I'm trying to integrate this function over the interval
pdf[x_, bb_] = Sqrt[(x-a[bb]) (b[bb]-x)] / (2 Pi bb x);
a[bb_] = (Sqrt[bb] - 1)^2; b[bb_] = (Sqrt[bb] + 1)^2;
Currently, I calculate the indefinite integral then plug in the limits of integration but Mathematica gives divide by zero error but I've calulated it by hand using Ryzhik and Gradshteyns Tables of Integrals and it equals 1 over this interval, no problems.
I've also used NIntegrate over this interval and it does equal 1.0.
If anyone can help to get it to work in Mathematica that'll be great as I'm wanting to integrate moments f[x]pdf[x,bb] over this interval too.