Question

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

Answer 1

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.

Answer 2

that was simpler than it looked :S

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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