Albert Rich schrieb:   
   >   
   > On Monday, November 21, 2016 at 6:35:36 PM UTC-10, Nasser M. Abbasi wrote:   
   > > 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))   
   > >   
   > > [...]   
   > >   
   > > 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.   
   > >   
   > > [...]   
   >   
   > Note that in addition to being the most compact, Rubi's antiderivative   
   > is always real when t is real, unlike the ones returned by   
   > Mathematica, Maple and Maxima. Also the other antiderivatives involve   
   > multiple instances of the integration variable.  This can result in   
   > catastrophic cancellation when these antiderivatives are numerically   
   > evaluated.   
   >   
   > However, if you still prefer an alternative antiderivative for sec(t),   
   > note that Rubi is an open-source, modular system.  So, all you have to   
   > do is change just one of Rubi's 6800+ integration rules to get the   
   > desired effect.  Specifically the rule   
   >   
   >     int(sec(c+d x),x) --> arctanh(sin(c+d x))/d   
   >   
      
   A zero imaginary part for Rubi's antiderivative on the entire real line   
   comes at the price of having two branch cuts terminate at each of its   
   pole locations t = n*pi/2 (n = +-1, +-3, +-5, ...) instead of just one   
   branch cut. One may consider this a reason to change the current Rubi   
   rule.   
      
   Martin.   
      
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