I cant solve this exactly but who can help me with it.. I also need the primitive of sin x
If an exact value can be found for that definite integral, I suspect you should make a contour integral in the complex plane in order to crack it.
Hint: try to decompose the integral into two integrals. one should have limits of integration from 0 to pi/2
exploit symmetry and manipulate the limits of integration to solve the problem. these identities might also help: sin(x) = sin(pi - x), 2sin(x)cos(x) = sin(2x).
Yes, I agree it's a series of tricks. I just solved it yesterday and was amazed at the elegance of the solution. Dick's hint in the other thread proves to be very helpful.