What is the integral of (8x+3)e^x ?

The integral of (8x+3)e^x is 8e^xx-5e^x+C

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integral of (8x+3)e^x

\int (8 x + 3) e^{x} d x

8 e^{x} x - 5 e^{x} + C

Solution steps

\int (8 x + 3) e^{x} d x

Apply Integration By Parts

= (8 x + 3) e^{x} - \int 8 e^{x} d x

\int 8 e^{x} d x = 8 e^{x}

= (8 x + 3) e^{x} - 8 e^{x}

Simplify

(8 x + 3) e^{x} - 8 e^{x} : 8 e^{x} x - 5 e^{x}

= 8 e^{x} x - 5 e^{x}

Add a constant to the solution

= 8 e^{x} x - 5 e^{x} + C