October 2nd, 2011, 07:54 PM  #1 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  indefinite? 
October 2nd, 2011, 07:58 PM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,767 Thanks: 5  Re: indefinite?
There are multiple ways for an integral to be improper, not just when the limits are +/ infinity. For instance, the second one has a vertical asymptote at x = 1/2, which is within the limits of integration... 
October 2nd, 2011, 08:01 PM  #3 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Re: indefinite?
do you think it's only those two?

October 2nd, 2011, 08:07 PM  #4 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Re: indefinite?
The second one is the only one that Wolfram wouldn't integrate they called it a Nonintegrable singularity

October 2nd, 2011, 08:23 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: indefinite?
The first one is ok, since its vertical asymptote is not within the limits of integration. The second one is improper, as noted above. The third one is improper since the limits are not finite. The fourth one is improper since the lower limit of integration is not within the domain of the integrand, it's on a vertical asymptote. 

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