This is for my homies taking Calculus.

U-substitution is the opposite of the Chain Rule.  Integration by parts is the opposite of the Product Rule.

Don’t believe me?

Take u and v to be the left and right parts of some formula.

derivation of Integration-by-Parts formuladerivation of Integration-by-Parts formula

Now switch some symbols around and you’ve arrived at the formula for Integration by Parts.

By the way, I normally use L and R for the left and right groups of symbols when I’m teaching Product Rule.  Here I just used u and v because that’s probably how you’ve seen the formula be written.

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