What is the integral of u*e^{-u} ?

The integral of u*e^{-u} is -e^{-u}u-e^{-u}+C

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integral of u*e^{-u}

\int u \cdot e^{- u} d u

- e^{- u} u - e^{- u} + C

Solution steps

\int u e^{- u} d u

Apply Integration By Parts

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

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

= - e^{- u} u - e^{- u}

Add a constant to the solution

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

What is the integral of u*e^{-u} ?
The integral of u*e^{-u} is -e^{-u}u-e^{-u}+C