What is the integral of (3x-2)*e^{-x} ?

The integral of (3x-2)*e^{-x} is -3e^{-x}x-e^{-x}+C

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integral of (3x-2)*e^{-x}

\int (3 x - 2) \cdot e^{- x} d x

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

Solution steps

\int (3 x - 2) e^{- x} d x

Apply Integration By Parts

: - e^{- x} (3 x - 2) - \int - 3 e^{- x} d x

= - e^{- x} (3 x - 2) - \int - 3 e^{- x} d x

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

= - e^{- x} (3 x - 2) - 3 e^{- x}

Simplify

- e^{- x} (3 x - 2) - 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

x \to 5 + lim (5 - x)

\frac{d}{d x} (\frac{1}{( x + 3 )})

\int x^{3} (3 - x^{4})^{10} d x

\int x (6 x + 7)^{8} d x

What is the integral of (3x-2)*e^{-x} ?
The integral of (3x-2)*e^{-x} is -3e^{-x}x-e^{-x}+C