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Silicon photonic integration has gained great success in many application fields owing to the excellent optical device properties and complementary metal-oxide semiconductor (CMOS) compatibility. Realizing monolithic integration of III-V lasers and silicon photonic components on single silicon wafer is recognized as a long-standing obstacle for ultra-dense photonic integration, which can provide considerable economical, energy efficient and foundry-scalable on-chip light sources, that has not been reported yet. Here, we demonstrate embedded InAs/GaAs quantum dot (QD) lasers directly grown on trenched silicon-on-insulator (SOI) substrate, enabling monolithic integration with butt-coupled silicon waveguides. By utilizing the patterned grating structures inside pre-defined SOI trenches and unique epitaxial method via molecular beam epitaxy (MBE), high-performance embedded InAs QD lasers with out-coupled silicon waveguide are achieved on such template. By resolving the epitaxy and fabrication challenges in such monolithic integrated architecture, embedded III-V lasers on SOI with continuous-wave lasing up to 85 oC are obtained. The maximum output power of 6.8 mW can be measured from the end tip of the butt-coupled silicon waveguides, with estimated coupling efficiency of approximately -7.35 dB. The results presented here provide a scalable and low-cost epitaxial method for realization of on-chip light sources directly coupling to the silicon photonic components for future high-density photonic integration.