2543.sagews

var('a b')
assume(a>0)
assume(b>0)
assume(b-a>0)
integral(sqrt((x-a)*(b-x))/x,x,a,b)

(a + b)*arcsin(-sqrt(a^2 - 2*a*b + b^2)/(a - b)) - 2*sqrt(a)*sqrt(b)*arcsin(-sqrt(a^2 - 2*a*b + b^2)/(a - b))