I don't think thats particularly an integration by parts question
If you had integration of (3x^2)(e^x^3), you could probably straight away tell that that came from e^x^3 as when you differentiate e^x^3 you get (3x^2)(e^x^3).
The only difference with what you asked is that instead of (3x^2)(e^x^3) you want integration of (x^2)(e^x^3) so to get rid of the extra 3, just write a 1/3 in front of e^x^3 so that when it differentiates, it cancels out the 3.
I hope that made sense!
(if you really really want to do integration by parts however, make u = x^2 and v' =e^x^3, then you will have to do integration by parts two more times within that integration by parts - but after that third time it should work out.