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.
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.