# Find the Integral xe^(-x)

Integrate by parts using the formula , where and .
Simplify.
Move to the left of .
Rewrite as .
Since is constant with respect to , move out of the integral.
Simplify.
Multiply by .
Multiply by .
Let . Then , so . Rewrite using and .
Let . Find .
Differentiate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Rewrite the problem using and .
Since is constant with respect to , move out of the integral.
The integral of with respect to is .
Simplify.
Replace all occurrences of with .
Find the Integral xe^(-x)

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