Re: Integral giving complex answer
- To: mathgroup at smc.vnet.net
- Subject: [mg59267] Re: Integral giving complex answer
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Thu, 4 Aug 2005 02:07:51 -0400 (EDT)
- Organization: The Open University, Milton Keynes, U.K.
- References: <dcples$6mm$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
David Sagan wrote: > Hello: > > I am tring to do simple integrals but I am running into problems in that > Mathematica gives the answer using complex numbers. For example, > Integrate[1/(1 + 5x^2), x] gives a result in terms of logarithms of a > complex argument instead of the usual arctan formula. If I integrate > something like Integrate[1/(1 + a x^2), x] I get the answer in the form > I want using the arctan. > > My question is how to avoid getting the answer to Integrate[1/(1 + > 5x^2), x] in terms of complex logarithms. I know I could just integrate > 1/(1 + a x^2) and substitute a -> 5 later but in actuality I am dealing > with more complex integrals and it would be helpful if I did not have to > be making such substitutions. > > -- Thanks for any help, David Sagan > Hi David, What version/platform are you using? Here what I get with Mathematica 5.2 and 5.1.1 on Windows Xp (no complex logarithm, just arctan in both cases): In[1]:= $Version Out[1]= "5.2 for Microsoft Windows (June 20, 2005)" In[2]:= Integrate[1/(1 + 5*x^2), x] Out[2]= ArcTan[Sqrt[5]*x]/Sqrt[5] In[3]:= Integrate[1/(1 + a*x^2), x] Out[3]= ArcTan[Sqrt[a]*x]/Sqrt[a] In[1]:= $Version Out[1]= "5.1 for Microsoft Windows (January 27, 2005)" In[2]:= Integrate[1/(1 + 5*x^2), x] Out[2]= ArcTan[Sqrt[5]*x]/Sqrt[5] In[3]:= Integrate[1/(1 + a*x^2), x] Out[3]= ArcTan[Sqrt[a]*x]/Sqrt[a] Best regards, /J.M.