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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add similar elements:

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

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

Add a constant to the solution

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

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