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

The integral of x*e^{-x/2} is -2e^{-x/2}x-4e^{-x/2}+C

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

\int x \cdot 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

Apply Integration By Parts

= - 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

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