       Integrate bug in v 9.0.0

• To: mathgroup at smc.vnet.net
• Subject: [mg129647] Integrate bug in v 9.0.0
• From: "Alexey Popkov" <lehin.p at gmail.com>
• Date: Sat, 2 Feb 2013 01:17:27 -0500 (EST)
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• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
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```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

```

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