A high compression ratio compressor having multiple stages of airfoils to produce the high pressure rations, where the last stage airfoils are cooled by passing cooling air through the airfoils without discharging film cooling air. The cooling air for the airfoils is bled off from an upstream stage of the compressor, passed through the airfoil to provide for the cooling, passed through a heat exchanger to preheat a fuel, where the preheated fuel is passed into the combustor. the cooled cooling air form the heat exchanger can be reintroduced back into the compressor or passed through the turbine to cool last stage airfoils in the turbine.