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

The integral of xe^{-x/y} is -ye^{-x/y}x-y^2e^{-x/y}+C

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integral of xe^{-x/y}

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

What is the integral of xe^{-x/y} ?
The integral of xe^{-x/y} is -ye^{-x/y}x-y^2e^{-x/y}+C