"Nasser M. Abbasi" schrieb: > > I've update the listing of the first 10 integrals. Added your optimal > results there, and also added result from Sage 5.4. > > http://www.12000.org/my_notes/ten_hard_integrals/index.htm > > Each integral is now on a separate web page instead of them > all on the same page to make it easier to see the results > of each. > > There is also a pdf file. > > Here is a quick summary of the first 10 integral results, > I just counted if CAS gave result or not. No checking for > anything else. Some results are clearly not optimal and > few results take many pages. > > 1. Mathematica: did 1,2,3,4,6,8,9,10 did not: 5,7 > 2. Maple: did 1,2,3,4,5,6,7,8 did not: 9,10 > 3. Rubi4: did 2,3(?),4,5,6,7,8,9,10 did not: 1 > 4. Sage: did: 1,2,3,4,7,9 did not: 5,6,8,10 > > I do not understand Rubi4 result for 3. I do not know what > Subst[....] is supposed to mean, but I have not looked it > up, I am sure it is explained somewhere. Any errors, please > let me know. >
I noticed that your MMA and Rubi integrands for problem #7 have and extra outer root.
I strongly suspect that "Sage" always means "Maxima" (not e.g. "Sympy"): see the Runtime Error Message for problem #8.
Rubi's SUBST means "substitute": SUBST(a+b,b,c+d) = a+(c+d). Since Rubi's answer to problem #3 contains an unresolved integral inside the SUBST statemant, it must be counted as "not done".