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so we can write
\[(u e^{-a \frac{t^2}{2}})'=e^{-\frac{a t^2}{2}} \sin(t)\]

Now integrate both sides

If I remember correctly D:

\[u e^{\frac{-a t^2}{2}}=\int\limits_{}^{}e^{\frac{-a t^2}{2}} \sin(t) dt +C\]

so lets look at that part we haven't integrated

so far I have performed one round on integration by parts

Okay, so this was integration by parts once?

And you must integrate by parts again then on the remaining integral?

i just wanted to clean some stuff up
yes we need to do it again lol

this is nasty looking but yes we need to do it again

no it is not just one more

this thing looks more beastly to me

Yeah, it's pretty bad. It's supposed to be ODE review in a PDE class.

i'm starting to think this isn't gonna work

oh you know what?

this isn't an elementary integral

so we can't use our elementary ways

and that is all i know

I'm not sure I know of any non-elementary ways to integrate.

http://www.wolframalpha.com/input/?i=integrate%28e%5E%28-a+t%5E2%2F2%29+sin%28t%29%2Ct%29

Okay, well thank you for all of your time and help. I'll check out your link.

I think you need to use an integrating factor here of:\[e^{\int{atdt}}\]

Oh no, the error function again. This is what I originally was running into problems with.

hey asnaseer thats not where we were having the problem

sorry - missed a minus sign

yes you need that lol

\[\int\limits\limits_{}^{}e^{\frac{-a t^2}{2}} \sin(t) dt= \]

this is the part we got stuck on

and ike robin says we are getting the error function

by the way thanks for coming asanaseer

np

Thank you both for helping.

yw - I'm off to do some research on this interesting problem - I'll be back if I find a solution

Good luck, I've been working on this for hours!

ok - thx for the clarification - really appreciated.

Yes - I tried that as well :)