What is the integral of (2x-1)e^{-x} ?

The integral of (2x-1)e^{-x} is -2e^{-x}x-e^{-x}+C

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integral of (2x-1)e^{-x}

\int (2 x - 1) e^{- x} d x

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

Solution steps

\int (2 x - 1) e^{- x} d x

Apply Integration By Parts

: - e^{- x} (2 x - 1) - \int - 2 e^{- x} d x

= - e^{- x} (2 x - 1) - \int - 2 e^{- x} d x

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

= - e^{- x} (2 x - 1) - 2 e^{- x}

Simplify

- e^{- x} (2 x - 1) - 2 e^{- x} : - 2 e^{- x} x - e^{- x}

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

Add a constant to the solution

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

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What is the integral of (2x-1)e^{-x} ?
The integral of (2x-1)e^{-x} is -2e^{-x}x-e^{-x}+C