May 11th, 2017, 02:51 PM  #1 
Newbie Joined: May 2017 From: Houston Posts: 4 Thanks: 0  Integral
Could you please solve that integral step by step integral from 0 to 1 : ln(x^2+1)/(x+1) Also, I attached as a photo.. 
May 12th, 2017, 09:28 AM  #2 
Member Joined: Feb 2015 From: Southwest Posts: 96 Thanks: 24 
I ran your problem through wolfram just to see if its easily solvable. WolframAlpha: Computational Knowledge Engine It doesn't look simple, you may want to make sure you have it written correctly. 
May 12th, 2017, 07:07 PM  #3 
Newbie Joined: May 2017 From: Houston Posts: 4 Thanks: 0 
Yes, it is not simple.. And it has boundaries.. It has special solution, and that is what I want  if you are able to solve.  It should has something like that . Actually this question asked by our professor in college as a hard question, but he said that it has a trick, and solvable by some of the series.. You have to do a lot of times IBT(Integration By Part), and cut at somewhere, and find something with Series.. Answer is π^2/48 + (3 log^2(2))/4 according to WolframAlpha: WolframAlpha: Computational Knowledge Engine) . After first IBT I got at the integral side : integral 2x[ln(x+1)/(x^2+1)]dx. From 0 to 1 integral of ln(x+1)/(x^2+1) equals (ln(2)π)/8 but, because of I'm not an advance about IBT for definite integrals, I could not walk anymore.. Thanks in advance for your helps Misty 
May 20th, 2017, 01:56 AM  #4 
Newbie Joined: May 2017 From: Houston Posts: 4 Thanks: 0 
Yes, it is hard!! There should be some tricks to solve it, and it has boundaries.. Thanks.. 

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