The powerful and bluesy "I've Got A Feeling," which John Lennon jokingly called "I've Got A Fever," is a true Lennon/McCartney composition. It blends — via alternation and superimposition — two incomplete songs, one by Paul McCartney, one by Lennon.
Both happened to have been written around the same period and based on the same two-chord motif built around a first-position A chord (with the high A note fingered with the pinky). It is the last true collaboration by Lennon and McCartney.
McCartney's share of the song, called "I've Got A Feeling" from the get-go, includes a verse, chorus and bridge and was inspired by his relationship with his soon-to-be-wife, Linda Eastman. Lennon provides alternate verses inspired by his personal upheavals of 1968.
Source: Guitar World