From: Albert_Rich@msn.com   
      
   On Wednesday, March 11, 2020 at 9:16:15 PM UTC-10, Nasser M. Abbasi wrote:   
   > On 3/12/2020 12:47 AM, Albert Rich wrote:   
   > > On Wednesday, March 11, 2020 at 6:22:34 AM UTC-10, anti...@m   
   th.uni.wroc.pl wrote:   
   > >> [...]   
   > >>   
   > >> And of course, having no better method one could use Rubi way:   
   > >> add lookup table and retrive precomputed answer from the table.   
   > >>   
   > >> --    
   > >>                                Waldek Hebisch   
   > >    
   > > Rubi does NOT use a lookup table of specific precomputed integrals.    
   Rather it uses generic reduction and terminal rules to iteratively integrate   
   large classes of expressions.  For example, when Martin presents a specific   
   example Rubi cannot    
   integrate, it usually leads to a generic rule able to produce optimal   
   antiderivatives for the whole class of integrands for which the example is a   
   special case.   
   > >    
   > > Instead of using rule-based integration when there is “no better   
   method”, I contend it should be used BEFORE resorting to advanced methods   
   like Risch.  There are numerous advantages of a properly implemented   
   rule-based integrator:   
   > >    
   > > 1. If a rule does apply, the optimal antiderivative will quickly and   
   reliably be found.   
   > > 2. Rule-based systems can show the rules applied and the resulting   
   intermediate steps.   
   > > 3. The rules are self-contained and easily verified by differentiation.   
   > > 4. The individual rules are elementary in nature and thus comprehensible   
   to mere humans, like first year calculus students.   
   > > 5. This makes rule-based systems great pedagogical tools in the classroom.   
   > > 6. Rules can be developed, debugged and tested in a modular fashion rather   
   than as a monolith.   
   > > 7. Holes in the rule-based decision tree point to where new mathematical   
   knowledge (in this case, integration formulas) is crying out to be discovered.   
   > > 8. It’s quickly determined when no rule applies, so the delay in   
   resorting to advanced methods is negligible, especially compared to the amount   
   time such methods often require.   
   > >    
   > > Albert   
   > >    
   >    
   > Good summary.   
   >    
   > But I really like this idea of using Rule-based (Like Rubi) as   
   > a first phase to the integrate command, and if that fails, then   
   > a second phase is called which uses the traditional methods currently   
   > implemented by CAS systems (i.e. Risch, etc...).   
   >    
   > May be someone from Wolfram could look into this (given that Rubi is   
   > already implemented in Mathematica (i.e. Wolfram Language), this   
   > will be easier to integrate it into the Mathematica Integrate command than   
   > with other CAS systems.   
   >    
   > --Nasser   
      
   You don't need Wolfram Research to make Rubi resort to Mathematica's built-in   
   integrator if it is unable to integrate an expression.   
      
   In the functions Unintegrable and CannotIntegrate defined near the of the file   
   Rubi.m replace "Defer[Int]" with "Integrate".  Rubi.m is located on your   
   computer at the path given by the Mathematica command   
      
      First[PacletFind["Rubi"]]["Location"]   
      
   Also you will need to delete the fast loading .mx file in the Kernel   
   directory, so the .mx file will be rebuilt next time Rubi is run.   
      
   Albert   
      
   --- SoupGate-Win32 v1.05   
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