What is the integral of (5x+2)e^x ?

The integral of (5x+2)e^x is 5e^xx-3e^x+C

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integral of (5x+2)e^x

\int (5 x + 2) e^{x} d x

5 e^{x} x - 3 e^{x} + C

Solution steps

\int (5 x + 2) e^{x} d x

Apply Integration By Parts

: (5 x + 2) e^{x} - \int 5 e^{x} d x

= (5 x + 2) e^{x} - \int 5 e^{x} d x

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

= (5 x + 2) e^{x} - 5 e^{x}

Simplify

(5 x + 2) e^{x} - 5 e^{x} : 5 e^{x} x - 3 e^{x}

= 5 e^{x} x - 3 e^{x}

Add a constant to the solution

= 5 e^{x} x - 3 e^{x} + C

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