Integration

Calculus Level 4

I(n)=0πln(12ncosx+n2)dx\large I(n) = \int_0^\pi \ln (1-2n\cos x + n^2) \, dx

For 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)}.

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