Integrate by parts using the formula , where and .

Combine and .

Move to the left of .

Combine and .

Since is constant with respect to , move out of the integral.

Multiply by .

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 .

Multiply by the reciprocal of the fraction to divide by .

Multiply by .

Move to the left of .

Since is constant with respect to , move out of the integral.

Multiply by .

The integral of with respect to is .

Rewrite as .

Replace all occurrences of with .

Reorder terms.

Evaluate integral of xe^(x/3) with respect to x