Atomic force microscope (AFM) cantilevers with integrated actuation and sensing provide several distinct advantages over conventional cantilever instrumentation. These include clean frequency responses, the possibility of down-scaling and parallelization to cantilever arrays as well as the absence of optical interference. While cantilever microfabrication technology has continuously advanced over the years, the overall design has remained largely unchanged; a passive rectangular shaped cantilever design has been adopted as the industry wide standard. In this article, we demonstrate multimode AFM imaging on higher eigenmodes as well as bimodal AFM imaging with cantilevers using fully integrated piezoelectric actuation and sensing. The cantilever design maximizes the higher eigenmode deflection sensitivity by optimizing the transducer layout according to the strain mode shape. Without the need for feedthrough cancellation, the read-out method achieves close to zero actuator/sensor feedthrough and the sensitivity is sufficient to resolve the cantilever Brownian motion.