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

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

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integral of x^2(e^{-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

= - 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

x \to - 1 f lim (x)

g (x) = x^{2}, g (x) = x^{k} 0, 1

\int \frac{y}{y - 1} d y

\frac{d}{d x} ((3 x - 2)^{6})

\frac{d}{d x} (\frac{1}{1 + 2 x ^{2}})

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