Question

How to determine what you should substitute for \(u\) and \(du\)? (Substitution Rule)

Answer 1

you don't substitute anything to du...

Answer 2

du is derivative of u

Answer 3

Let me start with an example:\[ \int\left(1 - {1 \over w} \right) \cos (w -\ln w)dw\]

Answer 4

Oh, yeah.

Answer 5

you can start by letting u = 1/w

Answer 6

How do you know what to substitute for \(u\)?

Answer 7

if you're used to derivatives...then you can see them...

Answer 8

on second thought u= 1/w is wrong

Answer 9

let u = w - ln w

Answer 10

\[\int f(g(x))g'(x) dx= \int f(u)du \text{ where }u = g(x) \]

Answer 11

So in this case, \(\cos w = f(w)\) and \(w - \ln w = g(w)\)

Answer 12

And the rule says that \(u = g(w)\) so \(u = w - \ln w\), right?

Answer 13

yes u = w - ln w

Answer 14

OK, thank you very much. :)