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

The integral of (5x+1)e^{5x} is e^{5x}x+C

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

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

e^{5 x} x + C

Solution steps

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

Apply Integration By Parts

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

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

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

= e^{5 x} x + \frac{1}{5} e^{5 x} - \frac{1}{5} e^{5 x}

Add similar elements:

\frac{1}{5} e^{5 x} - \frac{1}{5} e^{5 x} = 0

= e^{5 x} x

Add a constant to the solution

= e^{5 x} x + C

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