What is the integral of xe^{x+3} ?

The integral of xe^{x+3} is e^{3+x}x-e^{3+x}+C

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integral of xe^{x+3}

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int e^{3 + x} d x = e^{3 + x}

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

Add a constant to the solution

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

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What is the integral of xe^{x+3} ?
The integral of xe^{x+3} is e^{3+x}x-e^{3+x}+C