What is the integral of (7-5x)e^{3-2x} ?

The integral of (7-5x)e^{3-2x} is 5/2 e^{-2x+3}x-9/4 e^{-2x+3}+C

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integral of (7-5x)e^{3-2x}

\int (7 - 5 x) e^{3 - 2 x} d x

\frac{5}{2} e^{- 2 x + 3} x - \frac{9}{4} e^{- 2 x + 3} + C

Solution steps

\int (7 - 5 x) e^{3 - 2 x} d x

Apply Integration By Parts

= - \frac{1}{2} e^{3 - 2 x} (7 - 5 x) - \int \frac{5}{2} e^{3 - 2 x} d x

\int \frac{5}{2} e^{3 - 2 x} d x = - \frac{5}{4} e^{3 - 2 x}

= - \frac{1}{2} e^{3 - 2 x} (7 - 5 x) - (- \frac{5}{4} e^{3 - 2 x})

Simplify

- \frac{1}{2} e^{3 - 2 x} (7 - 5 x) - (- \frac{5}{4} e^{3 - 2 x}) : \frac{5}{2} e^{- 2 x + 3} x - \frac{9}{4} e^{- 2 x + 3}

= \frac{5}{2} e^{- 2 x + 3} x - \frac{9}{4} e^{- 2 x + 3}

Add a constant to the solution

= \frac{5}{2} e^{- 2 x + 3} x - \frac{9}{4} e^{- 2 x + 3} + C

What is the integral of (7-5x)e^{3-2x} ?
The integral of (7-5x)e^{3-2x} is 5/2 e^{-2x+3}x-9/4 e^{-2x+3}+C