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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   
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