Richard Fateman  wrote:   
   > On Monday, December 27, 2021 at 2:48:09 AM UTC-8, Nasser M. Abbasi wrote:   
   > > On 12/27/2021 2:27 AM, ??????? ???????????? wrote:   
   > >   
   > > >   
   > > > Also please test on Integrate from Wolfram Math. 13.0.0,   
   > > > since it has IntegrateAlgebraic indide.   
   > > There should be a new build of CAS independent integration   
   > > tests which will have Mathematica V 13.0. But waiting for   
   > > Maple 2022 and sagemath 9.6 and most important for the next   
   > > version of Rubi to be released with its new test input files   
   > > with new integrals added.   
   > >   
   > > This is because it takes about 2 months and lots of effort and   
   > > time to run all these tests, and do not want to do this now   
   > > and then have to do it again few months later.   
   > >   
   > > Hopefully sometime next year.   
   > >   
   > > --Nasser   
   > The long expression posted previously that Maxima could not integrate can be   
   expanded and much of it is then integrated.   
   >   
   >         v:   
   >         (((-2)*x^3+34*x^2+392*x+800)*log((((-25)*x+(-100))*log   
   x)+(x^2+x))/(25*x+100))+((-6)*x^3+102*x^2+1176*x+2400))/((25*x^3   
   200*x^2+400*x)*log(x)+((-1)*x^4+(-5)*x^3+(-4)*x^2));   
   >         ((-2*x^3+34*x^2+392*x+800)*log(((-25*x-100)*log(x)+x^2   
   x)/(25*x+100))-6*x^3+102*x^2+1176*x+2400)/((25*x^3+200*x^2+400*x   
   *log(x)-x^4-5*x^3-4*x^2)   
   >   
   >  There's one piece of the expansion that doesn't come out in the wash,   
   >   
   > integrate((3*x^6-119*x^5-608*x^4+27320*x^3+339296*x^2+1411200*   
   +1920000)/((150*x^2+1200*x+2400)*log(x)-6*x^3-30*x^2-24*x),x)   
   >   
   > So this  after tossing out what I thought were extraneous to come up with a   
   simple   
   > "bug report"  I came to the problem  integrate( 1/(log(x)+x),  x)    which   
   Maxima 5.45.1  apparently cannot do.   
      
   I am not sure what you did.  However, integral of v is elementary.  AFAICS   
   the two other integrals are not elementary.  So, its looks like mistake   
   in reduction.   
      
   > It seems to me that one can generate increasingly more challenging examples   
   in a systematic fashion that would illustrate points of failure more   
   effectively than trying out random algebraic tree generation.   
   > For instance, irreducible polynomials of increasing degrees;  one, two, ...   
   more   logarithmic extensions, exponential extensions, both, ..   
      
   Well, you can do that for _known_ difficulties.  Random examples   
   generate some unexpected difficulties.  Also, in practice   
   integrator may exhibit nonlinear behaviour: can handle   
   each difficulty separately, but fails when two are in   
   single example.  Pattern matchers are very sensitive   
   to exact form of integrand.  In particular unsimplified   
   derivatives leave a lot of hints for integrator.  That   
   is why all expamples I provided are expanded.  Related   
   is that simple integrators frequently split sums term   
   by term.  This is correct in simple "reduced" cases   
   but easily fails when integrand contains some irrelevant   
   junk.   
      
   Another aspect is that using tilu techinque you can put   
   whole Rubi testsuite into database of known cases.  That   
   would be cheating, but you could claim 100% success rate   
   on integrable examples.  In case of Risch algorithm probably   
   100 examples is enough to cover all branches.   
      
   With small set of test cases one could easily hide them in   
   bigger database and claim that database outperforms Risch.   
   Random examples discourage cheating: the whole pool is so   
   large that it is probably impractical to put them in   
   database.  And if somebody managed to invent clever   
   compression scheme, I would consider such compression   
   as very interesting result...   
      
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