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
* Origin: fsxNet Usenet Gateway (21:1/5)