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troubling simple integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91336] troubling simple integral
  • From: did <didier.oslo at hotmail.com>
  • Date: Sat, 16 Aug 2008 05:54:11 -0400 (EDT)

Mathematica 6.0.3.0 has trouble computing the quite simple integral

In[2]:= FullSimplify[ Integrate[ (b + k*x) / k^2 * Exp[-k*x] *
Sin[k*a] * Sin[k*y] , {k, 0,Infinity},
  Assumptions -> x > 0 && Im[a] == 0 && Im[b] == 0 && Im[y] == 0 ]]

Out[2]= -(1/8) I (b + 2 I x Log[1 + (4 a y)/(x^2 + (a - y)^2)])

which is obviously wrong. Repeating the computation, I get different
results.

What should I do to get a correct answer?
(This one I can do by hand, but I have more complicated similar ones
to evaluate.)


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