Hi. Keep up the great work! Thanks to you, we have to double check our
work via something like this. It is apparent from your posts that
Mathematica 6 has serious bugs with "Integrate."
equ = Integrate[ArcTan[Sqrt[z]]/(z + 1)^2, z]
(Sqrt[z] + (-1 + z)*ArcTan[Sqrt[z]])/(2*(1 + z))
equ /. z -> Infinity
Indeterminate
Hmmm. No go. Let's try Limits:
Limit[equ, z -> Infinity]
Pi/4
Limit[equ, z -> 0]
0
--
Dana
"Vladimir Bondarenko" <vb@[EMAIL PROTECTED]
> wrote in message
news:cb5c6663-7944-4379-b7ea-04809b491a32@[EMAIL PROTECTED]
> -----------------------------------------------------------------
> -- NOT FIXED BUGS ARE DANGEROUS: THEY TEND TO GET MORE SEVERE --
> -----------------------------------------------------------------
>
> Quality of CASs is our #1 care.
>
> So our little demo continues.... Hello again from the VM machine
> which hopefully soon will be used by CAS manufacturers to the
> benefit of their customers.
>
> This example demonstrates YET ANOTHER case of bad defects in
> Wolfram Research Quality Assurance process. Consider, it cannot
> trap and fix efficiently bugs the long livers, even simple ones.
>
> This is also an example of a MULTIPLE regression bug when the
> invalid answer is now here, now not depending on the concrete
> version.
>
> -----------------------------------------------------------------
>
> Just like our previous example, the following integral is
> trivial, too.
>
> -----------------------------------------------------------------
>
> N[ Pi/4 ]
> NIntegrate[ArcTan[Sqrt[z]]/(1+z)^2, {z, 0, Infinity}]
>
> 0.785398
> 0.785398
>
> -----------------------------------------------------------------
>
> Integrate[ArcTan[Sqrt[z]]/(1+z)^2, {z, 0, Infinity}]
>
> -----------------------------------------------------------------
> VERSION OUTPUT RESOLUTION
> -----------------------------------------------------------------
>
> Mathematica 6.0 0 <-------------------------------------- BUG
>
> Mathematica 5.2 Pi/4 OK
>
> Mathematica 4.2 0 <-------------------------------------- BUG
>
> Mathematica 3.0 Pi/4 OK
>
> -----------------------------------------------------------------
>
> Derive is a $99 computer algebra system developed by Albert Rich
> et al and acquired in 1999 by Texas Instruments. In Derive, the
> customer just clicks and instantly sees the correct result.
>
> Free fully functional 30 days trial (6.2 Mb, Win 98/ME/2000/XP)
>
> http://derive.en.softonic.com/
>
> -----------------------------------------------------------------
>
> Derive 6.1 INT(ATAN(SQRT(z))/(z+1)^2,z,0,inf)
>
> pi/4
>
> -----------------------------------------------------------------
>
> Maple 11.02> int(arctan(sqrt(z))/(1+z)^2, z=0..infinity);
>
> 1/4*Pi
>
> -----------------------------------------------------------------
>
> Best wishes,
>
> Vladimir Bondarenko
>
> VM and GEMM architect
> Co-founder, CEO, Mathematical Director
>
> http://www.cybertester.com/
Cyber Tester, LLC
> http://maple.bug-list.org/
Maple Bugs Encyclopaedia
> http://www.CAS-testing.org/
CAS Testing
>
> -----------------------------------------------------------------
>
> "We must understand that technologies
> like these are the way of the future."
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