What is the integral of-5xe^{-x+1} ?

The integral of-5xe^{-x+1} is -5(-e^{-x+1}x-e^{-x+1})+C

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integral of-5xe^{-x+1}

\int - 5 x e^{- x + 1} d x

- 5 (- e^{- x + 1} x - e^{- x + 1}) + C

Solution steps

\int - 5 x e^{- x + 1} d x

Take the constant out:

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

= - 5 \cdot \int x e^{- x + 1} d x

Apply Integration By Parts

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

= - 5 (- e^{- x + 1} x - \int - e^{- x + 1} d x)

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

= - 5 (- e^{- x + 1} x - e^{- x + 1})

Add a constant to the solution

= - 5 (- e^{- x + 1} x - e^{- x + 1}) + C

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What is the integral of-5xe^{-x+1} ?
The integral of-5xe^{-x+1} is -5(-e^{-x+1}x-e^{-x+1})+C