integral of 1/(x^4+3*x^2+1) fails



On Mon, Jun 2, 2008 at 8:44 AM, ahmet alper parker <aaparker at gmail.com> wrote:
> integrate(1/x, x, 0, 1);
> zero (or negative)
> give an error message.
> Should not it give a result (whether the result is not found/meaningful or
> not) instead of an error message?

This is certainly not a bug in the sense that it is by design. And
here is the rationale:

Presumably you would want he result to be 'inf'; but the problem with
that is that subsequent operations may give incorrect or meaningless
results, e.g.

       0*integrate(1/x,x,0,1)

would give 0, not und.  Even if it returns a noun form,
'integrate(1/x,x,0,1), multiplying this by 0 will return 0, which is
of course incorrect.  Perhaps if and when 0*inf, inf-inf, etc. are
changed to simplify to und, there will be an argument for changing
this behavior.

Of course, currently divergent integrals which aren't recognized as
divergent already simplify incorrectly, e.g.

     0 * integrate(exp(1/x),x,0,1) => 0

Not sure how best to handle that....

             -s