What is the integral of (7x+2)e^x ?

The integral of (7x+2)e^x is 7e^xx-5e^x+C

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integral of (7x+2)e^x

\int (7 x + 2) e^{x} d x

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

Solution steps

\int (7 x + 2) e^{x} d x

Apply Integration By Parts

: (7 x + 2) e^{x} - \int 7 e^{x} d x

= (7 x + 2) e^{x} - \int 7 e^{x} d x

\int 7 e^{x} d x = 7 e^{x}

= (7 x + 2) e^{x} - 7 e^{x}

Simplify

(7 x + 2) e^{x} - 7 e^{x} : 7 e^{x} x - 5 e^{x}

= 7 e^{x} x - 5 e^{x}

Add a constant to the solution

= 7 e^{x} x - 5 e^{x} + C

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