If \( \int \frac{2e^{x} + 3e^{-x}}{4e^{x} + 7e^{-x}} \, dx = \frac{1}{14}\left( ux + v \log_{e}(4e^{x} + 7e^{-x}) \right) + C \), where \( C \) is a constant of integration, then \( u + v \) is equal to ________.
