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Two efficient integral-based exponential time differencing (ETD) algorithms for general dispersive media in the finite-difference time domain (FDTD) are introduced. The first employs a linear approximation for the field over an integral time step in the integrand (denoted Algorithm I), and the second employs a Taylor series for approximating the field over the integral time step (denoted Algorithm II). Compared with the auxiliary differential equation (ADE) method and the piecewise linear recursive convolution (PLRC) method, the proposed algorithms have the same second-order accuracy but can lead to a substantial saving in both the memory space and CPU time consumption. To complete the scheme for the open region problems, a novel integral-based ETD implementation of the complex frequency shifted perfectly matched layer (CFS-PML) is proposed. Compared with the well-known recursive convolution implementation of the CFS-PML (CPML), this new implementation can lead to a substantial saving in the CPU time and a significant improvement of around 20 dB in the absorbing performance. And through the integral-based ETD algorithm, a much simpler interpretation of the CPML is presented.