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Re: Simple integration that Mathematica can't do?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg27651] Re: Simple integration that Mathematica can't do?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 10 Mar 2001 00:49:40 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <98a200$cr8@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

I'm suprised too because

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

Out[]=(2*Sqrt[a^3]*(1 + a))/(a^2*E^a)

with my Mathematica 4.1.

Regards
  Jens

"A. E. Siegman" wrote:
> 
> 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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