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I(n)=∫0πln(1−2ncosx+n2) dx\large I(n) = \int_0^\pi \ln (1-2n\cos x + n^2) \, dxI(n)=∫0πln(1−2ncosx+n2)dx
For I(n)I(n)I(n) as defined above, find I(100)I(10)⋅I(36)I(6)\dfrac {I(100)}{I(10)}\cdot \dfrac {I(36)}{I(6)}I(10)I(100)⋅I(6)I(36).
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