Evaluating $\frac{1}{\pi} \int_a^b \frac{1}{\sqrt{x(1-x)}}dx$ I can't calculate the following integral:
$$\frac{1}{\pi} \int_a^b \frac{1}{\sqrt{x(1-x)}}dx,$$
where $[a, b] \subset [0,1]$.
Can someone, please, give me a hint?
Thank you!

Anoteher simple substitution exploiting the symmetry of the integrand: $x=1/2 + u \implies dx=du$.
$$\int\frac{1}{\sqrt{x(1-x)}}dx=\int\frac{1}{\sqrt{(1/2+u)(1/2-u)}}du$$
