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   sci.math.symbolic      Symbolic algebra discussion      10,432 messages   

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   Message 9,222 of 10,432   
   clicliclic@freenet.de to Albert Rich   
   Re: integration of sec(t)   
   14 Dec 16 18:11:18   
   
   Albert Rich schrieb:   
   >   
   > What would you recommend changing it to?   
   >   
      
   I don't necessarily recommend to change it: What is the most appropriate   
   antiderivative should follow from your choice of design principles.   
      
   In fact, I myself seem to have introduced antiderivatives of the   
   ATANH(SIN(t)) type in my sci.math.symbolic post of Sun, 21 Apr 2013   
   18:20:53 +0200 to the thread "An independent integration test suite".   
      
   This form of antiderivative is real on the entire real line just as the   
   integrand is. The alternative LN(TAN(pi/4 + t/2)) is almost as simple,   
   but its branch cuts in the complex plane are less disruptive while its   
   imaginary part along the real line jumps between zero and pi.   
      
   Many of the antiderivatives that exhibit logarithmic poles should admit   
   two or more alternative forms like this.   
      
   Martin.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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