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first step I get
1/2 (u-1/u+1)^-1/2
not sure what to do next. I am brain dead at the moment.

what was original function
did you replace dx with du
du = dx/2sqrt(x-1)

sorry i think im mistaken, ignore what i just said
but you will use du

take what you have and you will multiply it by derivative of (u-1)/(u+1)
use quotient rule

correct looks like you did that already in the 1st post

ok, after that do I use quotient rule?

yes
(f'g -fg')/g^2

ok after that I get (u+1)-(u-1)/(u+1)^2 which ends up being 2/(u+1)^2

correct, now simplify and then you have to multiply by du ans replace u with x

do I need to take derivative of U first?

yes
sorry that was what i meant by du (derivative of u)
then replace all the u's with sqrt(x-1)

so derivative of u would be 1/2(x-1)^-1/2

correct

so
2/(u+1)^2 * 1/2(x-1)^-1/2
U= sqrt x-1 and x=34/9
????

yes but dont forget what you had originally
1/2 (u-1/u+1)^-1/2
thats part of it still too

I am lost now
would it be
1/2 [(sqrt x-1)-1]/sqrt [(x-1)+1]^-1/2 * 1/2 (34/9-1)^-1/2
????

this answer really seems wrong, I am sure I did something wrong in my math but I get 2025/136

sorry wrong
2025/128

why did you take 1 over everything

because everything had a power of -1/2 right, that means its on the denominator

oh I see now, didn't think of that

so what equation I am using to replace with?

??