HELPP!!

Using the substitution x=(1-u)^2, find *integral*--> 1/(1-√x) dx

Can you lead me on the right path ie. start me off because then i'll easily do the rest this is such a stubborn one i've done all the other questions.

you're saying to sub u in but we've been given x as a substitution

Same difference in effect, but in this case it's fairly straightforward:

substitute x = ... into the function you're integrating and see what it turns into as a function of u
Work out dx/du and use this to replace the dx by (something) x du

I subbed x in and I got 1/1-√(1-u)^2 and for dx/du is it u^2-2u?

ok - if it is easier for you to think that way

So - That is not correct for dx/du I am not really sure how you got that

I subbed x in and I got 1/1-√(1-u)^2 and for dx/du is it u^2-2u?

$\frac{dx}{du} = 2(1-u)$

Can you go from there?

Ohh I see I expanded it out silly me so you'd replace dx by this in the integral

Ohh I see I expanded it out silly me so you'd replace dx by this in the integral

Please enlighten me on your methods

right i seem to have got -2ln(1-√x)+2(1-√x)+C ??

On symbolab which is this partially decent site they use u=√x and end up with -2ln(√x-1)-2√x +C? so can you get different indefinite integrals depending on which substitution you take???

Yes provided the difference is only a constant, which in this case it is

(There is a slight subtlety here in that one of the logs only works if root(x) - 1 > 0 and the other only works if 1 - root(x) > 0 but you're not expected to worry about this in this particular question )

Thanks did you end up with the same answer as me right?