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|    sci.math.symbolic    |    Symbolic algebra discussion    |    10,432 messages    |
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|    Message 9,626 of 10,432    |
|    clicliclic@freenet.de to clicliclic@freenet.de    |
|    Re: can your system handle 4th-root pseu    |
|    20 Sep 17 20:37:57    |
   
   clicliclic@freenet.de schrieb:   
   >   
   > I have the following antiderivative:   
   >   
   > INT((a + b*x)/((2 - x^2)*(x^2 - 1)^(1/4)), x) = SQRT(2)*a/4   
   > *(ATANH(SQRT(2)*(x^2 - 1)^(1/4)/x) + ATAN(x/(SQRT(2)*(x^2 - 1)^(1/4))))   
   > + b*(ATANH(1/(x^2 - 1)^(1/4)) - ATAN((x^2 - 1)^(1/4)))   
   >   
      
   In fact, Leonhard Euler derives this version too in §13 - §19 ("Alia   
   Resolutio ...") of E688. He goes on to establish the equivalence of the   
   two antiderivatives in §20 - §23 ("Demonstratio Consensus ...").   
      
   Martin.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   
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