A pressurized water reactor (PWR) includes a vertical cylindrical pressure vessel having a lower portion containing a nuclear reactor core and a vessel head defining an integral pressurizer. A reactor coolant pump (RCP) mounted on the vessel head includes an impeller inside the pressure vessel, a pump motor outside the pressure vessel, and a vertical drive shaft connecting the motor and impeller. The drive shaft does not pass through the integral pressurizer. The drive shaft passes through a vessel penetration of the pressure vessel that is at least large enough for the impeller to pass through.