From: nma@12000.org   
      
   On 10/3/2016 5:38 PM, clicliclic@freenet.de wrote:   
      
   >   
   > Good news: having tried the FriCAS web interface once in a while, I have   
   > found it to be working again, with:   
   >   
   >   )version   
   >   
   > reporting:   
   >   
   >   Value = "FriCAS 1.3.0 compiled at Thu Sep  1 17:01:37 UTC 2016"   
   >   
   > now. And I find that:   
   >   
   >   integrate((a + b*x)/((3 + x^2)*(1 - x^2)^(1/3)), x)   
   >   
   > and:   
   >   
   >   integrate((a + b*x)/((3 - x^2)*(1 + x^2)^(1/3)), x)   
   >   
   > are still too difficult:   
   >   
   >   >> Error detected within library code:   
   >      integrate: implementation incomplete (trace 0)   
   >   
   > So there appears to be room for further growth ...   
   >   
   > Martin.   
   >   
      
   I get same message on my Linux build also for ver 1.3.   
      
   btw, I tried the above on the new Mathematica 11.0.1   
   and on Maple 2016.1 and Rubi 4.9.2, Mathematica gave   
   the simplist answer. Maple did not do it. Rubi answer   
   contained complex numbers. Here is the result   
      
   Mathematica   
   ==============   
   In[29]:= Integrate[(a + b*x)/((3 + x^2)*(1 - x^2)^(1/3)), x]   
      
   Out[29]= (1/3)*a*x*AppellF1[1/2, 1/3, 1, 3/2, x^2, -(x^2/3)] + (1/6)*   
      b*x^2*AppellF1[1, 1/3, 1, 2, x^2, -(x^2/3)]   
      
   In[30]:= Integrate[(a + b*x)/((3 - x^2)*(1 + x^2)^(1/3)), x]   
      
   Out[30]= (1/6)*x*(2*a*AppellF1[1/2, 1/3, 1, 3/2, -x^2, x^2/3] +   
       b*x*AppellF1[1, 1/3, 1, 2, -x^2, x^2/3])   
      
   Rubi: 4.9.2   
   ============   
   In[62]:= ShowSteps = False;   
   In[63]:= Int[(a + b*x)/((3 + x^2)*(1 - x^2)^(1/3)), x]   
      
   Out[63]= ((I*Sqrt[3]*a -   
          3*b)*((1 - x)/(I*Sqrt[3] - x))^(1/   
           3)*(-((1 + x)/(I*Sqrt[3] - x)))^(1/3)*   
        AppellF1[2/3, 1/3, 1/3, 5/3, -((1 - I*Sqrt[3])/(I*Sqrt[3] - x)),   
              (1 + I*Sqrt[3])/(I*Sqrt[3] - x)])/(4*(1 - x^2)^(1/3)) - ((I*   
           Sqrt[3]*a +   
          3*b)*(-((1 - x)/(I*Sqrt[3] + x)))^(1/   
           3)*((1 + x)/(I*Sqrt[3] + x))^(1/3)*   
            AppellF1[2/3, 1/3, 1/3,   
         5/3, (1 + I*Sqrt[3])/(I*Sqrt[3] +   
            x), -((1 - I*Sqrt[3])/(I*Sqrt[3] + x))])/(4*(1 - x^2)^(1/3))   
      
   In[64]:= Int[(a + b*x)/((3 - x^2)*(1 + x^2)^(1/3)), x]   
      
   Out[64]= ((Sqrt[3]*a +   
          3*b)*((I - x)/(Sqrt[3] - x))^(1/   
           3)*(-((I + x)/(Sqrt[3] - x)))^(1/3)*   
        AppellF1[2/3, 1/3, 1/3, 5/3, (I + Sqrt[3])/(Sqrt[3] - x),   
              -((I - Sqrt[3])/(Sqrt[3] - x))])/(4*(1 + x^2)^(1/   
           3)) - ((Sqrt[3]*a -   
          3*b)*(-((I - x)/(Sqrt[3] + x)))^(1/   
           3)*((I + x)/(Sqrt[3] + x))^(1/3)*   
            AppellF1[2/3, 1/3, 1/3,   
         5/3, -((I - Sqrt[3])/(Sqrt[3] + x)), (I + Sqrt[3])/(Sqrt[3] +   
            x)])/(4*(1 + x^2)^(1/3))   
      
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)