oldk1331@gmail.com schrieb:   
   >   
   > [...] 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.   
      
   Wow - we could all become world-famous if this proves to be the first   
   parametrized algebraic integrand with this property! Alas, my Derive   
   oracle says:   
      
     goursat5a((x + 1)/(x^2 + x + 1), x, a, 0, 0, b)   
      
     [false, false, false, true, true]   
      
   which means integrable :(. Might something else perhaps be amiss with   
   the current "demonstration-only" code of FriCAS?   
      
   >   
   > [...] For this example, I have post a small patch to fricas-devel.   
   > After my patch, FriCAS gives continuous result, same as SymPy.   
      
   Thanks, I myself obtain (up to some piecewise constant):   
      
     ATAN(SQRT(11)*(10*x + 3)/(80*x^2 + 10*x - 9)) =   
      - ATAN(SQRT(11)*(800*x^3 - 40*x^2 + 30*x + 57)/66)   
      - ATAN(SQRT(11)*(40*x - 7)/55)   
      
   Martin.   
      
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