[mGGPrometheus]

Originally Posted by pinealan

er, I still cant work out the answer... do I have to use integration by part?
What I now have is
Not sure if it is correct. May I ask for a bit more help?

After letting u = sin(x), du = cos(x)dx, the integral becomes . Then you just need to use partial fractions.



Since this must be true for all u, we can try different values of u. Letting u = -1, we see that D = 1/8. Letting u = 1, A = 1/8. Letting u = 0, A+B+C+D+E+F = 1, so B+C+E+F = 3/4, so B = 3/4 - C - E - F. Then you expand the RHS so you get a cubic in 'u' and equate the terms on both sides to solve for the other constants. In the end you get



And ^ can be integrated pretty easily. I didn't want to type the working out because it's quite a messy problem