What is the integral of (9x+11)e^x ?

The integral of (9x+11)e^x is 9e^xx+2e^x+C

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integral of (9x+11)e^x

\int (9 x + 11) e^{x} d x

9 e^{x} x + 2 e^{x} + C

Solution steps

\int (9 x + 11) e^{x} d x

Apply Integration By Parts

: (9 x + 11) e^{x} - \int 9 e^{x} d x

= (9 x + 11) e^{x} - \int 9 e^{x} d x

\int 9 e^{x} d x = 9 e^{x}

= (9 x + 11) e^{x} - 9 e^{x}

Simplify

(9 x + 11) e^{x} - 9 e^{x} : 9 e^{x} x + 2 e^{x}

= 9 e^{x} x + 2 e^{x}

Add a constant to the solution

= 9 e^{x} x + 2 e^{x} + C

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