Integration Error



I'm trying to integrate a function that is a ratio of polynomials in the
general form

        f(x)/g(x)^(3/2)

where f(x) and g(x) are relatively complicated polynomials in x. If the
integration succeeds, I should have the x-component of the magnetic field
(B) for a cubic spline curve segment located in the x-y plane.

After many hours, Maxima quits with the error:

Polynomial quotient is not exact
 -- an error.  Quitting.  To debug this try DEBUGMODE(TRUE);)

My questions:

1) Is there a simple explanation of this problem? What is the "polynomial
quotient?" All exponents in the polynomials are integers, but their ratios
are not, sometimes.

2) Does this indicate that the function can not be integrated at all, or is
it a Lisp/Maxima problem?

3) Are there any work-arounds or alternative approaches suggested. There may
be some elliptic integrals lurking in the problem, or it could simply be
nonintegrable.

I've been trying to solve this problem on-and-off for over ten years as a
kind of stress test for Maxima and Mathematica. This is the first time the
computer has had enough memory and speed to actually give me an error
instead of just running out of resources. If this works, I think it could be
a useful tool for designing magnet sets, if it doesn't, no harm done.

I can post the batch script if it would help. Thanks for any suggestions.

Joe Koski