What is the integral of xe^{(-x)/5} ?

The integral of xe^{(-x)/5} is -5e^{-x/5}x-25e^{-x/5}+C

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integral of xe^{(-x)/5}

\int x e^{\frac{- x}{5}} d x

- 5 e^{- \frac{x}{5}} x - 25 e^{- \frac{x}{5}} + C

Solution steps

\int x e^{\frac{- x}{5}} d x

Simplify

= \int e^{- \frac{x}{5}} x d x

Apply Integration By Parts

: - 5 e^{- \frac{x}{5}} x - \int - 5 e^{- \frac{x}{5}} d x

= - 5 e^{- \frac{x}{5}} x - \int - 5 e^{- \frac{x}{5}} d x

\int - 5 e^{- \frac{x}{5}} d x = 25 e^{- \frac{x}{5}}

= - 5 e^{- \frac{x}{5}} x - 25 e^{- \frac{x}{5}}

Add a constant to the solution

= - 5 e^{- \frac{x}{5}} x - 25 e^{- \frac{x}{5}} + C

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What is the integral of xe^{(-x)/5} ?
The integral of xe^{(-x)/5} is -5e^{-x/5}x-25e^{-x/5}+C