Incorrect spelling, explanation: there is no such form as recouperate; the correct form is recuperate, because the word comes from the Latin word recuperare. Thus the spelling remains and recuperate is the correct form.

Correct spelling, explanation: this form is the correct one because the word comes from Latin recuperare, thus it’s spelled with u, not ou. Recouperate is a mistake, and it was probably made due to similar French pronunciation of the ou sound. Recuperate is the correct form, though.

Definition of recuperate:
verb, to restore health or recover e.g. financially
Supermarkets should recuperate unsold food, for example by giving it away to the homeless.
We should recuperate before going further.