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Simple integration that Mathematica can't do?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg27641] Simple integration that Mathematica can't do?
  • From: "A. E. Siegman" <siegman at stanford.edu>
  • Date: Fri, 9 Mar 2001 02:35:55 -0500 (EST)
  • Organization: Stanford University
  • Sender: owner-wri-mathgroup at wolfram.com

I'm a little surprised that Mathematica can't do the following fairly 
simple calculation:

   f[x_] := Sqrt[4a^3] x Exp[-a x]

   u = Integrate[ f[x] f[x - 1],  {x, 1, Infinity}, 
          Assumptions -> {Re[a] > 0}]

even though if I break it apart by hand into the form

   u1 = 4a^3 Exp[a] Integrate[x^2  Exp[-2a x], {x, 1, Infinity}, 
           Assumptions -> {Re[a] > 0}]

   u2 = 4a^3 Exp[a] Integrate[x  Exp[-2a x], {x, 1, Infinity}, 
           Assumptions -> {Re[a] > 0}]

   u = u1 - u2

it can do both of the component integrals with no problem.


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