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