\[ \int \frac{3e^x + 5e^{-x}}{1 - 4e^{-x}} \, dx = 3f(x) + \frac{5}{4}g(x) + \frac{53}{4}\log h(x) + c \] Given the above conditions, find: \[ f(1) + g(1) + h(1) \]