\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f\) be defined on \(\mathbb{R}\) by \(f(x) = e^{-7x} + x\).
Determine the unique antiderivative \(F\) of \(f\) such that \(F(0) = -\frac{1}{7}\).
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