n ln (n))

What is the integral of (x^2e^{-x}) ?
The integral of (x^2e^{-x}) is -e^{-x}x^2+2(-e^{-x}x-e^{-x})+C