Non-Elementary Integration · Superchallenge problem

Using $B(a,b)=\displaystyle\int_0^1x^{a-1}(1-x)^{b-1}\,dx=\Gamma(a)\Gamma(b)/\Gamma(a+b)$ and the reflection formula $\Gamma(s)\Gamma(1-s)=\dfrac{\pi}{\sin\pi s}$, evaluate $\displaystyle\int_0^1\dfrac{dx}{x^{3/4}(1-x)^{1/4}}$.