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May 11th, 2017, 02:51 PM   #1
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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..
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mistybreeding is offline  
 
May 12th, 2017, 09:28 AM   #2
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I ran your problem through wolfram just to see if its easily solvable.

Wolfram|Alpha: Computational Knowledge Engine

It doesn't look simple, you may want to make sure you have it written correctly.
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May 12th, 2017, 07:07 PM   #3
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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: Wolfram|Alpha: 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
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May 20th, 2017, 01:56 AM   #4
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Yes, it is hard!! There should be some tricks to solve it, and it has boundaries..

Thanks..
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