What is the integral of x^2e^{-x/4} ?

The integral of x^2e^{-x/4} is -4e^{-x/4}x^2+8(-4e^{-x/4}x-16e^{-x/4})+C

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integral of x^2e^{-x/4}

\int x^{2} e^{- \frac{x}{4}} d x

- 4 e^{- \frac{x}{4}} x^{2} + 8 (- 4 e^{- \frac{x}{4}} x - 16 e^{- \frac{x}{4}}) + C

Solution steps

\int x^{2} e^{- \frac{x}{4}} d x

Apply Integration By Parts

: - 4 e^{- \frac{x}{4}} x^{2} - \int - 8 e^{- \frac{x}{4}} x d x

= - 4 e^{- \frac{x}{4}} x^{2} - \int - 8 e^{- \frac{x}{4}} x d x

\int - 8 e^{- \frac{x}{4}} x d x = - 8 (- 4 e^{- \frac{x}{4}} x - 16 e^{- \frac{x}{4}})

= - 4 e^{- \frac{x}{4}} x^{2} - (- 8 (- 4 e^{- \frac{x}{4}} x - 16 e^{- \frac{x}{4}}))

Simplify

= - 4 e^{- \frac{x}{4}} x^{2} + 8 (- 4 e^{- \frac{x}{4}} x - 16 e^{- \frac{x}{4}})

Add a constant to the solution

= - 4 e^{- \frac{x}{4}} x^{2} + 8 (- 4 e^{- \frac{x}{4}} x - 16 e^{- \frac{x}{4}}) + C

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What is the integral of x^2e^{-x/4} ?
The integral of x^2e^{-x/4} is -4e^{-x/4}x^2+8(-4e^{-x/4}x-16e^{-x/4})+C