       Re: Integrate bug in v 9.0.0

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• 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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```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:= Integrate[x^2/(x^2 - x0^2), {x, x1, x2},
>
>  Assumptions -> x0 > x2 > x1 >= 0]
>
>
>
> During evaluation of In:= Integrate::idiv: Integral of x^2/(x^2-x0^2)
>
> does not converge on {x1,x2}. >>
>
>
>
> Out= 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:= Integrate[x^2/(x^2 - x0^2), {x, x1, x2},
>
>  Assumptions -> x0 > x2 > x1 >= 0]
>
>
>
> Out= -x1 + x2 + x0 ArcTanh[(x0 (x1 - x2))/(x0^2 - x1 x2)]
>
>
>
> In:=
>
> Integrate[x^2/(x^2-x0^2),{x,x1,x2},Assumptions->x0>x2>x1>=0]
>
> Out=
>
> -x1+x2+1/2 x0 (Log[x0+x1]+Log[x0-x2]-Log[(x0-x1) (x0+x2)])
>
>
>
> In:= 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= 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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