"Nasser M. Abbasi" schrieb:   
   >   
   > On 1/20/2018 10:26 PM, clicliclic@freenet.de wrote:   
   > >   
   > > can you favorite CAS baby digest these pseudo-elliptic integrals?   
   > >   
   > >    INT(x/((4 - x^3)*SQRT(1 - x^3)), x) = ?   
   > >   
   > >    INT(x/((x^3 + 8)*SQRT(x^3 - 1)), x) = ?   
   > >   
   > >    INT((2 + x^3)/((4 - x^3)*SQRT(1 - x^3)), x) = ?   
   > >   
   > >    INT((x^3 - 4)/((x^3 + 8)*SQRT(x^3 - 1)), x) = ?   
   > >   
   > > In particular, can you do better than FriCAS, whose elementary   
   > > output contains (-1)^(1/6) I believe?   
   > >   
   >   
   > Mathematica 11.2 gives results using AppellF1   
   > ================   
   >   
   > [...]   
   >   
   > Rubi 4.14.4 uses Appell for the last 3 only   
   > ===========   
   >   
   > In[33]:= Int[x/((4-x^3)*Sqrt[1-x^3]),x]   
   > Out[33]= -(ArcTan[1/Sqrt[3]-(2^(2/3) (1-Sqrt[1-x^3]))/(Sqrt[3] x)]/(3   
   2^(2/3) Sqrt[3]))+ArcTan[1/Sqrt[3]-(2^(2/3) (1+Sqrt[1-x^3]))/(Sqrt[3] x)]/(3   
   2^(2/3) Sqrt[3])+ArcTanh[Sqrt[1-x^3]]/(9 2^(2/3))+Log[1+2^(1/3)    
   -Sqrt[1-x^3]]/(6 2^(2/3))-Log[1+2^(1/3)    
   x+Sqrt[1-x^3]]/(6 2^(2/3))   
   >   
      
   Wow! But what makes this first integral special?   
      
   >   
   > [...]   
   >   
   > Maple 2017.3 seems to like Elliptic special functions   
   >   
   > [...]   
   >   
   > So Fricas wins on these integrals.   
   >   
      
   ... and Rubi comes second.   
      
   >   
   > btw, I found the Fricas server   
   >   
   > http://axiom-wiki.newsynthesis.org/FriCASIntegration   
   >   
   > gives an error when I add   
   >   
   >       unparse(ii::InputForm)   
   >   
   > As last command:   
   >   
   > \begin{axiom}   
   > setSimplifyDenomsFlag(true)   
   > )set output algebra on;   
   > ii:=integrate((x^3 - 4)/((x^3 + 8)*sqrt(x^3 - 1)), x);   
   > unparse(ii::InputForm)   
   > \end{axiom}   
   >   
   > ====>   
   > The proxy server received an invalid response from an upstream server.   
   > The proxy server could not handle the request POST /FriCASIntegration.   
   > Reason: Error reading from remote server   
   >   
      
   If I remember correctly, this is what a regular timeout (about 5   
   minutes) on the FriCAS web interface looks like.   
      
   Martin.   
      
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