What is the integral of (x+8)e^{9x} ?

The integral of (x+8)e^{9x} is 1/9 e^{9x}x+71/81 e^{9x}+C

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integral of (x+8)e^{9x}

\int (x + 8) e^{9 x} d x

\frac{1}{9} e^{9 x} x + \frac{71}{81} e^{9 x} + C

Solution steps

\int (x + 8) e^{9 x} d x

Apply Integration By Parts

: \frac{1}{9} e^{9 x} (x + 8) - \int \frac{1}{9} e^{9 x} d x

= \frac{1}{9} e^{9 x} (x + 8) - \int \frac{1}{9} e^{9 x} d x

\int \frac{1}{9} e^{9 x} d x = \frac{1}{81} e^{9 x}

= \frac{1}{9} e^{9 x} (x + 8) - \frac{1}{81} e^{9 x}

Simplify

\frac{1}{9} e^{9 x} (x + 8) - \frac{1}{81} e^{9 x} : \frac{1}{9} e^{9 x} x + \frac{71}{81} e^{9 x}

= \frac{1}{9} e^{9 x} x + \frac{71}{81} e^{9 x}

Add a constant to the solution

= \frac{1}{9} e^{9 x} x + \frac{71}{81} e^{9 x} + C

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What is the integral of (x+8)e^{9x} ?
The integral of (x+8)e^{9x} is 1/9 e^{9x}x+71/81 e^{9x}+C