How do you solve the integral

1. Feb 21, 2012

chapsticks

1. The problem statement, all variables and given/known data
∫ x sinx cosx dx =

2. Relevant equations
note that sinx cosx = (1/2) sin 2x

3. The attempt at a solution
1/2) ∫ x sin 2x dx =
(1/2) [(-1/2)x cos 2x - ∫ (-1/2)cos 2x dx] =
(1/2) [(-1/2)x cos 2x +(1/2) ∫ cos 2x dx] =
(-1/4)x cos 2x +(1/4) ∫ cos 2x dx =
(-1/4)x cos 2x +(1/4)(1/2) sin 2x + c =
(-1/4)x cos 2x +(1/8) sin 2x + c =

2. Feb 21, 2012

Dick

That looks just fine. What's the question?

3. Feb 21, 2012

The_Duck

It seems like you have an answer. So what's the issue?