The invention relates to an electric motor with an integrated cooling device, which uses in particular bleed air as the primary coolant for cooling components of the stator and/or the rotor. Ambient air accelerated by the propulsion means, for example by a propeller, that is driven by the electric motor is used here as the bleed air. A channel system is integrated within the stator housing that has one or more channels for the targeted feed of the primary coolant to the component to be cooled. In the case of cooling the stator, a heat exchanger is also integrated within the stator housing, for example an annular heat exchanger that is arranged coaxially with respect to the stator and to which the primary coolant is fed. For cooling the rotor, a coolant passage is provided that also includes the air gap of the electric machine, for example.