Integrators are widely used in many modern automation and counting and solving devices. They are used, in particular, to determine the coordinates of the location of some object if its velocity is known. Often the characteristic input signal of a dynamic system, or one of its components, is a random process. Then the output is also a random process, the parameters of which must be determined. We come to the formulation of such a problem, in particular, when determining the random component of the error at the output of the integrating drive.