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From: Dave Rusin on 14 Mar 2005 19:03
In article <LCmZd.18662$Pz7.2918(a)newssvr13.news.prodigy.com>,
W. Dale Hall <mailtodhall(a)farir.com> wrote:

>Anolethron wrote:
>> What substitution do you think is convenient ? I tried arctanx=y but it
>> doesn't lead anywhere good.
>>
>> Int [xe^(arctanx)]/{Sqrt[(1+x^2)^3]} dx ??

[WDH carries this out, including the line...]
>which ( identifying sqrt(sec^2(y)) with sec(y) ) is this:

>The identification of sqrt(sec^2(y)) with sec(y) is of course
>not entirely correct; properly, one should write |sec(y)| instead.

Interestingly, Maple (v.8, SUN SPARC SOLARIS) is stumped by the
integral in the initial form but _can_ do int(tan(y)*exp(y)/abs(sec(y)), y);
Just goes to show that calculus students can outwit a machine sometimes!

(I don't quite know what Maple's "thinking" is, but I know that as a
rule, Maple assumes by default that functions are defined on portions
of the complex plane, so sqrt(sec^2(y)) is neither sec(y) nor
the real number abs(sec(y)) but rather either sec(y) or -sec(y),
depending on where y is located. As soon as someone tried to code
in the sign selections, someone else would surely find a way to pick
endpoints so that the implied choices would be wrong.)

dave
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