Dynamic X-ray studies can reach temporal resolutions limited by only the X-ray pulse duration if the detector is fast enough to segregate synchrotron pulses. An analog integrating pixel array detector with in-pixel storage and temporal resolution of around 150 ns, sufficient to isolate pulses, is presented. Analog integration minimizes count-rate limitations and in-pixel storage captures successive pulses. Fundamental tests of noise and linearity as well as high-speed laser measurements are shown. The detector resolved individual bunch trains at the Cornell High Energy Synchrotron Source at levels of up to 3.7×10$^3$ X-rays per pixel per train. When applied to turn-by-turn X-ray beam characterization, single-shot intensity measurements were made with a repeatability of 0.4% and horizontal oscillations of the positron cloud were detected.