[Reduce-algebra-developers] An integral that takes forever

[Rainer S. <rai...@gm...>]

This expression:

   p2:=1/(sqrt(d-x)*sqrt(c-x)*sqrt(b-x)*sqrt(a-x)*(a*b-a*x-b*x+x**2));

takes forever to integrate.

With the new switch trintsubst (to trace only the substitutions) you see that 
more and more complex substitutions are tried, without any reasonable result:

load_package int;
on trintsubst;
int(p2,x);

As you can see, at one point there appears the square root of polynomials of 
hyperbolic functions, which isn't a sensible way to go, in my opinion.

I added another new switch nointsubst to switch off the substitution attempts 
entirely. With "on nointsubst", the integral is returned unevaluated within a 
very short time.

I think this needs some heuristics to stop these substitutions when they lead to 
overly complicated integrands. Maybe stop when surds or exponentials with 
transcendental functions appear.

Any ideas?

    Rainer