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Bug introduced in 9.0 and fixed in 10.1


I am trying to run the following integral in version 9.0, but it fails:

Integrate[
 2 I (-1 + 
  x) ((-8 + 12 x - 6 mπ^2 x - 2 mπ^2 x^2 - 
   4 x^3)/((1 - x)^2 + 
   mπ^2 x) + ((4 - 2 x + 4 mπ^2 x - 8 x^2 + 
   6 mπ^2 x^2 + 6 x^3) Log[
    1/((1 - x)^2 + mπ^2 x)])/((1 - x)^2 + mπ^2 x)), {x, 0, 
  1}, Assumptions -> mπ > 0 && mπ < .1]

Version 9.0.1: Version 9.0

But in version 8.0, it works:

enter image description here

Is this a bug, or is the integral really non-convergent? What's a possible workaround, since I don't have easy v8 access?

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  • $\begingroup$ BTW shouldn't there a space between m and pi, or is this intentional? $\endgroup$ – Sjoerd C. de Vries Mar 8 '13 at 22:59
  • $\begingroup$ $m\pi$ represents a single symbol. $\endgroup$ – QuantumDot Mar 8 '13 at 23:00
  • $\begingroup$ I can reproduce this, but in future, please do not use the bugs tag until a few users have confirmed the behaviour. $\endgroup$ – rm -rf Mar 8 '13 at 23:03
  • $\begingroup$ Thanks for reproducing; I have removed the bugs tag. $\endgroup$ – QuantumDot Mar 8 '13 at 23:04
  • 1
    $\begingroup$ Thanks god 2πR can't be used as a symbol name $\endgroup$ – Dr. belisarius Mar 8 '13 at 23:21
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As explained in the comments, this problem has been fixed in version 10. The result in version 10.3 is:

enter image description here

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