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

\frac{d}{d x} (2 x^{4} + x^{2} - x^{2} + 4)

\frac{\partial}{\partial x} (y \cdot e^{x y})

\frac{s + 1}{s ^{2} + 2}

x^{2} - 9 x

\frac{d}{d x} (- x sin (x) - cos (x))

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