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.