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MathGroup Archive 2006

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Re: Integral problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65667] Re: Integral problem
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 12 Apr 2006 06:00:35 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <e1fq2r$bmo$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

ivan.svaljek at gmail.com wrote:
> I've tried running an integral expression through mathematica 5.0 and
> came up with this:
> 
> http://aspspider.net/isvaljek/mathematica/index.html
> 
> First two are from mathematica, and the last one is from a site running
> web mathematica.
> 
Taking the first derivative of each integral you can check that they are 
equal:

In[1]:=
Integrate[x^3/(x^8 - 2), x]

Out[1]=
                4                   4
Log[Sqrt[2] - x ] - Log[Sqrt[2] + x ]
-------------------------------------
               8 Sqrt[2]

In[2]:=
D[(Log[Sqrt[2] - x^4] - Log[Sqrt[2] + x^4])/
    (8*Sqrt[2]), x]

Out[2]=
          3               3
       4 x             4 x
-(------------) - ------------
              4               4
   Sqrt[2] - x     Sqrt[2] + x
------------------------------
           8 Sqrt[2]

In[3]:=
Simplify[%]

Out[3]=
    3
   x
-------
       8
-2 + x

In[4]:=
D[(Log[x^4 - Sqrt[2]] - Log[Sqrt[2] + x^4])/
    (8*Sqrt[2]), x]

Out[4]=
        3               3
     4 x             4 x
------------- - ------------
             4              4
-Sqrt[2] + x    Sqrt[2] + x
----------------------------
          8 Sqrt[2]

In[5]:=
Simplify[%]

Out[5]=
    3
   x
-------
       8
-2 + x

Regards,
Jean-Marc


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