Online Etymology Dictionary

inestimable (adj.): late 14c., "beyond estimation or measure, not to be computed," from Old French inestimable "priceless" (14c.) or directly from Latin inaestimabilis "invaluable, incalculable," also "not estimable, valueless," from in- "not, opposite of" (see in- (1)) + aestimabilis "valuable, estimable," from aestimare (see esteem (v.)). Meaning "too precious to set a value on, priceless" is attested by 1570s. Related: Inestimably; inestimability.
inevitability (n.): 1640s, from inevitable + -ity. Perhaps modeled on French inévitabilité.
inevitable (adj.): "unavoidable," mid-15c., from Latin inevitabilis "unavoidable," from in- "not, opposite of" (see in- (1)) + evitabilis "avoidable," from evitare "to avoid," from ex- "out" (see ex-) + vitare "shun," originally "go out of the way." As a noun from 1850. Related: Inevitableness.
inevitably (adv.): mid-15c., from inevitable + -ly (2).
inexact (adj.): 1791, from in- (1) "not, opposite of" + exact (adj.). Perhaps modeled on French inexact (18c.). Related: Inexactly.
inexactitude (n.): 1786, from in- (1) "not, opposite of" + exactitude. Perhaps modeled on French inexactitude (18c.).
inexcusable (adj.): early 15c., from Latin inexcusabilis "without excuse; affording no excuse," from in- "not, opposite of" (see in- (1)) + excusabilis, from excusare "apologize, make an excuse for" (see excuse (v.)). Related: Inexcusably.
inexhaustible (adj.): c. 1600, from in- (1) "not, opposite of" + exhaustible (see exhaust (v.)). Perhaps modeled on French inexhaustible (15c.). Related: Inexhaustibly.
inexorable (adj.): "unyielding, unrelenting," 1550s, from Middle French inexorable and directly from Latin inexorabilis "that cannot be moved by entreaty, unyielding," from in- "not, opposite of" (see in- (1)) + exorabilis "able to be entreated," from exorare "to prevail upon," from ex- "out" (see ex-) + orare "pray" (see orator). Related: Inexorably; inexorability.
inexpediency (n.): 1640s; see inexpedient + -cy.
inexpedient (adj.): "not suitable to the purpose or circumstances," c. 1600, from in- (1) "not, opposite of" + expedient. Related: Inexpedience; inexpediently.
inexpensive (adj.): 1670s, from in- (1) "not, opposite of" + expensive. Related: Inexpensively.
inexperience (n.): 1590s, from French inexpérience (15c.) or directly from Late Latin inexperientia "inexperience," from in- "not, opposite of" (see in- (1)) + Latin experientia "experimental knowledge; experiment; effort" (see experience (n.)).
inexperienced (adj.): "lacking the knowledge or skill gained by experience," 1620s, past-participle adjective from inexperience.
inexpert (adj.): mid-15c., from in- (1) "not, opposite of" + expert (adj.), or else from Old French inexpert or directly from Latin inexpertus "without experience, unpracticed; untried, untested." Related: Inexpertly.
inexpiable (adj.): 1560s, from Latin inexpiabilis "that cannot be atoned for," from in- "not" (see in- (1)) + expiabilis, from expiare "make amends for, purify, purge by sacrifice" (see expiation). The Inexpiable War was between Carthage and its Libyan mercenaries after the end of the First Punic War (241 B.C.E.). Related: Inexpiably.
inexplicable (adj.): early 15c., from Middle French inexplicable or directly from Latin inexplicabilis "that cannot be unfolded or disentangled, very intricate," figuratively, "inexplicable," from in- "not, opposite of" (see in- (1)) + explicabilis "that may be explained" (see explicable).

