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MathGroup Archive 2002

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a complex function appears in a real integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg33992] a complex function appears in a real integration
  • From: "Shaofeng Bian" <sfbian at public2.zz.ha.cn>
  • Date: Thu, 25 Apr 2002 03:00:31 -0400 (EDT)
  • Organization: Department of Geodesy, ZISM
  • Reply-to: "Shaofeng Bian" <sfbian at public2.zz.ha.cn>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

recently I involve into an integration of potential of mass body. The 
integration is as below

Integrate[1/Sqrt[x^2+y^2+z^2],x]

As a result, it yields

ln[x+Sqrt[x^2+y^2+z^2]]

Then, I integrate it in the y-direction

Integrate[ln[x+Sqrt[x^2+y^2+z^2]]]

It is very strange that a complex function appears in a real 
integration. First, I think that the Mathematica can not integrate this 
integration and the result is wrong. After I check and simplify it, 
however, the complex expression can converted into a real one as I want.

My problem is, "Can I believe a complex result always when I integrate a 
real function". If it is true, I will be on a lucky position . I don't 
need to integrate it by hand or simplify it to a real expression.

Hopefully, colleagues who have such experiences can give me some tips 
and a definite answer.

Bian


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