1. An integrated method for determining the quality of batteries comprising the steps of: probing of the inner volume of a battery found in initial charged state of the battery with ultrasonic pulses with a high-frequency filling by a shadow mode by using ultrasonic probes containing polyurethane protectors for ultrasonic energy injection; probing of the inner volume of the battery found in initial charged state of the battery with an eddy magnetic field by using first and second eddy current probes spatially integrated with emitting and receiving ultrasonic probes formed compound measuring transducers and arranged on both sides of the battery; artificially discharging the battery being diagnosed to a low fixed test charge value; using the signals of the eddy current probes for determining continuity of the discharge current during the artificial discharging process; repeating battery probing with the ultrasonic pulses after the artificial discharge; determining signals of the eddy current probes after the artificial discharge; forming a resultant eddy current signal; determining the deviation of the resultant eddy current signal generated at the initial state of the battery being diagnosed from an average state of the same signal preliminary obtained on a training sample of batteries; determining the ultrasonic signal gradient versus the battery capacity; determining the gradient of the resultant eddy current signal versus the battery capacity; determining the deviation of the ultrasonic signal gradient for the battery being diagnosed from the average state of the same gradient preliminary obtained on the training sample of batteries; determining the deviation of the gradient of the resultant eddy current signal for the battery being diagnosed from the average state of the same gradient preliminary obtained on the training sample of batteries; forming probability density functions for the deviations of the eddy current resultant signal obtained in the initial state of the battery, and the gradients of the ultrasonic and eddy current resultant signals; forming binary signals for the deviations of the eddy current resulting signal obtained in the initial state of the battery, and the gradients of the ultrasonic and eddy current resultant signals while using corresponding thresholds; determining probabilities of the obtained binary signals for the battery being diagnosed using corresponding probability density functions; using the obtained binary signals with their probability values and a logical rule set to determine a battery rejection probability and a battery rejection signal; rejecting batteries being diagnosed based on the battery rejection signal.