clicliclic@freenet.de schrieb:   
   >   
   > The pair of cube-root pseudo-elliptic integrals found by Euler:   
   >   
   >   integrate((a + b*x)/((3 - x^2)*(1 - 3*x^2)^(1/3)), x)   
   >   
   >   integrate((a + b*x)/((3 + x^2)*(1 + 3*x^2)^(1/3)), x)   
   >   
   > and the pair found (or implied) by Legendre:   
   >   
   >   integrate((a + b*x)/((3 + x^2)*(1 - x^2)^(1/3)), x)   
   >   
   >   integrate((a + b*x)/((3 - x^2)*(1 + x^2)^(1/3)), x)   
   >   
   > look very similar. But FriCAS 1.3.1 (the current web-interface   
   > version) returns:   
   >   
   > >> Error detected within library code: integrate: implementation   
   >    incomplete (residue poly has multiple non-linear factors)   
   >   
   > for Euler's pair and:   
   >   
   > >> Error detected within library code: integrate: implementation   
   >    incomplete (trace 0)   
   >   
   > for Legendre's pair. With the four integrands being so similar, this   
   > occurence of different failure modes is somewhat surprising.   
   >   
   > However, FriCAS can solve all of them for either a=0 or b=0, and thus   
   > also knows how to solve the general cases in a sense.   
   >   
      
   Actually, the first integral for a=0   
      
     integrate((b*x)/((3 - x^2)*(1 - 3*x^2)^(1/3)), x)   
      
   is solved readily while for b=0   
      
     integrate((a)/((3 - x^2)*(1 - 3*x^2)^(1/3)), x)   
      
   the FriCAS web interface runs into a 5-minute timeout. Replacing the   
   constant numerator (a) with unity makes the computation instantaneous. I   
   believe this behavior has been noted by oldk1331 already; I am inclined   
   to call it a bug.   
      
   Anyway, its existence puts the appropriateness of the "implementation   
   incomplete" exit for the full numerator (a + b*x) into some doubt.   
      
   I didn't check - but the other three integrands presumably exhibit the   
   same behavior.   
      
   Martin.   
      
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