Another integration question



Raymond Toy wrote:
> 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.

A bit late perhaps, but...

It is trying to use residues over the keyhole contour.  Maxima finds the 
roots of 6*x^4+16*x^3+18*x^2+1.  There are 4 distinct, complex roots. 
These are very, very messy.  Then you get to find the residues at each 
of these roots.  I think maxima can actually find the residues, but the 
expressions are so complex, it takes "forever".  And because they are so 
complex, I'm not sure maxima will be able to simplify them to something 
sensible.

For example, divide(6*x^4+16*x^3+18*x^2+1, x- <one root>) returns a huge 
expression and the remainder term can't be simplified to zero by maxima. 
   (Or at least, I don't know how to get maxima to simplify it to zero.)

Perhaps the solution is to tell maxima to try the indefinite integral 
first, or at least once maxima has determined that there are no bad 
points within the limits of integration.

Ray