# 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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