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This work proposes a new IIR integer order digital, so a new IIR fractional order integrators. The followed method includes two stages. First, the integer order integrator is obtained by interpolating well-known integration rulesnamely, Euler, bilinear and Simpsonas a weighted sum. Second the initial value theorem for the selection of initial value of the impulse response is used. Lastlythe Steiglitz-Mc-bride signal modeling technique is applied to find the parameters of rational approximation models. Numerical examples are presented to illustrate the performance of the proposed integrator. It was found that the Euler-bilinear-Simpson integrator yields high accuracy than the existing integrators.