How will you Integrate it?

Calculus Level 5

\[ (1 - f(x)) f(x+ \pi) = 1 + f(x) \]

Let \(f(x) \) be a function such that \(f: \mathbb R \rightarrow \mathbb R -\{1\} \) that satisfy the functional equation above, and that \( \displaystyle \int_\pi^{5\pi} f(x) \, dx = 2 \). Find the value of \( \displaystyle \int_{3\pi}^{2015\pi} f(x) \, dx \).

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