Question

Use the substitution \(r=1-x\) to evaluate
\[
\int\frac{x^2(1+x)}{1-x}\,dx
\]
I have no clue how to do it.

Answer 1

hmm

Answer 2

i've never seen this used... i'm wondering if it wants you to use r=1-x to find x^2 and 1+x so you have all in terms of r

Answer 3

Yah, I wrote it out, it looks a bit messy to replace all of the pieces. But you end up with just R in the bottom, instead of 1-x. Allowing you to easily break up the top into a bunch of different fractions that are easy to differentiate.

Answer 4

Oh looks like he logged off :3 heh

Answer 5

I figured it out. Just replace all x with 1-r.