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From: steiner@bgsuvax.UUCP (Ray Steiner)
Newsgroups: net.math,net.physics
Subject: Re: value of an integral
Message-ID: <3@bgsuvax.UUCP>
Date: Wed, 26-Feb-86 14:11:50 EST
Article-I.D.: bgsuvax.3
Posted: Wed Feb 26 14:11:50 1986
Date-Received: Fri, 28-Feb-86 07:02:01 EST
References: <823@drux2.UUCP>
Organization: Bowling Green State University,OH
Lines: 58
Xref: watmath net.math:2894 net.physics:3885

> 
> 
> Can someone out "there" show me an elementary (but, perhaps
> involving "tricks") method for integrating the following
> function:
> 
> int from 0 to inf s sup 3 over {e sup s - 1} ds
> 
> or "written" out:
> 
>       ( oo
>       |        3
>       |       s
>       | -------------- ds
>       |     s
>       |    e  -  1
>       ) 0
> 
> By elementary, I mean you can't use the fact that the integral
> is related to both the Gamma Function and the Riemann Zeta Func-
> tion or use techniques from the theory of complex variables.
> Essentially, using only techniques from the standard undergraduate
> calculus sequence, find the value of the integral.
> 
> However, techniques as used to find the value of:
> 
> int from 0 to inf e sup x sup 2 dx
> 
> are acceptable.
> 
> The value of the integral, if my memory has not failed me, is pi^2/15.
> 
> This integral results when considering the radiated power of a black
> body, integrated over all wavelengths.  Hence, the cross posting to
> net.physics.
> 
> Note to net.math readers (if it applies to you read it, otherwise
> no offense intended!):
> 
> I know I'm in for some scathing remarks that this is not mathematics,
> (high school algebra: yes, calculus: maybe) in that there is no group
> theory, no topology, and no set theory involved.  Well, those of us
> in applied mathematics are already tired of comments of that sort,
> so please don't bother :-).
> 
> Maybe what is needed is net.math.appld, and our pure mathematics
> brethren wouldn't have to read such (from their perspective)
> tom-foolery as this article.
> 
> Thanx in advance!
> 				larry cler
> 				ihnp4!drux2!ljc

Apropos of this same article, does anyone out there know if
the indefinite integral of e**x*sec(x) is expressible in terms
of elementary functions?  I have been wrestling with this
little teaser for 25 years without finding a solution!!
                                Ray Steiner