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Re[3]: Re: Simplification of definite integral?

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  • Subject: [mg40740] Re[3]: [mg40701] Re: Simplification of definite integral?
  • From: Vladimir Bondarenko <vvb at mail.strace.net>
  • Date: Tue, 15 Apr 2003 04:00:44 -0400 (EDT)
  • Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"David W. Cantrell" <DWCantrell at sigmaxi.org> wrote on Tuesday, April 15, 2003, 1:12:22 AM:

DWC> any direct way to get Mathematica to give a correct answer for
DWC> this integral. Suggestions anyone?

Eureka ;)

func = Sin[z - 1]/(z - 1) Sin[z + 1]/(z + 1);
i1 = Integrate[func, {z, 0, Infinity}, PrincipalValue -> True];
i2 = Integrate[func, {z, 0, 2}, PrincipalValue -> True];

FullSimplify[i1 - i2]

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


We the Russians name this 'via...' Oh, I can't proceed, 'am ashamed :)


Best wishes,

Vladimir Bondarenko
Mathematical and Production Director
Symbolic Testing Group

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