Sense of "have as a plan, have in mind or purpose" (late 14c.) was present in Latin. A Germanic word for this was ettle, from Old Norse ætla "to think, conjecture, propose," from Proto-Germanic *ahta "consideration, attention" (source also of Old English eaht, German acht). Related: Intended; intending.
late 14c., "eager, assiduous; attentive, paying attention," from Old French ententif, intentif "attentive, solicitous, assiduous" (12c.), from Late Latin intentivus, from intent-, past-participle stem of Latin intendere "turn one's attention" (see intend). Related: Intentively; intentiveness.
Grammatical meaning "expressing intensity" is from c. 1600; as a noun, "something expressing intensity," 1813, from the adjective. Alternative intensitive is a malformation. Intensive care attested from 1958. Related: Intensively; intensiveness.