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Re: strange behaviour of Integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89055] Re: strange behaviour of Integration
  • From: Alois Steindl <Alois.Steindl at tuwien.ac.at>
  • Date: Sat, 24 May 2008 03:57:43 -0400 (EDT)
  • Organization: Inst. f. Mechanics II, TU Vienna
  • References: <g11ra1$afj$1@smc.vnet.net>

Hello,
I just want to add strange results with Mathematica 6.0.1.0:
(I experienced this problem also with 6.0.2)

If I calculate

ih = Integrate[(ri - r)^2/r, {r, rim1, ri}, 
  Assumptions -> {Element[rim1, Reals] && Element[ri, Reals] && 
     rim1 > 0 && ri > rim1}]

I get the correct result
-((3 ri^2)/2) + 2 ri rim1 - rim1^2/2 + ri^2 Log[ri/rim1]

But when I divide the integrand by the constant (ri-rim1)^2:

ih2 = Integrate[(ri - r)^2/r/(ri - rim1)^2, {r, rim1, ri}, 
  Assumptions -> {Element[rim1, Reals] && Element[ri, Reals] && 
     rim1 > 0 && ri > rim1}]

Mathematica gives
(ri^2 (-3 + 2 Log[ri] - 2 Log[rim1]))/(2 (ri - rim1)^2)

Here the contribution  (2 ri rim1 - rim1^2/2)/(ri-rim1)^2 
is simply missing.

How can that happen?

Alois


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