# Integral of x^{-1/2}*(1-x)^-1

Claim: $\int\frac{dx}{\sqrt{x}(1-x)}=\log{\frac{1+\sqrt{x}}{1-\sqrt{x}}}$
Derivation confirms this, but how was this answer arrived at? IBP seems not to work, can't find a good u-substitution...

What about the substitution $x=u^2$, followed by partial fraction decomposition?

phyzguy
$$\frac{1}{\sqrt{x}(1-x)} = \frac{1}{\sqrt{x}(1+\sqrt{x})(1-\sqrt{x})}$$