What is the integral of (x+3)e^{5x} ?

The integral of (x+3)e^{5x} is 1/5 e^{5x}x+14/25 e^{5x}+C

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integral of (x+3)e^{5x}

\int (x + 3) e^{5 x} d x

\frac{1}{5} e^{5 x} x + \frac{14}{25} e^{5 x} + C

Solution steps

\int (x + 3) e^{5 x} d x

Apply Integration By Parts

= \frac{1}{5} e^{5 x} (x + 3) - \int \frac{1}{5} e^{5 x} d x

\int \frac{1}{5} e^{5 x} d x = \frac{1}{25} e^{5 x}

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

Simplify

\frac{1}{5} e^{5 x} (x + 3) - \frac{1}{25} e^{5 x} : \frac{1}{5} e^{5 x} x + \frac{14}{25} e^{5 x}

= \frac{1}{5} e^{5 x} x + \frac{14}{25} e^{5 x}

Add a constant to the solution

= \frac{1}{5} e^{5 x} x + \frac{14}{25} e^{5 x} + C

What is the integral of (x+3)e^{5x} ?
The integral of (x+3)e^{5x} is 1/5 e^{5x}x+14/25 e^{5x}+C