More integration….

What did you do for the denominator?

I didn’t do anything
I differentiated the substitution to get (rootx-2)-1
But if I subbed that back into the integral I wouldn’t get 1+ Root x-2 only 3-x/root x-2

You should have u+1 on the denominator.
I don't follow what youre saying here.

The denominator is 1+sqrt(x-2). You can't just "cancel" the sqrt(x-2) part.

u/(u+1) is not 1.

I didn’t try to cancel it , I left it blank but anyways it wouldn’t work

I get what you mean but how would I get that 1+

WHat do you think the denominator of the original function is in terms of x?
Write down clearly how it transforms to u.

I’m stuck on the denominator

How? You start with
1 + sqrt(x-2)
In terms of u it is ...

That’s just U+1

Yes.
So replace dx with the corresponding expression in terms of u and du, and modify the limits so they're in terms of u.

I can't help thinking you;re overcomplicating it at the start by not saying dx/du = 2u directly, then simply doing the substitution for each part, then cancelling if necessary.

This is really not working out for me
I need to get 3-u^2+2/U+1
I’m getting 3-u^2+2/2U

Can you clearly show your working when you substitute for u in the
* numerator,
* denominator
* dx
and then any simplifcation when you put them together with the transformed limits.

What you "need to get" is wrong. But so is what youre currently gettting.

Youre not doing it clearly. For the numerator
3 - x = 3 - (u^2 + 2) = 1 - u^2
The 2 on the numerator is subtracted if you write it down clearly. You had it as +2.

As above (several times)
dx = 2u du
You arguably complicate it by expressing u = sqrt(...) then differentiating to get dx/du in terms of x and then trying to manipulate more complex expressions in x.

As above, the denominator is
u+1

Simply put the three things together with the transformed limits and see if you can simplify then integrate.

I am infuriating…