From: samuel.thomas.blake@gmail.com   
      
   This was an interesting error from FriCAS   
      
   -> integrate(x*(-b+a*x^2)^(1/2)*(b-a*x^2+c*x*(-b+a*x^2)^(1/2))^(-3/2),x)   
      
      >> Error detected within library code:   
      Denominator not equal to 1   
      
   The answer is   
      
   In[415]:= IntegrateAlgebraic[x*(-b + a*x^2)^(1/2)*(b - a*x^2 + c*x*(-b +   
   a*x^2)^(1/2))^(-3/2), x]   
      
   Out[415]= (2 Sqrt[-b + a x^2])/((a - c^2) Sqrt[b - a x^2 + c x Sqrt[-b + a   
   x^2]]) -   
    ArcTan[((Sqrt[a] Sqrt[-b + a x^2])/Sqrt[a - Sqrt[a] c] - (c Sqrt[-b + a   
   x^2])/Sqrt[a - Sqrt[a] c])/Sqrt[b - a x^2 + c x Sqrt[-b + a x^2]]]/((Sqrt[a] -   
   c) Sqrt[a - Sqrt[a] c]) -   
    ArcTan[((Sqrt[a] Sqrt[-b + a x^2])/Sqrt[a + Sqrt[a] c] + (c Sqrt[-b + a   
   x^2])/Sqrt[a + Sqrt[a] c])/Sqrt[b - a x^2 + c x Sqrt[-b + a x^2]]]/((Sqrt[a] +   
   c) Sqrt[a + Sqrt[a] c])   
      
   --- SoupGate-Win32 v1.05   
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