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From: Rainer S. <rai...@gm...> - 2012-11-17 13:59:06
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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
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