What is the integral of (1-x)e^{-x} ?

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

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integral of (1-x)e^{-x}

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

e^{- x} x + C

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

- e^{- x} (1 - x) - (- e^{- x}) : e^{- x} x

= e^{- x} x

Add a constant to the solution

= e^{- x} x + C

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