What is the integral of xe^{-x/9} ?

The integral of xe^{-x/9} is -9e^{-x/9}x-81e^{-x/9}+C

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integral of xe^{-x/9}

\int x e^{- \frac{x}{9}} d x

- 9 e^{- \frac{x}{9}} x - 81 e^{- \frac{x}{9}} + C

Solution steps

\int x e^{- \frac{x}{9}} d x

Apply Integration By Parts

: - 9 e^{- \frac{x}{9}} x - \int - 9 e^{- \frac{x}{9}} d x

= - 9 e^{- \frac{x}{9}} x - \int - 9 e^{- \frac{x}{9}} d x

\int - 9 e^{- \frac{x}{9}} d x = 81 e^{- \frac{x}{9}}

= - 9 e^{- \frac{x}{9}} x - 81 e^{- \frac{x}{9}}

Add a constant to the solution

= - 9 e^{- \frac{x}{9}} x - 81 e^{- \frac{x}{9}} + C

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What is the integral of xe^{-x/9} ?
The integral of xe^{-x/9} is -9e^{-x/9}x-81e^{-x/9}+C