November 21st, 2018, 09:06 AM  #1 
Newbie Joined: Oct 2015 From: algeria Posts: 5 Thanks: 0  Improper integral of a function
I want to study the nature of an improper integral. I separate the integral from 0 to 1 and from 1 to ∞. The first integral is divergent (I proved that it is equivalent to Riemann integral, which is divergent in the neighborhood of 0). But I didn't find how I can prove the convergence or divergence of the second one. The integral can be found in attach file. Thank you 
November 21st, 2018, 10:54 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,203 Thanks: 1157 
It certainly looks like the integral blows up at multiples of $\pi$, i.e. where $\sin^2(x)=0$ 
November 21st, 2018, 02:41 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,642 Thanks: 626 
It is not divergent at x=0, since $log(1+x)^2\approx x^2$ there. However as romsek points out it will blow up at multiples of $\pi$.


Tags 
function, improper, integral 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Improper integral  DavidSzalai  Calculus  1  March 19th, 2017 11:30 AM 
Improper Integral  Stelios  Calculus  0  September 5th, 2015 11:42 PM 
Improper integral with e  unwisetome3  Calculus  2  April 8th, 2013 11:45 AM 
Integral improper.  ZardoZ  Complex Analysis  10  April 13th, 2011 04:32 AM 
improper integral of a twodimensional Gaussian function  neonsubbs  Calculus  7  March 5th, 2009 01:33 PM 