Indefinite Integration of a Rational Expression

1. Aug 12, 2012

communitycoll

1. The problem statement, all variables and given/known data
<Indefinite integral sign here>[r^2 -2r] / [r^3 - 3r^2 + 1]dr
or the second example in the "Substitution" section here:
http://people.clarkson.edu/~sfulton/ma132/parfrac.pdf

2. Relevant equations

3. The attempt at a solution
Nothing to really attempt, I just don't get what they do with the numerator (i.e., how it turns into a 1).

2. Aug 12, 2012

tiny-tim

hi communitycoll!
(have an integral: ∫ and try using the X2 button just above the Reply box )
ah, nooo, the numerator isn't r2 - 2r, it's (r2 - 2r)dr !!

(and of course that's 1 times dw )

the trick in substitution is that you always have to substitute the "d" part also!

3. Aug 12, 2012

eumyang

If you read that attachment carefully, you would have seen this:
So they let
w = r3 - 3r2 + 1,
so
dw = 3r2 - 6r dr,
which is the same as
dw = 3(r2 - 2r) dr.

Do you see it now?

4. Aug 14, 2012

communitycoll

Okay then. Yeah, I understand now. Thanks.