Is There a Proof for Tabular Integration?

[MadViolinist]

Today we learned tabular integration as a shortcut method for integration by parts. Is there a proof that legitimizes tabular integration out there, or some general formula? Because there has to be some sort of logic for the process of creating the diagonal lines, or assigning pluses and minuses. Thanks in advance.

 

[Vorde]

There isn't really a proof for tabular integration, it's just shorthand for integration by parts. If you did a integration by parts using placeholder functions for u and v (meaning the actual functions could be whatever you want) you'll see that it expands to the same thing that tabular integration does, it just saves time doing by remembering the tabular way.