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Re: Re: Simplification of definite integral?

• To: mathgroup at smc.vnet.net
• Subject: [mg40736] Re: [mg40701] Re: Simplification of definite integral?
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Tue, 15 Apr 2003 04:00:10 -0400 (EDT)
• References: <b7avdo$qlg$1@smc.vnet.net> <200304140801.EAA06363@smc.vnet.net> <oprnmjummvkcjuc2@smtp.cox-internet.com>
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In a recent post, I noted that Mathematica gives an incorrect answer for

Integrate[Sin[x-1]/(x-1) Sin[x+1]/(x+1), {x, 2, Infinity}]

and commented that I thought, based on numerical investigations, that the
correct answer was approximately -0.14 . Upon a little further thought, 
I now realize that a precise (correct) answer is

(Cos[2]*(CosIntegral[2] - CosIntegral[6] + Log[3]) + Sin[2]*(Pi -
SinIntegral[2] - SinIntegral[6]))/4

but I still do not know any direct way to get Mathematica to give a
correct answer for this integral. Suggestions anyone?

Regards,
David Cantrell

• References:
  • Re: Simplification of definite integral?
    • From: "David W. Cantrell" <DWCantrell@sigmaxi.org>