Even though I've been through countless instances where I needed to use integration by parts, to this day, I still derive it from the chain rule, identify my 'parts' and apply the formula.
At some lecture a while back, one of my profs did a two step integration by parts in like 30 seconds. It went so fast, looked so easy, and I never caught on to how he did it. The answer just fell out.
What are you favorite tricks for quick integration by parts? Everything goes, mnemonics, special notation, or maybe some other trickery?
Speed is the number one priority here. I'd rather have a fast method that requires some practice to master, than have a slow method that can be learnt quickly!
Thanks in advance!