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Re: Integrate bug in v 9.0.0

  • To: mathgroup at smc.vnet.net
  • Subject: [mg129697] Re: Integrate bug in v 9.0.0
  • From: danl at wolfram.com
  • Date: Mon, 4 Feb 2013 22:24:43 -0500 (EST)
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  • References: <keiaug$qqn$1@smc.vnet.net>

On Saturday, February 2, 2013 12:15:44 AM UTC-6, Alexey Popkov wrote:
> In version 9.0.0 the following integral is reported as divergent:
> 
> 
> 
> In[71]:= Integrate[x^2/(x^2 - x0^2), {x, x1, x2},
> 
>  Assumptions -> x0 > x2 > x1 >= 0]
> 
> 
> 
> During evaluation of In[71]:= Integrate::idiv: Integral of x^2/(x^2-x0^2) 
> 
> does not converge on {x1,x2}. >>
> 
> 
> 
> Out[71]= Integrate[x^2/(x^2 - x0^2), {x, x1, x2},
> 
>  Assumptions -> x0 > x2 > x1 >= 0]
> 
> 
> 
> Versions 8.0.4 and 5.2 give equivalent expressions:
> 
> 
> 
> In[2]:= Integrate[x^2/(x^2 - x0^2), {x, x1, x2},
> 
>  Assumptions -> x0 > x2 > x1 >= 0]
> 
> 
> 
> Out[2]= -x1 + x2 + x0 ArcTanh[(x0 (x1 - x2))/(x0^2 - x1 x2)]
> 
> 
> 
> In[9]:=
> 
> Integrate[x^2/(x^2-x0^2),{x,x1,x2},Assumptions->x0>x2>x1>=0]
> 
> Out[9]=
> 
> -x1+x2+1/2 x0 (Log[x0+x1]+Log[x0-x2]-Log[(x0-x1) (x0+x2)])
> 
> 
> 
> In[8]:= FullSimplify[-x1 + x2 +
> 
>    1/2 x0 (Log[x0 + x1] + Log[x0 - x2] -
> 
>       Log[(x0 - x1) (x0 + x2)]) == -x1 + x2 +
> 
>    x0 ArcTanh[(x0 (x1 - x2))/(x0^2 - x1 x2)],
> 
>  Assumptions -> x0 > x2 > x1 >= 0]
> 
> 
> 
> Out[8]= True
> 
> 
> 
> Alexey

Appears to be substantially the same underlying issue as was reported here.

http://mathematica.stackexchange.com/questions/18348/mathematica-9-cannot-solve-this-integral-mathematica-8-could-is-this-a-bug

It is provisionally fixed in the version currently under development.

Daniel Lichtblau
Wolfram Research



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