From: samuel.thomas.blake@gmail.com   
      
   On Friday, July 23, 2010 at 7:52:06 AM UTC+10, clicl...@freenet.de wrote:   
   > "Nasser M. Abbasi" schrieb:   
   > >   
   > > On 7/21/2010 11:08 AM, clicl...@freenet.de wrote:   
   > > >   
   > > > FriCAS has been working on   
   > > >   
   > > > INT(SQRT(SQRT(x^4+1)+x^2)/((x+1)^2*SQRT(x^4+1)),x)   
   > > >   
   > > > for thirty days now!   
   > > >   
   > >   
   > > How do you know it is actually doing something useful and not stuck in > a   
   loop?   
   > >   
   > > Does FriCAS has an indicator saying it is actually doing different   
   > > things? Do you have tracing on?   
   > >   
   > I have to pass these questions on to Waldek Hebisch, who announced this   
   > calculation one month ago - I just provided the integral.   
   > > What possibly it can be doing in these 30 days? trying what? is risch   
   > > algorithm used here?   
   > >   
   > > Let us know when and if it completes ;)   
   > >   
   > Waldek seemed to be confident that FriCAS would ultimately be   
   > successful, but he has warned already about running times reaching weeks   
   > or months. The latter prediction is already borne out!   
   > Are you and Vladimir advocating to show mercy by terminating this   
   > calculation? There are no objections from my side, but it is for Wakdek   
   > to decide.   
   > Martin.   
      
   12 years late to this thread - Mathematica 13.2 get this one in under 5   
   seconds on my laptop:   
      
   In[5296]:= $Version   
   Out[5296]= "13.2.0 for Mac OS X x86 (64-bit) (November 18, 2022)"   
      
   In[5297]:= Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((1 + x)^2 Sqrt[1 + x^4]), x]   
      
   Out[5297]= 1/2 ((-1 - 2 x^4 - Sqrt[1 + x^4] - x^2 (1 + 2 Sqrt[1 + x^4]))/((1 +   
   x) (x^2 + Sqrt[1 + x^4])^(3/2)) +   
       ArcTan[Sqrt[1 + Sqrt[2]] Sqrt[x^2 + Sqrt[1 + x^4]]]/Sqrt[-1 + Sqrt[2]] -   
      Sqrt[1 + Sqrt[2]]ArcTan[(Sqrt[2 (-1 + Sqrt[2])] x Sqrt[x^2 + Sqrt[1 +   
   x^4]])/(   
        1 + x^2 + Sqrt[1 + x^4])] - ArcTanh[Sqrt[-1 + Sqrt[2]] Sqrt[x^2 + Sqrt[1   
   + x^4]]]/Sqrt[   
      1 + Sqrt[2]] + Sqrt[-1 + Sqrt[2]]ArcTanh[(Sqrt[2 (1 + Sqrt[2])] x Sqrt[x^2   
   + Sqrt[1 + x^4]])/(1 + x^2 + Sqrt[1 + x^4])])   
      
   If the time constraint to IntegrateAlgebraic in increased then it can also   
   compute   
      
   Integrate[Sqrt[x^2 + Sqrt[1 + x^4]]/((a x + b)^2 Sqrt[1 + x^4]), x]   
      
   --- SoupGate-Win32 v1.05   
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