Re: Will Integrate[] ever finish?

• To: mathgroup at smc.vnet.net
• Subject: [mg23632] Re: [mg23622] Will Integrate[] ever finish?
• From: "Mark Harder" <harderm at ucs.orst.edu>
• Date: Thu, 25 May 2000 01:00:43 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```>I don't know if Integrate will solve my function.  The most general form is
>
>Integrate[1/(1+a*x+b*Sqrt[c-x^2])^(3/2),x]
>
I don't know, either.  It looks difficult to me. Can't help you here.

>It has been running for over a day and I don't know if it will ever
resolve.
>Is it possible that Integrate will go into some infinite loop and never
>stop, ...?

You bet it can.  If you're using a reasonably modern system, equivalent
roughly to a Pentium or better, my guess is that there's probably no
solution Mathematica can still be making progress in 24 hrs.  Even if it
can, I would rather spend my time looking up the answer in a good table of
integrals or trying to transform the problem by hand.  Better to limit the
time on problems like this with the TimeConstrained[] function.  I gave the
problem a little over 3 min.:

In[1]:=
TimeConstrained[Integrate[(1 + a*x + b*Sqrt[c - x^2])^(-3/2), x], 200.]
Out[1]=
\$Aborted

Other related things:  Mathematica can take significant  time preparing
printed output.  If you suspect that your answer will be a long one, better
to assign it to a variable and suppress printing, then print out the answer
after you know there is an answer. In earlier versions of Mathematica, the
Abort command (in the Kernel menu) didn't always work, or was very slow in
itself.  When I went from v3.0 to 4.0, I noticed a very significant