Another integration question



Barton Willis wrote:
> -----maxima-bounces at math.utexas.edu wrote: -----
> 
>> To: maxima at math.utexas.edu
>> From: max.e.brown at gmail.com
>> Sent by: maxima-bounces at math.utexas.edu
>> Date: 08/21/2007 08:19AM
>> Subject: Another integration question
>>
>> I stumbled across a definite integral that seems to make Maxima
>> hang. Has anyone seen this before?
>>
>> -8<------------
>> (%i1) integrate( (x^3+1)/(x^4 + 4*x + 1), x);
>>                           4
>>                        log(x  + 4 x + 1)
>> (%o1)                         -----------------
>>                              4
>> (%i2) integrate( (x^3+1)/(x^4 + 4*x + 1), x, 0, 1);
>>
>> [... no output, sblc cpu usage at 87%  ...]
> 
> I don't know what happens if you don't stop Maxima, but
> I think you should file a bug report.
> 
> To see in part what is going on, try this:
> 
> (%i4) trace(?csign);
> (%o4) [csign]
> (%i5) integrate( (x^3+1)/(x^4 + 4*x + 1), x, 0, 1);
> 
> --> Yikes! all kinds of junk!
> 

Neat.

I'm not exactly sure what's going on, but when I stopped it, the 
backtrace said it was trying to use contour integration of

(6*x^3+12*x^2+9*x+2)*plog(-x)/(6*x^4+16*x^3+18*x^2+8*x+1)

over the keyhole contour (a circle with a slit on the positive real 
axis).  And plog is the principal log function.

I don't know if this is where it gets stuck in a loop or if this method 
fails and another is attempted.

Ray