I have been trying to solve the following integral $$\int_{0}^{\frac {\pi}{2}} \ln\left (\frac {\ln^2 (\sin x)}{\pi^2+\ln^2 (\sin x)}\right) \frac {\ln \cos x}{\tan x} dx$$ I tried substituting for $\frac {\ln^2 (\sin x)}{\pi^2+\ln^2 (\sin x)}$ and using the properties of definite integrals, but I am not able to proceed with the integral as the $\ln \cos x$ term doesn't get substituted. Is there any other trick that I can employ?
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from where did you got this integral? – Dr. Sonnhard Graubner Oct 25 '14 at 13:52
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Oh I saw it on a forum a couple of days ago and wanted to work on it. – Artemisia Oct 25 '14 at 13:59
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1@Artemisia, http://math.stackexchange.com/questions/985686/integral-contest – Galc127 Oct 25 '14 at 14:12
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Oh I found it on quora haha. I guess someone was trying to solve it on there :/ – Artemisia Oct 25 '14 at 14:19
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This problem has been stolen, the Prosecutor General has started an investigation into this grave matter. – Count Iblis Oct 25 '14 at 19:12
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Erm... Someone posted the question on quora and I saw it. The person who posted the question here is the same person who posted it on quora. Huh? – Artemisia Oct 25 '14 at 19:42
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@Artemisia Yes, indeed. It's me. Sorry for closing your OP. Please no hurt feeling. Cheers! ٩(˘◡˘ ) – Anastasiya-Romanova 秀 Oct 26 '14 at 13:43
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@CountIblis Are you Ukrainian? If so, I'm apologized if my ava on Brilliant.org or info of my profile makes you uncomfortable – Anastasiya-Romanova 秀 Oct 26 '14 at 13:46
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@Anastasiya-Romanova No, it's actually quite a fun profile! While I'm not from the region, I would guess a little humor would not be bad :) . – Count Iblis Oct 26 '14 at 15:26
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@CountIblis Oh my bad. I had bad days recently concerning to my recent OP. I was not fully aware with your joke & I thought you tried to make fun of me. I'm really sorry for that ≧◠‿◠≦✌ – Anastasiya-Romanova 秀 Oct 26 '14 at 15:31