What is the integral of (8x+1)e^{5x} ?

The integral of (8x+1)e^{5x} is 8/5 e^{5x}x-3/25 e^{5x}+C

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integral of (8x+1)e^{5x}

\int (8 x + 1) e^{5 x} d x

\frac{8}{5} e^{5 x} x - \frac{3}{25} e^{5 x} + C

Solution steps

\int (8 x + 1) e^{5 x} d x

Apply Integration By Parts

: \frac{1}{5} e^{5 x} (8 x + 1) - \int \frac{8}{5} e^{5 x} d x

= \frac{1}{5} e^{5 x} (8 x + 1) - \int \frac{8}{5} e^{5 x} d x

\int \frac{8}{5} e^{5 x} d x = \frac{8}{25} e^{5 x}

= \frac{1}{5} e^{5 x} (8 x + 1) - \frac{8}{25} e^{5 x}

Simplify

\frac{1}{5} e^{5 x} (8 x + 1) - \frac{8}{25} e^{5 x} : \frac{8}{5} e^{5 x} x - \frac{3}{25} e^{5 x}

= \frac{8}{5} e^{5 x} x - \frac{3}{25} e^{5 x}

Add a constant to the solution

= \frac{8}{5} e^{5 x} x - \frac{3}{25} e^{5 x} + C

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What is the integral of (8x+1)e^{5x} ?
The integral of (8x+1)e^{5x} is 8/5 e^{5x}x-3/25 e^{5x}+C