The following integral

f := u-> int(-1/(x*sqrt(-1+u^2*(x+1)^2*x^2)), x = (1/2)*(-u-sqrt(u^2-4*u))/u .. (1/2)*(-u+sqrt(u^2-4*u))/u);

arised in an applied research. I was asked about its properties:

plot on RealRange(4,infinity), limit(f(u),u=4,right), limit(f(u),u=infinity).

Unfortunately, I lost a file. As far as I remember it, I have had a problem with

the last-named one only:

limit(f(u), u = infinity);

MultiSeries:-limit(f(u), u = infinity);

asympt(f(u), u, 2);

Error, (in asympt) unable to compute series

Hope my colleagues will make progress with it. The assumed value is Pi/2.