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