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What's wrong with Integrate [ 1/x, {x,1,Infinity}]?

• To: mathgroup at smc.vnet.net
• Subject: [mg66546] What's wrong with Integrate [ 1/x, {x,1,Infinity}]?
• From: Pavel Pokorny <Pavel.Pokorny at vscht.RemoveMe.MeToo.cz>
• Date: Fri, 19 May 2006 03:40:32 -0400 (EDT)
• Organization: Czech Technical University
• Sender: owner-wri-mathgroup at wolfram.com

  Dear Mathematica friends

what is the reason Mathematica 5.2 does not compute 

In[1]:= Integrate [ 1/x, {x,1,Infinity}]

                             1
Integrate::idiv: Integral of - does not converge on {1, Infinity}.
                             x

                  1
Out[1]= Integrate[-, {x, 1, Infinity}]
                  x

while this works:

In[2]:= Limit [ Integrate [ 1/x, {x,1,b}], b->Infinity]

Out[2]= Infinity

I always thought the first formulation 
is just a shorthand of the second one,
being equivalent in its meaning.

-- 
Pavel Pokorny
Math Dept, Prague Institute of Chemical Technology
http://www.vscht.cz/mat/Pavel.Pokorny

• Follow-Ups:
  • Re: What's wrong with Integrate [ 1/x, {x,1,Infinity}]?
    • From: Daniel Lichtblau <danl@wolfram.com>