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

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

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integral of xe^{B-x}

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

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

Solution steps

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

Simplify

e^{B - x} : e^{B} e^{- x}

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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