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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