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Calculus Level 4

Let \(f(x) \) be a differentiable function such that \( \displaystyle \dfrac{d}{dx} f(x) = f(x) + \int_0^2 f(x) \, dx \) and \(f(0) = \dfrac{4-e^2}3 \), find \(f(2) \).

Round your answer correct to 2 decimal places.

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