MathGroup Archive 2012

[Date Index] [Thread Index] [Author Index]

Search the Archive

Integration anomaly?

  • To: mathgroup at
  • Subject: [mg127008] Integration anomaly?
  • From: "Szumiloski, John" <john_szumiloski at>
  • Date: Sat, 23 Jun 2012 04:16:48 -0400 (EDT)
  • Delivered-to:


I recently was playing around with the function Log[1 + 1 / ( t^n ) ], and exploring positive values of n.  (I have no interest in nonpositive or complex n)   In particular, I wanted to look at its integral, so I did this: (v8.0.4, Windows XP)

              Integrate[ Log[1+1/(t^n)], { t, 0, Infinity } ]

which gave:

             ConditionalExpression[ -(Pi Csc[Pi/n]), Re[n]<0 ]

Now I am no analysis expert, but it seems pretty clear to me that the integral diverges for negative (real) n.

After doing some further specific symbolic and numeric integrations, I suspect the correct value of this integral is actually

             ConditionalExpression[ Pi Csc[Pi/n], Re[n]>1 ]

although I cannot prove it.

But in any case, the answer Mathematica gave seems clearly wrong.  Can anyone reproduce this (and thus, should someone at WRI look into this), or is my system (or my brain) quirking out?

John  Szumiloski,  Ph.D.

Senior Biometrician
Biometrics Research
Merck Research Laboratories
P.O. Box 0004
West Point, PA 19486-0004
(215) 652-7346 (PH)
(215) 993-1835 (FAX)
These opinions are my own and do not necessarily reflect that of
Merck & Co., Inc.

Notice:  This e-mail message, together with any attachments, contains
information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station,
New Jersey, USA 08889), and/or its affiliates Direct contact information
for affiliates is available at that may be confidential,
proprietary copyrighted and/or legally privileged. It is intended solely
for the use of the individual or entity named on this message. If you are
not the intended recipient, and have received this message in error,
please notify us immediately by reply e-mail and then delete it from 
your system.

  • Prev by Date: Re: Default path for opening files
  • Next by Date: Re: Varying a constant in an ODE to Manipulate solution
  • Previous by thread: Error estimates in the Gauss-Kronrod rule
  • Next by thread: Re: Integration anomaly?