What is the integral of (2x-1)e^{2x} ?

The integral of (2x-1)e^{2x} is e^{2x}x-e^{2x}+C

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integral of (2x-1)e^{2x}

\int (2 x - 1) e^{2 x} d x

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

Solution steps

\int (2 x - 1) e^{2 x} d x

Apply Integration By Parts

: e^{2 x} x - \frac{1}{2} e^{2 x} - \int e^{2 x} d x

= e^{2 x} x - \frac{1}{2} e^{2 x} - \int e^{2 x} d x

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

= e^{2 x} x - \frac{1}{2} e^{2 x} - \frac{1}{2} e^{2 x}

Add similar elements:

- \frac{1}{2} e^{2 x} - \frac{1}{2} e^{2 x} = - e^{2 x}

= e^{2 x} x - e^{2 x}

Add a constant to the solution

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

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What is the integral of (2x-1)e^{2x} ?
The integral of (2x-1)e^{2x} is e^{2x}x-e^{2x}+C