An apparatus, system, and method for transmitting measurements while drilling are adapted for use with a drill string equipped with a mud motor. The drill string may comprise a plurality of interconnected drill pipe joints or a plurality of interconnected casing joints. The apparatus comprises a measurement-while-drilling tool adapted for placement in the drill string beneath the mud motor. The measurement-while-drilling tool has a system for transmitting telemetry signals, such as mud-pulse telemetry signals, upwardly through the mud motor and the drill string. In particular embodiments, the measurement-while-drilling tool has a system for transmitting mud-pulse telemetry signals upwardly through the mud motor and the drill string at frequencies below approximately 1 Hz, although other frequencies may be employed to advantage. The apparatus may further comprise a rotary steerable system for placement in the drill string beneath the mud motor. The rotary steerable system may be a point-the-bit system or a push-the-bit system. In particular embodiments, the rotary steerable system and the measurement-while-drilling tool are integrated.