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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