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

The integral of e^x(2x-1) is 2e^xx-3e^x+C

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integral of e^x(2x-1)

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

2 e^{x} x - 3 e^{x} + C

Solution steps

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

Apply Integration By Parts

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

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

= (2 x - 1) e^{x} - 2 e^{x}

Simplify

(2 x - 1) e^{x} - 2 e^{x} : 2 e^{x} x - 3 e^{x}

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

Add a constant to the solution

= 2 e^{x} x - 3 e^{x} + C