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February 28th, 2013, 10:36 PM  #1 
Newbie Joined: Feb 2013 Posts: 4 Thanks: 0  Stuck on an improper integral problem
My friend and I are completely stuck on this problem. When I get to the point to take the limit as t>infinity it would come out to lninfinity/infinity and that doesn't "work" right? We are just really confused. If someone could help explain that would be great. My Work 
March 1st, 2013, 12:07 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Stuck on an improper integral problem
You have correctly derived: As we observe that hence: 
March 1st, 2013, 08:27 AM  #3 
Newbie Joined: Feb 2013 Posts: 4 Thanks: 0  Re: Stuck on an improper integral problem
Thanks! Now that I see what you did it's like "duh!" I think the part that was confusing us was taking the limit as t>infinity of lnt/(2t+1). Just to clarify, you used l'Hôpital's rule to get 1/2, correct? 
March 1st, 2013, 09:56 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Stuck on an improper integral problem
While you can use L'Hôpital's rule, you could also rewrite the expression by dividing each term in the numerator and denominator by t: 

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