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.
>