As a noun, 1745, "something that cannot be explained;" jocular inexplicables "trousers" is from 1829. Related: Inexplicably; inexplicability.
inexplicit (adj.): 1775 (implied in inexplicitly), from in- (1) "not, opposite of" + explicit. Or else from Latin inexplicitus "not to be unfolded; unexplained." Related: Inexplicitly; inexplicitness.
inexpressible (adj.): 1620s, from in- (1) "not" + expressible (see express (v.)). Inexpressibles "trousers" is from 1790. Related: Inexpressibly.
I have retain'd the word BREECHES, as they are known by no other name amongst country folk.--The change from vulgarity to refinement, in cities and towns, has introduced other appellations; there they are generally called SMALL CLOTHES, but some ladies of high rank and extreme delicacy call them INEXPRESSIBLES. [footnote in "Poems Miscellaneous and Humorous," by Edward Nairne, Canterbury, 1791]
Inexpressibles is the earliest recorded and thus seems to have begotten the trend: Unmentionables (1806); indispensibles (1820); ineffables (1823); unutterables (1826); innominables (1827); and inexplicables (1829) followed.
inexpugnable (adj.): late 15c., from Old French inexpugnable (14c.) or directly from Latin inexpugnabilis "not to be taken by assault, not to be rooted out, invincible," from in- "not" (see in- (1)) + expugnabilis "assailable," from expugnare (see expugn). Figurative sense, in reference to arguments, etc., is from 1530s.
inexpungible (adj.): 1610s, from in- (1) "not, opposite of" + expungible (see expunge).
inextinguishable (adj.): c. 1500, from in- (2) "not" + extinguishable. Earlier was inextinguible (early 15c.), from Old French inextinguible or directly from Latin inextinguibilis. Related: Inextinguishably; inextinguishability.
inextirpable (adj.): 1620s, from in- (1) "not, opposite of" + extirpable (see extirpate).
inextricable (adj.): early 15c., from Latin inextricabilis "that cannot be disentangled," from in- "not, opposite of" (see in- (1)) + extricare "to disentangle" (see extricate). Related: Inextricably; inextricability.
Inez: fem. proper name, Spanish form of Agnes (q.v.).
infallibility (n.): "quality of being incapable of error," 1610s, from Medieval Latin infallibilitas, from infallibilis (see infallible).
infallible (adj.): "exempt from error in judgment, knowledge, or opinion," early 15c., from Medieval Latin infallibilis, from in- "not, opposite of" (see in- (1)) + Late Latin fallibilis (see fallible). In reference to Popes, attested from 1870, hence infallibilism, the doctrine of this; infallibilist. Related: Infallibly.
infamous (adj.): a 16c. merger of two Middle English words, with the form of infamous "not well-known" (early 15c.) and the sense of infamis (late 14c.), "of ill repute, famous for badness." Infamous is from Medieval Latin infamosus, from in- "not, opposite of" (see in- (1)) + Latin famosus "celebrated" (see famous). Infamis is from Latin infamis "of ill fame" (see infamy).

Meaning "causing infamy" is from 1550s. As a legal term, "disqualified from certain rights of citizens because of conviction for certain crimes" (late 14c.). The neutral fameless (in the sense original to infamous) is recorded from 1590s. Related: Infamously.
infamy (n.): early 15c., "public disgrace, dishonor, evil fame," from Old French infamie "dishonor, infamous person" (14c.) and directly from Latin infamia "ill fame, bad repute, dishonor," from infamis "disreputable, notorious, of ill fame," from in- "not, without" (see in- (1)) + fama "reputation" (see fame (n.)). Meaning "quality of being shamefully vile" is from 1510s.

An earlier form in Middle English was infame (late 14c.), from Old French infame, an earlier form of infamie. Infame also was the Middle English verb in this set, "brand with infamy," from Old French infamer, from Latin infamare "bring into ill repute, defame," from infamis. The verb has become archaic in English (infamize is attested from 1590s).
infancy (n.): late 14c., "condition of babyhood," also "childhood, youth," from Anglo-French enfaunce and directly from Latin infantia "early childhood," from infantem "young child," literally "one unable to speak" (see infant). Restriction to the earliest months of life is a return to the etymological sense of the word but is a recent development in English. In old legal language it meant "condition of being a minor" and could mean any age up to 21.
infant (n.): late 14c., infant, infaunt, "a child," also especially "child during earliest period of life, a newborn" (sometimes meaning a fetus), from Latin infantem (nominative infans) "young child, babe in arms," noun use of adjective meaning "not able to speak," from in- "not, opposite of" (see in- (1)) + fans, present participle of fari "to speak," from PIE root *bha- (2) "to speak, tell, say" (see fame (n.)). As an adjective in English, 1580s, from the noun.

