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

The integral of xe^{-x/4} is -4e^{-x/4}x-16e^{-x/4}+C

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integral of xe^{-x/4}

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

- 4 e^{- \frac{x}{4}} x - 16 e^{- \frac{x}{4}} + C

Solution steps

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

Apply Integration By Parts

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

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

= - 4 e^{- \frac{x}{4}} x - 16 e^{- \frac{x}{4}}

Add a constant to the solution

= - 4 e^{- \frac{x}{4}} x - 16 e^{- \frac{x}{4}} + C

What is the integral of xe^{-x/4} ?
The integral of xe^{-x/4} is -4e^{-x/4}x-16e^{-x/4}+C