From: nma@12000.org   
      
   On 5/1/2020 11:44 PM, samuel.thomas.blake@gmail.com wrote:   
      
   > Hi Waldek,   
   >   
   > I appreciate your explanations.   
   >   
   > Here's an example which generates an interesting error message in FriCAS.   
   >   
   > (4) -> integrate(((-1+x^6)*(1+2*x^3+x^6)^(-1/3))/(1+x^6),x)   
   >   
   >     >> Error detected within library code:   
   >     impossible   
   >   
      
   hi Sam,   
      
   Using 1.3.6   
      
   48) -> ii:=integrate(((-1+x^6)*(1+2*x^3+x^6)^(-1/3))/(1+x^6),x);   
      
                                             Type: Union(Expression(Integer),...)   
   (49) -> unparse(ii::InputForm)   
      
       (49)   
      "(2*3^(1/2)*log((3*x*(2^(1/3))^2*((x^6+2*x^3+1)^(1/3))^2+(-6)   
   x^2*(x^6+2*x^3+   
      1)^(1/3)+((-1)*x^6+(-1))*2^(1/3))/(x^6+1))+((-1)*3^(1/2)*log(   
   (6*x^7+36*x^4+6   
      *x)*((x^6+2*x^3+1)^(1/3))^2+(12*x^8+36*x^5+12*x^2)*2^(1/3)*(x   
   6+2*x^3+1)^(1/3   
      )+(x^12+18*x^9+38*x^6+18*x^3+1)*(2^(1/3))^2)/(x^12+2*x^6+1))+   
   *atan((6*x*(2^(   
      1/3))^2*3^(1/2)*((x^6+2*x^3+1)^(1/3))^2+6*x^2*3^(1/2)*(x^6+2*   
   ^3+1)^(1/3)+(x^   
      6+1)*2^(1/3)*3^(1/2))/(18*x^2*(x^6+2*x^3+1)^(1/3)+((-3)*x^6+(   
   3))*2^(1/3)))))   
      /(18*2^(1/3)*3^(1/2))"   
                                                                     Type: String   
      
   I posted instructions earlier on how to install 1.3.6 on OSX, since you   
   mentioned   
   you use OSX and could not find binaries for latest Fricas.   
      
   >   
   > Here's the solution to this integral.   
   >   
   > In[1605]:= solveAlgebraicIntegral[(-1 + x^6)/((1 + 2 x^3 + x^6)^(1/3) (1 +   
   x^6)), x]   
   >   
   > Out[1605]= {0, 0, ArcTan[(x + 2^(2/3) (1 + 2 x^3 + x^6)^(1/3))/(Sqrt[3]   
   x)]/(2^(1/3) Sqrt[3]) + Log[-2 x + 2^(2/3) (1 + 2 x^3 + x^6)^(1/3)]/(3   
   2^(1/3)) - Log[2 x^2 + 2^(2/3) x (1 + 2 x^3 + x^6)^(1/3) + 2^(1/3) (1 + 2 x^3   
   + x^6)^(2/3)]/(6 2^(1/3))}   
   >   
   > Sam   
   >   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)