This paper presents a novel, generalized method for solving resource integration problems: the nonsmooth integration operator. Compared to current approaches, such as cascade analysis or the pinch location method, the nonsmooth integration operator is generalizable to any resource, including multiple resources simultaneously. Additionally, it is uniquely able to both solve for process variables and scale moderately with the number of sources and sinks in the system, and thus is well-equipped to handle large and complex multi-plant systems, easily embedded in process optimization problems, and readily extendable to new applications. The nonsmooth integration operator is a system of two nonsmooth equations per resource that describe optimal conditions for pinch-constrained resource transfer with preclassified sources and sinks and limited to a single contaminant. The operators for multiple resources can be combined with process models, and the resulting equation system is solved by using new advances in nonsmooth equation solving. The operator can also be extended to automatically identify threshold problems. This paper details the formulation and use of the nonsmooth integration operator and includes several example problems to demonstrate its strengths and flexibility. These problems show that the nonsmooth integration operator can solve for unknown process variables, include process models, and simultaneously integrate multiple resources. They also cover a wide range of problem types, including mass integration, water and hydrogen networks, and carbon-constrained energy planning, to show the utility of a generalizable approach to the integration problem.