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On inconsistency in Integrate command

ruiming Zhang
Posted 11 years ago

It seems there exists an inconsistency in the integration algorithms. For example, if you do Integrate[x/(x^2+1),{x,-Infinity, Infinity}], you get 0, but if you compute Integrate[1/Log[x],{x,0,2}], you get divergence.
POSTED BY: ruiming Zhang
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POSTED BY: Henrik Schachner 
In[4]:= Integrate[x/(x^2 + 1), {x, -b, b}]

Out[4]= 0

which is what I expect due to the symmetry of the integrand under sign change.

I guess that integral goes to infinity - infinity as b goes to infinity.

In[5]:= $Version

Out[5]= "10.0 for Microsoft Windows (64-bit) (December 4, 2014)"
POSTED BY: Frank Kampas

General rule: indicate version of software.
POSTED BY: Daniel Lichtblau

For example, if you do Integrate[x/(x^2+1),{x,-Infinity, Infinity}], you get 0, but if you compute Integrate[1/Log[x],{x,0,2}], you get divergence.

That is not what I get:

enter image description here
POSTED BY: Nasser M. Abbasi
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