Hello:   
      
   In volume 1, we notice that if we inflate a polynomial, then integrals   
   squeezed in its space are solvable. For example a degree 6 polynomial:   
      
   P1:=x^6+1/1296*b1^5*t*x^5+5/432*b1^4*t*x^4+5/54*b1^3*t*x^3+5/12*   
   1^2*t*x^2+b1*t*x+t;   
      
   This polynomial has a Riccati representation. Although you may be able to   
   solve it with simple algebraic maneuvering.   
      
   If we now let b1-> b1(t), and t-> T(t), then differential equation   
   representing the new polynomial produces integral which is thus solvable.   
      
   As polynomials and Riccati representations becomes more complex, we can handle   
   elliptic integrals.   
      
   We do not in this new science consider a polynomial individually, but as a   
   class. The above class of polynomials solvable for any degree with its Riccati   
   representations (it is explained in Volume 1, coming up about 2 weeks).   
      
   Sincerely   
      
   Dr.Mehran Basti   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)