\[ \large I = \lim_{k\to\infty} \int_0^1 \dfrac x{2^k} \prod_{n=1}^k \left( e^{x/2^n} + e^{-x/2^n} \right) \, dx \]

If \(I \) can be expressed in the form of \( \dfrac{(e+A)^B}{Ce} \), where \(A,B\) and \(C\) are integers satisfying \(A+B+C<5\), find the product \(ABC\).

**Clarification**: \(e \approx 2.71828\) denotes the Euler's number.

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