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In this paper,the complex integral method is firstly put forward to compute hypersingular integrals on interval.Based on the classical Cauchy integral formula,the integral paths of hypersingular integrals is moved to the complex plane from the real axis so that there is no singular points in the new integral paths,and then the computational formulas of the exact value of hypersingular integrals is obtained.At the same time,the numerical algorithm of complex integral and error estimation are derived.Numerical examples are provided to show that the method is computationally efficient.