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.)).
word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
late 14c., "observation as the source of knowledge; actual observation; an event which has affected one," from Old French esperience "experiment, proof, experience" (13c.), from Latin experientia "a trial, proof, experiment; knowledge gained by repeated trials," from experientem (nominative experiens) "experienced, enterprising, active, industrious," present participle of experiri "to try, test," from ex "out of" (see ex-) + peritus "experienced, tested," from PIE *per-yo-, suffixed form of root *per- (3) "to try, risk." Meaning "state of having done something and gotten handy at it" is from late 15c.