What is the integral of xe^{(2x+3)} ?

The integral of xe^{(2x+3)} is 1/2 e^{2x+3}x-1/4 e^{2x+3}+C

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integral of xe^{(2x+3)}

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

\frac{1}{2} e^{2 x + 3} x - \frac{1}{4} e^{2 x + 3} + C

Solution steps

\int x e^{2 x + 3} d x

Apply Integration By Parts

= \frac{1}{2} e^{2 x + 3} x - \int \frac{1}{2} e^{2 x + 3} d x

\int \frac{1}{2} e^{2 x + 3} d x = \frac{1}{4} e^{2 x + 3}

= \frac{1}{2} e^{2 x + 3} x - \frac{1}{4} e^{2 x + 3}

Add a constant to the solution

= \frac{1}{2} e^{2 x + 3} x - \frac{1}{4} e^{2 x + 3} + C

What is the integral of xe^{(2x+3)} ?
The integral of xe^{(2x+3)} is 1/2 e^{2x+3}x-1/4 e^{2x+3}+C