What is the integral of (4x-3)e^{-x} ?

The integral of (4x-3)e^{-x} is -4e^{-x}x-e^{-x}+C

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integral of (4x-3)e^{-x}

\int (4 x - 3) e^{- x} d x

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

Solution steps

\int (4 x - 3) e^{- x} d x

Apply Integration By Parts

= - e^{- x} (4 x - 3) - \int - 4 e^{- x} d x

\int - 4 e^{- x} d x = 4 e^{- x}

= - e^{- x} (4 x - 3) - 4 e^{- x}

Simplify

- e^{- x} (4 x - 3) - 4 e^{- x} : - 4 e^{- x} x - e^{- x}

= - 4 e^{- x} x - e^{- x}

Add a constant to the solution

= - 4 e^{- x} x - e^{- x} + C

What is the integral of (4x-3)e^{-x} ?
The integral of (4x-3)e^{-x} is -4e^{-x}x-e^{-x}+C