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MathGroup Archive 1998

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Re: A couple of curious outputs from Integrate[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13655] Re: A couple of curious outputs from Integrate[]
  • From: Jean-Michel Collard <jcollard at iissun4.unil.ch>
  • Date: Sat, 08 Aug 1998 14:14:31 +0300
  • Organization: Universite de Lausanne
  • References: <6qbrkd$a8b@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

James Lawry wrote:
> 
> Here are a couple of Integrate[] commands that produce very odd results
> in Mathematica 3.0 for Sparc.
> 
> 1: Try
> Integrate[Exp[-x Log[x]] Sin[x], {x, 0, Infinity}]
> 
> This returns a value that contains x. This is silly, since it is a
> definite integral and x is a dummy variable of integration. Version 2.2
> returned this integral unevaluated.
> 
> 2: Make sure that there's nothing unsaved in your Mathematica session,
> and try
> 
> Integrate[Log[x]^2 Exp[-x], {x, 0, Infinity}]
> 
> This produces more spectacular results in the Sparc notebook version of
> Mathematica than in the text version, which just grumbles loudly for
> several minutes before producing the answer. Version 2.2 of Mathematica
> produced the answer in a few seconds.
> 
> James Lawry.


In[1]:= Integrate[Log[x]^2 Exp[-x], {x, 0, Infinity}]

                        2
                  2   Pi
Out[1]= EulerGamma  + ---
                       6
In[2]:= Integrate[Exp[-x Log[x]] Sin[x], {x, 0, Infinity}]

            Pi x
Out[2]= Cos[----] Gamma[1 - x]


Perfect.

JMC


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