An integrated turbo-compressor includes a compressor with a compressor outlet, a turbine with a turbine inlet, the turbine operatively connected to the compressor by an interconnect shaft, and a compounding drive. The compounding drive is connected to the turbine and has a variable gear ratio and an output member, the variable gear ratio coupling the turbine to the output member to compound output of an internal combustion engine using energy recovered from an exhaust flow received from the internal combustion engine and in excess of energy required to compress combustion air provided to the internal combustion engine. Internal combustion engines, aircraft, and methods of compounding output of internal combustion engines are also described.