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Re: What is wrong?


> 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

Simply substituting Infinity for x in the indefinite integral,
as in f[Infinity], won't work for computing the limit of the
indefinite integral at Infinity.  Infinity+I evaluates to Infinity,
which is in this example treated as a real infinity, thereby losing
some information that is needed for computing the limit.  The
Integrate function computes this limit correctly for the definite
integral, and so gets a correct answer.  The indefinite integral
is also correct, and with correct limits will give a correct
value for the definite integral.

Dave Withoff
Wolfram Research


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