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Originally Posted by ThePerfectHacker My point is that it is a lot easier to keep track of everything doing integration this way. Because you do not need to go out of your way to write  and  . |
I agree and I think this is quite a clever observation. However, from an educational standpoint, I think teaching this to a student who has never seen integration by parts, ie. Freshman level college, would be a mistake. The students would not likely be able to follow the "reverse product rule" formulation that you worked out.
-Dan