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