# To determine a definite integral [duplicate]

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?

• from where did you got this integral? – Dr. Sonnhard Graubner Oct 25 '14 at 13:52
• 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
• – Galc127 Oct 25 '14 at 14:12
• Oh I found it on quora haha. I guess someone was trying to solve it on there :/ – Artemisia Oct 25 '14 at 14:19
• This problem has been stolen, the Prosecutor General has started an investigation into this grave matter. – Count Iblis Oct 25 '14 at 19:12