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In polycrystalline thin films, formation of grain boundary grooving is investigated widely due to its effects on their properties. Infinite series solution of the interface of grain-boundary grooving by surface diffusion has been obtained. In this paper, with Fourier transform, a novel integral solution of the profile of grain boundary grooving is derived. Numerical examples are taken to test the performance of the integral solution. According to the numerical examples, we find that the novel solution is in accordance with the infinite series solution.