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A bug of Integrate[] in Mathematica 4.1


Hi!

While Mathematica 4.1 correctly solves the Integral:

Integrate[1 - x^a, {x, 0, 1}]

   a
----
1 + a

it gets stuck with an Integral like:

Integrate[1 - x^(-9999/10000), {x, 0, 1}]

(i.e. an exponent close to -1, but as a fraction of 2 large integer
numbers)

Mathematica 3.0, instead, was working well on this point.

A related problem is for definite integrals like:

Integrate[1 - x^((5 - q)/2), {x, 0, 1}]

Here, while Mathematica 3.0 did not check on the allowed interval for
the parameter q, Mathematica 4.1
does, but giving incorrect results.

In fact the quote interval of validity is:    Re[q]<2        (while it
should clearly be: Re[q]]<7)

Odd results come out for all this class of functions.

-------------

I have reported the problem to the Wolfram Support. The only result I
got are the following answers:

> Thank you for the report. Integrate[] appears to be behaving
erroneously in
> all of the cases you present. I have notified the the developers of
the
> problems. Unfortunately, there does not appear to be a workaround.

> Unfortunately, there are no bug lists available, and I will not be
informed
> of the status of the bug until it is fixed. Most likely, a patch will
not be
> made available.

Therefore, no solution is on the way, unfortunately.    JUST BE CAREFUL!

                                Best
regards,                                                    Rino





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