A Family of multipoint iterative functions with integral informations are construct-ed in this paper. It is shown that the order of convergence for the iterative functionwhich requires 1 evaluaion of f and n-1 evaluations of integral informations is about5×(1+2~(1/2))~(n-3). The application of these iterations in practice is profitable if the eva-luation cost of the value of integral is approximately equal to the evaluation cost offunction or its derivatives.