From: hebisch@antispam.uni.wroc.pl   
      
   clicliclic@freenet.de wrote:   
   >   
   > Hello!   
   >   
   > How long does it take the popular integrators to evaluate the following   
   > elementary indefinite integrals? Imagine them to appear in terms of some   
   > series expansion:   
   >   
   > INT(1/((1+x+2*x^2)^5*(3-2*x)^(11/2)),x)   
   >   
   > INT(1/((1+x+2*x^2)^10*(3-2*x)^(21/2)),x)   
   >   
   > INT(1/((1+x+2*x^2)^20*(3-2*x)^(41/2)),x)   
   >   
   > and:   
   >   
   > INT(1/((1+x+2*x^2)^5*(3-2*x+x^2)^(11/2)),x)   
   >   
   > INT(1/((1+x+2*x^2)^10*(3-2*x+x^2)^(21/2)),x)   
   >   
   > INT(1/((1+x+2*x^2)^20*(3-2*x+x^2)^(41/2)),x)   
   >   
   > Does Maple beat FriCAS? Does Rubi beat Mathematica?   
   >   
   > Martin.   
      
   For FriCAS results for 'integrate' are somewhat embarrassing:   
   0.20s, 0.49s, 21.85s, 0.53s, 1.89s and the sixth one would   
   take more than few hours.  Core integrator is reasonably fast,   
   calling 'lfintegrate' I get: 0.02s, 0.04s, 0.11s, 0.07s,   
   0.20s, 1.02s.  'integrate' tries to make result nicer and   
   in the process attempts to factor largish integers which   
   takes a lot of time...   
      
   Remark: 'lfintegrate' gives correct result only if certain   
   assumptions are satified.  'integrate' transforms integrals   
   so that 'lfintegrate' can handle them, calls 'lfintegrate'   
   and then tries to make the result nicer.  Your integrals   
   are simple and well-behaved, so can be sent directly to   
   'lfintegrate'.   
      
   --   
                                 Waldek Hebisch   
      
   --- SoupGate-Win32 v1.05   
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