How do i know which part of the function i should integrate and which one to derivate when doing integration by parts?

Question

As in, which one should i label as f(x) and which is g(x)? How should i think when i see a problem given?

Answer 1

Noor, a great question, and there's a direct answer that seems to help a lot of my students:  LIPET. 

 

You're going to take the derivative of f(x), so in an ideal world, differentiating should make f(x) simpler.  If the derivative of f(x) gets more complicated, then your new integral of f'(x)*g(x) could get uglier.  It doesn't always quite work that way, and you sometimes have to do it more than once, but that's at least what we're shooting for.

 

LIPET stands for different functions that you want to look for, in order of preference, for f(x): 

 

L:  logs

I:  inverse trig functions

P:  polynomials (not necessarily complicated ones...even "x" is a polynomial)

E:  exponentials (like e^x)

T:  trig

 

You can google it, too, for additional explanations and examples. 

 

Hope this helps!