> Oh, I thought I was the first to try this particular variation of a   
   > familar cube-root integrand. But to implement a loop over different   
   > pseudo-random numbers should be easy, and its omission may be a mere   
   > oversight. I will submit this integrand again to the next version.   
      
   After fixing this "division by zero" bug, your first integral seems to   
   loop indefinitely.  I think there is no symbolic result for   
   "integrate((1 + x)/((1 + x + x^2)*(a + b*x^3)^(1/3)), x)".   
   When a,b are integers, FriCAS can give symbolic results.   
      
   > Another thing has me wondering. Your antiderivatives of rational   
   > functions can be discontinuous because the ATAN part is not always   
   > rewritten to involve polynomial arguments only, as proposed by Rioboo.   
      
   For this example, I have post a small patch to fricas-devel.  After   
   my patch, FriCAS gives continuous result, same as SymPy.   
   I think this is a small programming mistake made by Manuel Bronstein.   
      
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