What is the integral of-e^{-x}(2x-2) ?

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

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integral of-e^{-x}(2x-2)

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

2 e^{- x} x + C

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

Simplify

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

= 2 e^{- x} x

Add a constant to the solution

= 2 e^{- x} x + C

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