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

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

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integral of xe^{(-x)/2}

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

- 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}} + C

Solution steps

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

Simplify

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

Apply Integration By Parts

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

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

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

= - 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}}

Add a constant to the solution

= - 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}} + C

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