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Let $f(x) = \int_0^x e^t f(t),dt + e^x$ be a differentiable function for all $x \in R$. Then $f(x)$ equals:
(1) $2e^{(e^x - 1)} - 1$
(2) $e^{(e^x - 1)}$
(3) $2e^{e^x} - 1$
(4) $e^{e^x} - 1$
BETA
