I find that if I start Maple10 and execute the following code, I typically end up with the warning. But if I re-execute the code once or twice again, the warning goes away and Maple evaluates the integral in terms of Elliptic functions. Great...but why should I have to re-execute the code a few times before getting a result?
> restart;
> assume(u1<0);assume(u2>0);assume(U>0);additionally(U<u2);
> assume(u0>0);additionally(u0<u2);
> u3:=1-u1-u2:
> int(1/(u^2*(1-u)*sqrt((u-u1)*(u-u2)*(u-u3))),u=u0..U):
Warning, unable to determine if 1-u1-u2~ is between u0~ and U~; try to use assumptions or set option _EnvAllSolutions to true
Why should I have to re-execute to get a result?
I tried your code above using the Classis Interface, with and without the semicolon on the last line, and I did not receive any warning messages. I am assuming that you put it there so you do not see the long list of output that is generated. Either way, the problem seems to be related to the Maple 10 interface. Classis 10 does not give warnings for this. Using Maple 10 I was able to recreate the warning message. Restarting Maple 10 and executing the code above with a semicolon at the end worked without a warning message. The input mode I used in Maple 10 was Maple Input, not 2D input.
Hope this helps, even though I did not answer your question as to why is happens.
Regards,
Georgios Kokovidis