If \( \int_{0}^{n \pi} \frac{x|\sin x|}{1+|\cos x|} d x(n \in N) \)...

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If \( \int_{0}^{n \pi} \frac{x|\sin x|}{1+|\cos x|} d x(n \in N) \) is equal to \( 100 \pi \ln 2 \), then find the value of \( n \).
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