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Re: How to help Mathematica take an integral

• To: mathgroup at smc.vnet.net
• Subject: [mg81886] Re: [mg81866] How to help Mathematica take an integral
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 6 Oct 2007 04:31:06 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200710050852.EAA00639@smc.vnet.net>
• Reply-to: murray at math.umass.edu

The indefinite integrals of Erf[Log[x]] are not elementary, so the real 
question is what kind of result would you like?

Here's one work-around that makes use of the Fundamental Theorem of 
Calculus:

   g[x_] = Integrate[Erf[Log[t]],{t,0,x}]]
   g[x] // InputFor
x*Erf[Log[x]] - E^(1/4)*Erfc[1/2 - Log[x]]

Given that, of course, Erf itself (and hence its "complement" Erfc) is 
defined in terms of integrals, does this do any good?


Aaron Fude wrote:
> Hi,
> 
> I would like to evaluate the indefinite integral of Erf[Log[x]].
> Mathematica seems to be able to do any definite integral, but not the
> indefinite version. Is there anything I can do to help Mathematica
> along?
> 
> Many thanks in advance,
> 
> Aaron Fude
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • How to help Mathematica take an integral
    • From: Aaron Fude <aaronfude@gmail.com>