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How do I integrate this guy? I've been stuck on this for hours..

$$I=\frac{1}{2}\int_{0}^{\frac{\pi }{2}}\frac{\ln(\sin y)\ln(\cos y)}{\sin y\cos y}dy$$

  • 7
    Is it really $dx$, and not $dy$?2012-12-22
  • 4
    [This](http://math.stackexchange.com/q/188921/11069) earlier question is very relevant.2012-12-22
  • 0
    @Sasha, I enjoyed your answer. Though the calculation becomes slightly harder in this problem as the singularity arises for both $z$ and $w$ for $\frac{\partial^2}{\partial z \partial w}\beta(z, w)$, they all cancel out and yield the correct answer.2012-12-22
  • 3
    The integral looks pretty sane to me. But really, we prefer to avoid subjective titles.2012-12-22

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