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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int - 3 e^{- x} d x = 3 e^{- x}

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

Simplify

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

= - 3 e^{- x} x + e^{- x}

Add a constant to the solution

= - 3 e^{- x} x + e^{- x} + C

f (x) = \frac{8}{x ^{2} + 4}, at x = 3

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