Having trouble with a rather nasty integration

[Link-Jun]

Ok, here's the problem:

integral ( sin( sqrt(a*t) ) ) dt

It's an indefinite integral and I've tried almost everything to try and solve it. All the different types of applicable techniques of integration in my book and also on various sites. I've put serious effort into this, I dont want you to think that I'm just being lazy. Any help asap would be incredibly helpful, thanks in advance!

 

[jimi]

Let u = sqrt (at)
u^2 = at
then we need to find integral (sin (u) dt)
dt = dt/du * du
du/dt = a/2u
dt/du = 2u/a
so we need: integral ((2u/a)sin (u) du) = 2/a (integral (u sin (u) du))
you now need to integrate u sin(u). You can use integration by parts. I'll leave this to you.

 

[Link-Jun]

Thanks a lot, man I wish there were ingenuity pills...