Re: Integrate question
- To: mathgroup at smc.vnet.net
- Subject: [mg82289] Re: [mg82250] Integrate question
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Wed, 17 Oct 2007 03:55:32 -0400 (EDT)
- References: <200710160728.DAA08846@smc.vnet.net>
Oskar Itzinger wrote:
> Mathematica 5.2 under IRIX complains that
>
> Integrate[x/(3 x^2 - 1)^3,{x,0,1}]
>
> doesn't converge on [0,1].
>
> However, Mathematica 2.1 under Windows gives the corrrect answer, (1/16).
>
> When did Mathematica lose the ability to do said integral?
>
> Thanks.
There is a nonintegrable singularity at 1/Sqrt[3]. You can check this
via Series.
In[6]:= Series[x/(3*x^2 - 1)^3, {x,1/Sqrt[3],2}]
1 1 1
Out[6]= -------------------- - ---------------------------- + ---------- -
1 3 1 2 32 Sqrt[3]
72 (-(-------) + x) 48 Sqrt[3] (-(-------) + x)
Sqrt[3] Sqrt[3]
1 1 2
5 (-(-------) + x) 9 Sqrt[3] (-(-------) + x)
Sqrt[3] Sqrt[3] 1 3
> ------------------ + --------------------------- + O[-(-------) + x]
128 256 Sqrt[3]
To get a regularized integral you can use GenerateConditions->False.
In[7]:= Integrate[x/(3*x^2 - 1)^3, {x,0,1}, GenerateConditions->False]
1
Out[7]= --
16
I realize this is an overloaded option and expect that in some future
version there will be a cleaner way to request regularized results of
definite integration.
Daniel Lichtblau
Wolfram Research
- References:
- Integrate question
- From: "Oskar Itzinger" <oskar@opec.org>
- Integrate question