Hybrid vertical takeoff and landing unmanned aerial vehicles are attractive for missions where flight dexterity and long ranges are needed. However, designing such kind of vehicle is troublesome, considering their broad flight envelope and controllability challenges. This paper focuses on the problem of simultaneously designing the vehicle and optimizing its flight trajectory. It continues from a previous work, which evaluated the insertion of a full control system with attitude control, velocity control, and guidance law in an MDO process. It starts with the description of the flight mechanics model, the two-fidelity aerodynamic tool used for integrated aero propulsive analysis, and the 3D modeling strategy that allows for weight and inertia prediction using the Engineering Sketch Pad. The trajectory optimization problem, that accounts for a symbolic mission with hover, transition hover-cruise, cruise, climb, and transition cruise-hover, is then presented. Optimizations with two different objective functions are performed: minimum time and minimum energy consumption. Two different results for each objective function are shown: one considering a fixed design and the other that is obtained with the full design-trajectory optimization. Simultaneous design and trajectory optimization leads to a better performance for the evaluated cases. We then discuss the closed loop feasibility of optimal trajectories, and perform a preliminary study to address the control law tuning for them. The paper finishes with conclusions and ideas for a future work with full integration of trajectory optimization and control law tuning.