'non-integrable' originates from the prefix 'non-' meaning 'not' and the word 'integrable', which comes from Latin 'integrabilis', meaning 'able to be made whole'.

'integrabilis' transformed into the English word 'integrable', and with the addition of the prefix 'non-', it became 'non-integrable'.

Initially, 'integrable' meant 'able to be made whole', and with the prefix 'non-', it evolved to mean 'not capable of being integrated'.