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Integrated solenoid inductors with magnetic core were fabricated and analyzed. An inductance above 70 nH was achieved while keeping the coil resistance below 1 Omega and the device area below 1 mm2 using a solenoid design with a single magnetic layer. The inductance of the magnetic inductor was more than 30 times that of the air core inductor of the identical geometry, and the quality factor of the magnetic inductor was >5. Novel inductor designs and the scalability were also examined, and an inductance density higher than 200 nH/mm2 was obtained. The measured device properties and engineering tradeoffs were well explained by analytical models we developed.