What is the integral of xe^{-x-1} ?

The integral of xe^{-x-1} is -e^{-x-1}x-e^{-x-1}+C

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integral of xe^{-x-1}

\int x e^{- x - 1} d x

- e^{- x - 1} x - e^{- x - 1} + C

Solution steps

\int x e^{- x - 1} d x

Apply Integration By Parts

: - e^{- x - 1} x - \int - e^{- x - 1} d x

= - e^{- x - 1} x - \int - e^{- x - 1} d x

\int - e^{- x - 1} d x = e^{- x - 1}

= - e^{- x - 1} x - e^{- x - 1}

Add a constant to the solution

= - e^{- x - 1} x - e^{- x - 1} + C

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What is the integral of xe^{-x-1} ?
The integral of xe^{-x-1} is -e^{-x-1}x-e^{-x-1}+C