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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

\int sec (7 x) tan (7 x) d x

\int y \cdot sin (y^{2}) d y

y = x^{3}, y = x

n = 0 \sum \infty n (\frac{1}{2})^{n}

\frac{d}{d x} (\frac{1}{y} e^{x y} - ln (y^{2}))

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