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

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

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integral of (x+3)e^x

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

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