What is the integral of (x+4)e^{2x} ?

The integral of (x+4)e^{2x} is 1/2 e^{2x}x+7/4 e^{2x}+C

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integral of (x+4)e^{2x}

\int (x + 4) e^{2 x} d x

\frac{1}{2} e^{2 x} x + \frac{7}{4} e^{2 x} + C

Solution steps

\int (x + 4) e^{2 x} d x

Apply Integration By Parts

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

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

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

Simplify

\frac{1}{2} e^{2 x} (x + 4) - \frac{1}{4} e^{2 x} : \frac{1}{2} e^{2 x} x + \frac{7}{4} e^{2 x}

= \frac{1}{2} e^{2 x} x + \frac{7}{4} e^{2 x}

Add a constant to the solution

= \frac{1}{2} e^{2 x} x + \frac{7}{4} e^{2 x} + C

What is the integral of (x+4)e^{2x} ?
The integral of (x+4)e^{2x} is 1/2 e^{2x}x+7/4 e^{2x}+C