I got the problem down to
(1/2)y + (1/4)sin2y
the sub I used was x = siny
how do i sub back to X?
I know the first part is sin inverse by how do i get the 2nd part?
If you have with , then .
Subbing back in yields .
Recall the double angle identity: .
Letting , we have .
Clearly , but maybe not so clearly: , because if you draw out the triangle, the angle whose sine is will have cosine .
Thus, .
Thus the final answer is .
=Thus, , which is what I assume you were integrating.
I hope this helped.