The Romans extended the sense of Latin infans to include older children, hence French enfant "child," Italian fanciullo, fanciulla. In English the word formerly also had the wider sense of "child" (commonly reckoned as up to age 7). The common Germanic words for "child" (represented in English by bairn and child) also are sense extensions of words that originally must have meant "newborn."
Infanta (n.): "daughter of a king of Spain or Portugal," c. 1600, from Spanish and Portuguese infanta, fem. of infante "a youth; a prince of royal blood," from Latin infantem (see infant).
infanticide (n.): 1650s, "the killing of infants," especially the killing of newborns or the unborn; 1670s, "one who kills an infant," from infant + -cide. Perhaps from French infanticide (16c.).
In Christian and Hebrew communities infanticide has always been regarded as not less criminal than any other kind of murder; but in most others, in both ancient and modern times, it has been practised and regarded as even excusable, and in some enjoined and legally performed, as in cases of congenital weakness or deformity among some of the communities of ancient Greece. [Century Dictionary]
infantile (adj.): mid-15c., "pertaining to infants," from Late Latin infantilis "pertaining to an infant," from infans "young child" (see infant). Sense of "infant-like" is from 1772.
infantilism (n.): 1894 in the psychological sense; see infantile + -ism. Earlier in a physiological sense, "retarded and imperfect physical development," perhaps from French infantilisme (1871).
infantry (n.): 1570s, from French infantrie, infanterie (16c.), from older Italian or Spanish infanteria "foot soldiers, force composed of those too inexperienced or low in rank to be cavalry," a collective noun from infante "foot soldier," originally "a youth," from Latin infantem (see infant). Meaning "infants collectively" is recorded from 1610s. A Middle English (c. 1200) word for "foot-soldiers" was going-folc, literally "going-folk."
infantryman (n.): 1837, from infantry + man (n.).
infarct (n.): substance of an infarction, 1873, from medical Latin infarctus (variant of infartus), past participle of infarcire "to stuff into" (see infarction).
infarction (n.): 1680s, noun of action from Latin infarcire "to stuff into," from in- "into" (see in- (2)) + farcire "to stuff" (see farce).
Formerly applied in pathology to a variety of morbid local conditions; now usually restricted to certain conditions caused by a local fault in the circulation. [Century Dictionary, 1902]
infatigable (adj.): "untiring," c. 1500, from French infatigable (15c.) or directly from Late Latin infatigabilis "that cannot be wearied," from in- "not, opposite of" (see in- (1)) + fatigabilis "that may be wearied," from Latin fatigare "to weary" (see fatigue (n.)).
infatuate (v.): 1530s, "turn (something) to foolishness, frustrate by making foolish," from Latin infatuatus, past participle of infatuare "make a fool of," from in- "in" (see in- (2)) + fatuus "foolish" (see fatuous). Specific sense of "inspire (in someone) a foolish passion beyond control of reason" is from 1620s. Related: Infatuated; infatuating.
infatuation (n.): 1640s, noun of action from infatuate (q.v.), or else from French infatuation or directly from Late Latin infatuationem (nominative infatuatio), from past participle stem of Latin infatuare "make a fool of."
infeasibility (n.): 1650s, from infeasible + -ity.
infeasible (adj.): 1530s, from in- (1) "not, opposite of" + feasible.
infect (v.): late 14c., "fill with disease, render pestilential; pollute, contaminate; to corrupt morally," from Latin infectus, past participle of inficere "to stain, tinge, dye," also "to corrupt, stain, spoil," literally "to put in to, dip into," from in- "in" (see in- (2)) + facere "to make, do, perform" (see factitious). In Middle English occasionally in a neutral sense "tinge, darken," but typically used of things indifferent or bad, and especially of disease. Related: Infected; infecting.
infection (n.): late 14c., "infectious disease; contaminated condition;" from Old French infeccion "contamination, poisoning" (13c.) and directly from Late Latin infectionem (nominative infectio) "infection, contagion," noun of action from past participle stem of Latin inficere "to spoil, to stain" (see infect). Meaning "communication of disease by agency of air or water" (distinguished from contagion, which is body-to-body communication), is from 1540s.
infectious (adj.): "catching, having the quality of spreading from person to person, communicable by infection," 1540s of diseases, 1610s of emotions, actions, etc.; see infection + -ous. Earlier in the same sense were infectuous (late 15c.), infective (late 14c.). Related: Infectiously; infectiousness.
infective (adj.): "infectious, communicable by infection," late 14c., from Latin infectivus, from infect-, past participle stem of inficere "to tinge, dye; stain, spoil" (see infect).
infecund (adj.): early 15c., from Latin infecundus, from in- "not, opposite of" (see in- (1)) + fecundus (see fecund). Related: Infecundity.
infelicitous (adj.): "unhappy, unlucky," 1754, from in- (1) "not, opposite of" + felicitous. Earlier was infelicious (1590s). Related: infelicitously; infelicitousness.