# Evaluate integral of xsin(x/2) with respect to x

Integrate by parts using the formula , where and .
Simplify.
Combine and .
Move to the left of .
Combine and .
Since is constant with respect to , move out of the integral.
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 .
Simplify.
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 xsin(x/2) with respect to x