We demonstrate for the first time the integration of a superconducting hot electron bolometer (HEB) mixer and a quantum cascade laser (QCL) on the same 4-K stage of a single cryostat, which is of particular interest for terahertz (THz) HEB/QCL integrated heterodyne receivers for practical applications. Two key issues are addressed. Firstly, a low power consumption QCL is adopted for preventing its heat dissipation from destroying the HEB's superconductivity. Secondly, a simple spherical lens located on the same 4-K stage is introduced to optimize the coupling between the HEB and the QCL, which has relatively limited output power owing to low input direct current (DC) power. Note that simulation techniques are used to design the HEB/QCL integrated heterodyne receiver to avoid the need for mechanical tuning. The integrated HEB/QCL receiver shows an uncorrected noise temperature of 1500 K at 2.7 THz, which is better than the performance of the same receiver with all the components not integrated.