Re: A FullSimplify Problem
- To: mathgroup at smc.vnet.net
- Subject: [mg41074] Re: A FullSimplify Problem
- From: "Dr. Wolfgang Hintze" <weh at snafu.de>
- Date: Thu, 1 May 2003 04:58:38 -0400 (EDT)
- References: <b8o20k$p28$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Ted,
Sorry, I made a mistake. Please ignore my previous answer.
Recently, in the thread "Simplification of definite integral?" in this
group I initiated a discussion on a similar problem with Integrate. Here
even wrong results were produced. The problem seems to be connected to
the integrand having a branch cut singularity (as e.g. Log, Sqrt have).
You can study this by looking at the simplified version of your
integral, viz.
In[1]=Integrate[Log[1-2a x +a^2],{x,0,1}]
starting with the general integral
In[2]=Integrate[Log[1-2a x + a^2], x]
Mathematica gives
Out[2] =
2
-x + x Log[1 + a - 2 a x] +
2 2
(-1 - a ) Log[-1 - a + 2 a x]
------------------------------
2 a
In the last Log we observe a negative sign of the term, i.e. mathematica
has (unmotivatedly??) moved to another branch of the Log-function.
Forming the derivative of Out[2] gives back the integrand, but the
derivative of the function with the positive sign under the second Log
gives the same result.
Hope this helps a bit. Summa summarus: mathematica seems to have a lot
of difficulties here.
Regards,
Wolfgang
Ersek, Ted R wrote:
> At http://mathworld.wolfram.com/LeibnizIntegralRule.html
> I learned that
> Integrate[Log[1-2a Cos[x]+a^2],{x,0,Pi}]
> = 2*Pi*Log[Abs[a]]
>
> Mathematica knows how to do this integral, but gives a much more complicated
> result. Can anyone explain how to use FullSimplify and other
> transformations to show that the complicated result Mathematica gives is
> equivalent to the answer above?
>
> Thanks,
> Ted Ersek
>
>
>