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    $\begingroup$ +1 just for the nice looking plots, as the math is too hard for me to follow :) $\endgroup$ Commented Mar 19, 2017 at 4:31
  • $\begingroup$ Thank you for the interesting and deep answer... So as far I understand I should fill a bug report to wolfram for the incorrect integral and not for the inconsistency, because it might be expected? $\endgroup$ Commented Mar 19, 2017 at 11:31
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    $\begingroup$ Yes, please file a bug report. From the comments to this older, similar problem, it seems that getting a general-purpose algorithm to do this right is harder to get right than to solve a single instance. But each example probably helps them find improvements. $\endgroup$ Commented Mar 19, 2017 at 12:57