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

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

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integral of xe^{x+y}

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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