# Functional Integrations

Calculus Level 3

Let $$f : \mathbb {R \to R}$$ be a continuous function such that $$f(x) = f(2x)$$ is true $$\forall \ x \in \mathbb R$$ and $$f(1)=3$$. Find $$\displaystyle \int_{-1}^1 f(f(f(x))) \, dx$$.

 Notation: $$\mathbb R$$ denotes the set of real numbers.

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