# Find the Integral xe^(-3x)

Integrate by parts using the formula , where and .
Simplify.
Combine and .
Combine and .
Combine and .
Since is constant with respect to , move out of the integral.
Simplify.
Multiply by .
Multiply by .
Since is constant with respect to , move out of the integral.
Let . Then , so . Rewrite using and .
Let . Find .
Rewrite.
Divide by .
Rewrite the problem using and .
Simplify.
Move the negative in front of the fraction.
Combine and .
Since is constant with respect to , move out of the integral.
Simplify.
Combine and .
Move the negative in front of the fraction.
Since is constant with respect to , move out of the integral.
Simplify.
Multiply and .
Multiply by .
The integral of with respect to is .
Simplify.
Rewrite as .
Simplify.
Combine and .
Combine and .
Replace all occurrences of with .
Combine and .
Reorder terms.
Find the Integral xe^(-3x)