Distributed electric propulsion is a key enabling technology for on-demand electric aircraft concepts. NASA's X-57 Maxwell X-plane is a demonstrator for this technology, and it features a row of high-lift propellers distributed along the leading edge of its wing to enable better aerodynamic efficiency at cruise and improved ride quality in addition to less noise and emissions. This study applies adjointbased multidisciplinary design optimization to this highly coupled design problem. The propulsion, aerodynamics, and structures are modeled using blade element momentum theory, the vortex lattice method, and finite element analysis, respectively, and the full mission profile is discretized and analyzed. The design variables in the optimization problem include the altitude profile, the velocity profile, battery weight, propeller diameters, propeller rotational speeds, blade profile parameters, wing thickness distribution, and angle of attack. Optimizations take on the order of 10 hours, and a 12% increase in range is observed.