Re: What is wrong?
- To: mathgroup at smc.vnet.net
- Subject: [mg7704] Re: What is wrong?
- From: Marc Mazzariol <Marc.Mazzariol at di.epfl.ch>
- Date: Wed, 2 Jul 1997 14:21:24 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Sergio Rojas wrote:
>
> In[1]:= Integrate[x*Sin[x]/(x^2+1),{x,0,Infinity}]
>
> Pi
> Out[1]= ---
> 2 E
>
> In[2]:= f[x_] = Evaluate[ Integrate[x*Sin[x]/(x^2+1),x]] ;
>
> In[3]:= ans = f[Infinity] - f[0]
>
> E Pi
> Out[3]= ----
> 2
>
> In[4]:= $Version
>
> Out[4]= DEC OSF/1 Alpha 2.2 (September 9, 1994)
>
> sergio
>
> E-mail: sergio at scisun.sci.ccny.cuny.edu
I don't know, but in the new version of Mathematica it seems to work :
In[23]:= Integrate[x Sin[x]/(x^2+1),{x,0,Infinity}]
Out[23]= Sqrt[Pi/2]*BesselK[1/2, 1]
In[24]:= N[%] == Pi/(2 E)
Out[24]= True
In[25]:= f[x_] = Evaluate[Integrate[x*Sin[x]/(x^2 + 1), x]]
Out[25]= 1/2*(I*CosIntegral[-I + x]*Sinh[1] -
I*CosIntegral[I + x]*Sinh[1] +
Cosh[1]*SinIntegral[-I + x] + Cosh[1]*SinIntegral[I + x])
In[26]:= f[Infinity] - f[0]
Out[26]= 1/2*Pi*Cosh[1] + 1/2*(-I*CosIntegral[-I]*Sinh[1] +
I*CosIntegral[I]*Sinh[1] - Cosh[1]*SinIntegral[-I] -
Cosh[1]*SinIntegral[I])
In[27]:= N[%] == Pi/(2 E)
Out[27]= True
In[28]:= $Version
Out[28]= "Microsoft Windows 3.0 (October 6, 1996)"
In an older version I've the same problem as you, maybe the difference
lies
in how Mathematica interpretes In[25] (I'm not sure) :
In[24]:= $Version
Out[24]= SPARC 2.2 (June 14, 1994)
In[25]:= f[x_] = Evaluate[ Integrate[x*Sin[x]/(x^2+1),x]]
2
Out[25]= (-I CosIntegral[I - x] + I E CosIntegral[I - x]
+ 2
I CosIntegral[I + x] - I E CosIntegral[I + x] -
SinIntegral[I - x] -
2 2
E SinIntegral[I - x] + SinIntegral[I + x] + E SinIntegral[I +
x])/
(4 E)
--
+--------------------------------------------------------+
| - No brain, no headache - |
+--------------------------------------------------------+
| Marc Mazzariol |
| Swiss Federal Institute of Technology (EPFL) |
| Peripheral Systems Laboratory (LSP) |
| CH-1015 Lausanne, Switzerland |
| Tel: +41 21 693 3944 |
| Fax: +41 21 693 6680 |
| E-mail: Marc.Mazzariol at di.epfl.ch |
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