'nonintegrable' originates from Modern English, specifically formed from the prefix 'non-' (from Latin 'non') and the adjective 'integrable' (from Latin 'integrare'), where 'non-' meant 'not' and 'integrare' meant 'to make whole'.

'integrable' comes from Latin 'integrare' (to make whole) via the verb 'integrate' in Late Latin/Medieval Latin and Middle English, with the adjectival suffix '-able' producing 'integrable'; the negative prefix 'non-' was later attached in Modern English to form 'nonintegrable'.

Initially related to the idea of 'not able to be made whole' through the sense of 'integrate'; over time it specialized in mathematics to mean 'not able to be integrated' (i.e., an integral does not exist or is not defined in a given sense).