  Particle accelerators represent an indispensable tool in science and
industry. However, the size and cost of conventional radio-frequency
accelerators limit the utility and reach of this technology. Dielectric laser
accelerators (DLAs) provide a compact and cost-effective solution to this
problem by driving accelerator nanostructures with visible or near-infrared
(NIR) pulsed lasers, resulting in a 10$^4$ reduction of scale. Current
implementations of DLAs rely on free-space lasers directly incident on the
accelerating structures, limiting the scalability and integrability of this
technology. Here we present the first experimental demonstration of a
waveguide-integrated DLA, designed using a photonic inverse design approach.
These on-chip devices accelerate sub-relativistic electrons of initial energy
83.4 keV by 1.21 keV over 30 um, providing peak acceleration gradients of 40.3
MeV/m. This progress represents a significant step towards a completely
integrated MeV-scale dielectric laser accelerator.
