Re: Bug in Mathematica 6 - Integrate - 20 - (Sqrt, false divergence) + a new, simpler bug manifestation

On Jun 28, 11:09 am, Vladimir Bondarenko <v...@xxxxxxxxxxxxxxx> wrote:
On Jun 28, 8:15 am, Daniel Lichtblau <d...@xxxxxxxxxxx> writes:

DL> it is a bug. It has been fixed for a future release.

Thanks you for your speedy reply! It's much pleasant to learn at
first hand that Wolfram Research team works so much efficiently.

One more question. Actually, indefinite integration & application
of NL rule produces a correct answer for this case. Could you give
any more explanation/detail about why this false divergence message
was generated in Mathematica 6 and Mathematica 5.2?

Some obscure special case code for handling Newton-Leibniz in presence
of RootSum in antiderivative. As best I could ascertain it was
guarding against a condition that is necessary but not sufficient for
divergence. It should have punted to a different handler rather than
signal divergence. The problem in question goes back to version 5.0,
at least: possibly earlier, though not with the examples in this note.


Yet another point.

(Hello again from the VM machine...) In Mathematica 6, the customer
observes this defect, for a *very* simple interand

Integrate[1/(1-(2+z) Sqrt[1+z]),{z,0,1}]
NIntegrate[1/(1-(2+z) Sqrt[1+z]),{z,0,1}]

Integral does not converge
-0.535538

I was wondering if the fix in your developer version handles this
integral, too, - or it would take a separate fix?

Thank you in advance.

Vladimir Bondarenko
Cyber Tester

Same bug, same fix.

In[1]:= InputForm[Integrate[1/(1-(2+z) Sqrt[1+z]),{z,0,1}]]
Out[1]//InputForm=
2*(RootSum[-1 + #1 + #1^3 & , (Log[1 - #1]*#1)/(1 + 3*#1^2) & ] -
RootSum[-1 + #1 + #1^3 & , (Log[Sqrt[2] - #1]*#1)/(1 + 3*#1^2) & ])

In[2]:= N[%]
Out[2]= -0.535538 + 0. I

In[3]:= NIntegrate[1/(1-(2+z) Sqrt[1+z]),{z,0,1}]
Out[3]= -0.535538

Daniel Lichtblau
Wolfram Research

.

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