In light of the integral role of integrators as crucial components of Rogowski coils, their performance significantly influences the measurement accuracy of Rogowski coils. This study aims to enhance the accuracy, stability, and reliability of digital integrators. By scrutinizing the sources of errors in digital integration algorithms and integrators, a novel digital integrator is designed. This integrator employs a reverse compensation method to mitigate DC errors, alongside the utilization of the compound trapezoidal algorithm as the digital integration method and the wavelet threshold denoising technique as the error reduction method. Finally, MATLAB simulations validate the designed digital integrator, demonstrating its capability to accurately integrate differential waveforms. This research provides robust methods and empirical support for improving the performance of digital integrators.