## anonymous 4 years ago What is my inner-function g if I integrate x/(2-x)^3 with the method of substitution?

1. EscherichiaRinku

If you think of powers as a function, then you will easily see that (2-x) is a function inside the power function. So, your g is g(x) = 2-x.

2. anonymous

that was simpler than it looked :S

3. anonymous

Escher, if you actually did that by integration, what would it look like?

4. anonymous

then of course you have to write $u=2-x, du = -dx$ $x=2-u$ and integrate $-\int \frac{2-u}{u^3}du$

5. anonymous

or if you prefer $\int \frac{u-2}{u^3}du$

6. EscherichiaRinku

And then substitute (2-x) back to get a result with the original terms :)

7. EscherichiaRinku

^I mean, substitute (2-x) back after integration :D

8. anonymous

Oh, I did not know that I´m also able to replace the x upstairs (which annoyed) with 2-u. Thank you very much.