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Re: Please explain this weird Integrate result

• To: mathgroup at smc.vnet.net
• Subject: [mg60153] Re: [mg60116] Please explain this weird Integrate result
• From: stephen layland <layland at wolfram.com>
• Date: Sun, 4 Sep 2005 03:02:24 -0400 (EDT)
• References: <200509030606.CAA19060@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

and thus spake Jose  Reckoner [2005.09.03 @ 01:15]:
> 
> Expand[Integrate[(2*x)/(2*x - 1), x]]
> 
> gives
> 
> -1/2 + x + Log[-1 + 2*x]/2
> 
> But,
> 
> Expand[Integrate[1 + 1/(-1 + 2*x), x]]
> 
> gives
> 
> x + Log[-1 + 2*x]/2
> 
> even though
> 
> (2*x)/(2*x - 1) == 1 + 1/(-1 + 2*x)
> 
> Where did the extra -1/2 in the first result come from?

Looks like a bug introduced in Mathematica 5.1.  Technically the result
is correct, however, since the result of an indefinite integral depends
on some constant term.  For some reason, the -1/2 isn't being lumped
into the constant is all.  

Note that the definite integrals are both correct:

In[9]:= Integrate[(2*x)/(2*x - 1),{x,1,10}]

            Log[19]
Out[9]= 9 + -------
               2

In[10]:= Integrate[1+1/(-1+2x),{x,1,10}]

             Log[19]
Out[10]= 9 + -------
                2

In[11]:= N[%]

Out[11]= 10.4722

In[12]:= NIntegrate[1+1/(-1+2x),{x,1,10}]

Out[12]= 10.4722

--
/*------------------------------*\
|        stephen layland         |
|    Documentation Programmer    |
| http://members.wri.com/layland |
\*------------------------------*/

• References:
  • Please explain this weird Integrate result
    • From: "Jose Reckoner" <reckoner@gmail.com>