Integrate by parts: \(\int e^x f'(x)\,dx = e^x f(x) - \int e^x f(x)\,dx\).

So \(\phi(x) = \int e^x f\,dx - \int e^x f'\,dx = \int e^x f\,dx - e^x f(x) + \int e^x f\,dx\)

\(2\int e^x f(x)\,dx = \phi(x) + e^x f(x)\)

\(\int e^x f(x)\,dx = \frac{1}{2}\left[\phi(x) + e^x f(x)\right]\)

Answer: (C)