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

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   Message 9,214 of 10,432   
   Nasser M. Abbasi to All   
   integration of sec(t)   
   21 Nov 16 22:35:34   
   
   From: nma@12000.org   
      
   It is interesting how different CAS outputs differ sometimes.   
   I was trying to verify book result for int(sec(t),t) and this   
   is what some CAS systems gave   
      
   Mathematica:     ln(cos(t/2)+sin(t/2))-ln(cos(t/2)-sin(t/2))   
   Rubi:            arctanh(sin(t))   
   Fricas:          1/2 ( ln(1+sin(t)) - ln(1-sin(t)) )   
   Maple & Maxima:  ln(sec(t)+tan(t))   
      
   Text Book happens to give result shown by Maple&Maxima.   
      
   Ofcourse all other results are also correct, I am sure,   
   and these can all be converted to each others.   
      
   Was Wondering if there is any preference, math-wise, to any one   
   of the above results. From the Mathematica result, it seems   
   to hint that it used the Tangent half-angle substitution,   
   also called Weierstrass substitution.   
      
   What does you CAS give to int(sec(t),t) if different from   
   the above?   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)   

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