An aircraft with an integrated boundary layer ingesting propulsion having a mechanically-distributed propulsion system. The mechanically-distributed propulsion system may include an engine to generate a mechanical drive power, a drive shaft, a direction-reversing transmission, and a propulsor fan. The drive shaft may be operatively coupled to the engine to receive the mechanical drive power. The direction-reversing transmission may have a first rotating shaft and a second rotating shaft, the first rotating shaft operatively coupled to the drive shaft to receive the mechanical drive power, which is configured to redirect the mechanical drive power received at the first rotating shaft from a first direction to face a second direction at the second rotating shaft. The propulsor fan may be coupled to the second rotating shaft to convert the mechanical drive power into thrust.