What is the integral of xe^{2-x} ?

The integral of xe^{2-x} is e^2(-e^{-x}x-e^{-x})+C

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integral of xe^{2-x}

\int x e^{2 - x} d x

e^{2} (- e^{- x} x - e^{- x}) + C

Solution steps

\int x e^{2 - x} d x

Simplify

e^{2 - x} : e^{2} e^{- x}

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{2} \cdot \int x e^{- x} d x

Apply Integration By Parts

= e^{2} (- e^{- x} x - \int - e^{- x} d x)

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

= e^{2} (- e^{- x} x - e^{- x})

Add a constant to the solution

= e^{2} (- e^{- x} x - e^{- x}) + C

What is the integral of xe^{2-x} ?
The integral of xe^{2-x} is e^2(-e^{-x}x-e^{-x})+C