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Re: Simple integration that Mathematica can't do?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg27660] Re: [mg27641] Simple integration that Mathematica can't do?
  • From: BobHanlon at aol.com
  • Date: Sat, 10 Mar 2001 00:49:49 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

$Version

"4.1 for Power Macintosh (November 2, 2000)"

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

Distribute[
    Integrate[Expand[f[x]*f[x-1]], {x, 1, Infinity}, 
      Assumptions -> Re[a] > 0]]//Simplify

(a + 1)/E^a

Bob Hanlon

In a message dated 2001/3/9 2:48:00 AM, siegman at stanford.edu writes:

>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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