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

The integral of (2x-3)e^{3x} is 2/3 e^{3x}x-11/9 e^{3x}+C

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

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

\frac{2}{3} e^{3 x} x - \frac{11}{9} e^{3 x} + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{2}{3} e^{3 x} d x = \frac{2}{9} e^{3 x}

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

Add similar elements:

- e^{3 x} - \frac{2}{9} e^{3 x} = - \frac{11}{9} e^{3 x}

= \frac{2}{3} e^{3 x} x - \frac{11}{9} e^{3 x}

Add a constant to the solution

= \frac{2}{3} e^{3 x} x - \frac{11}{9} e^{3 x} + C

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What is the integral of (2x-3)e^{3x} ?
The integral of (2x-3)e^{3x} is 2/3 e^{3x}x-11/9 e^{3x}+C