Albert Rich schrieb:   
   >   
   > [...]  Also, although large, the scope of Rubi is NOT infinite in   
   > extent.  Rather the goal is to provide a comprehensive set of rules   
   > for finding optimal antiderivatives of instances of a fixed set of   
   > well-defined forms of integrands.  For example, all instances of   
   > integrands of the form   
   >   
   >     (d+e x^n)^m (a+b x^n+c x^(2 n))^p   
   > and   
   >     cos(e+f x)^p (a+b sin(e+f x))^m (c+d sin(e+f x))^n   
   >   
   > Given this limited goal, I think a manageable number of integration   
   > rules will suffice.  Certainly under 10,000.  The uncompressed size   
   > of the Rubi 4.11 source text files is less than 1.9 megabytes.  This   
   > is tiny by today's standards, and leaves plenty of room for growth.   
   >   
      
   What you describe appears to be the back-end of an integrator only.   
      
   Users would surely wish that Rubi knew to integrate, for instance, (1)   
   polynomials P(x) of any degree, (2) any rational function R(x) whose   
   denominator can be split into linear or quadratic factors by the host   
   system, (3) any algebraic function R(x, SQRT(Q(x))) involving a linear   
   or quadratic polynomial Q(x), as well as (4) any such algebraic function   
   where Q(x) is a cubic or quartic polynomial that can be split into two   
   quadratics. To this should be added (5) all trigonometric integrands   
   f(SIN(x), COS(x)) reducible to one of these classes by the familiar   
   Weierstrass substitution t = TAN(x/2). And then (6) all product   
   integrands f(x)*g(x) reducible to any of the above five groups through   
   integration by parts, where f(x) or g(x) may equal unity. Of course,   
   apart from imaginary offsets appearing in logarithmic terms, Rubi's   
   antiderivatives should be valid functions of real analysis where the   
   integrands are real.   
      
   A separate integrator front-end would be required to make all class   
   members palatable to the system you describe. One can probably identify   
   many more integrand groups of the same generality, most of which should   
   be discussed in Timofeev's textbook.   
      
   Martin.   
      
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