Heterogeneously integrated III-V/Si lasers and semiconductor optical amplifiers (SOAs) are key devices for integrated photonics applications requiring miniaturized on-chip light sources, such as in optical communications, sensing, or spectroscopy. In this work, we present a widely tunable laser co-integrated with a semiconductor optical amplifier in a heterogeneous platform that combines AlGaInAs multiple quantum wells (MQWs) and InP-based materials with silicon-on-insulator (SOI) wafers containing photonic integrated circuits. The co-integrated device is compact, has a total device footprint of 0.5 mm2, a lasing current threshold of 10 mA, a selectable wavelength tuning range of 50 nm centered at λ = 1549 nm, a fiber-coupled output power of 10 mW, and a laser linewidth of ν = 259 KHz. The SOA provides an on-chip gain of 18 dB/mm. The total power consumption of the co-integrated devices remains below 0.5 W even for the most power demanding lasing wavelengths. Apart from the above-mentioned applications, the co-integration of compact widely tunable III-V/Si lasers with on-chip SOAs provides a step forward towards the development of highly efficient, portable, and low power systems for wavelength division multiplexed passive optical networks (WDM-PONs).