When I intergrated:

1/sqrt(x)sqrt(1-x) = I, Ive got sinh sqrtx. This i used a subsitution x=u^2

However, expanding the bottom;

I = 1/sqrt(x-x^2), then chaging the denominator to a perfect square:

I = 1/sqrt (1/4 - (1/2-x)^2), then using the same sin inverse identity, i got a complete different answer.

Can someone please explain to me this?