>> Someone please integrate this by hand: sin(3x^2) >I get -cos(x^3) in both cases. Do you have a problem with that? Yeah, I do: It's wrong. The integral of sin(3x^2) is hard to do. If you need an exact solution, i do not think that it is possible. The best you can get is a numeric solution anyways. The best I can tell you is that the integral converges to 1/2 as x->infinity. nick