What is the integral of (x+2)e^{8x} ?

The integral of (x+2)e^{8x} is 1/8 e^{8x}x+15/64 e^{8x}+C

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integral of (x+2)e^{8x}

\int (x + 2) e^{8 x} d x

\frac{1}{8} e^{8 x} x + \frac{15}{64} e^{8 x} + C

Solution steps

\int (x + 2) e^{8 x} d x

Apply Integration By Parts

: \frac{1}{8} e^{8 x} (x + 2) - \int \frac{1}{8} e^{8 x} d x

= \frac{1}{8} e^{8 x} (x + 2) - \int \frac{1}{8} e^{8 x} d x

\int \frac{1}{8} e^{8 x} d x = \frac{1}{64} e^{8 x}

= \frac{1}{8} e^{8 x} (x + 2) - \frac{1}{64} e^{8 x}

Simplify

\frac{1}{8} e^{8 x} (x + 2) - \frac{1}{64} e^{8 x} : \frac{1}{8} e^{8 x} x + \frac{15}{64} e^{8 x}

= \frac{1}{8} e^{8 x} x + \frac{15}{64} e^{8 x}

Add a constant to the solution

= \frac{1}{8} e^{8 x} x + \frac{15}{64} e^{8 x} + C

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What is the integral of (x+2)e^{8x} ?
The integral of (x+2)e^{8x} is 1/8 e^{8x}x+15/64 e^{8x}+C