What is the integral of xe^{2x-1} ?

The integral of xe^{2x-1} is 1/2 e^{2x-1}x-1/4 e^{2x-1}+C

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integral of xe^{2x-1}

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

\frac{1}{2} e^{2 x - 1} x - \frac{1}{4} e^{2 x - 1} + C

Solution steps

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

Apply Integration By Parts

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

\int \frac{1}{2} e^{2 x - 1} d x = \frac{1}{4} e^{2 x - 1}

= \frac{1}{2} e^{2 x - 1} x - \frac{1}{4} e^{2 x - 1}

Add a constant to the solution

= \frac{1}{2} e^{2 x - 1} x - \frac{1}{4} e^{2 x - 1} + C

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What is the integral of xe^{2x-1} ?
The integral of xe^{2x-1} is 1/2 e^{2x-1}x-1/4 e^{2x-1}+C