What is the integral of (x*e^{-x}) ?

The integral of (x*e^{-x}) is -e^{-x}x-e^{-x}+C

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integral of (x*e^{-x})

\int (x \cdot e^{- x}) d x

- e^{- x} x - e^{- x} + C

Solution steps

\int x e^{- x} d x

Apply Integration By Parts

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

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

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

= - e^{- x} x - e^{- x}

Add a constant to the solution

= - e^{- x} x - e^{- x} + C

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What is the integral of (x*e^{-x}) ?
The integral of (x*e^{-x}) is -e^{-x}x-e^{-x}+C