1828, from French insouciant "careless, thoughtless, heedless," from in- "not" (see in- (1)) + souciant "caring," present participle of soucier "to care," from Latin sollicitare "to agitate" (see solicit). Related: Insouciantly.
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.
early 15c., soliciten, "to disturb, trouble," from Old French soliciter, solliciter (14c.), from Latin sollicitare "to disturb, rouse, trouble, harass; stimulate, provoke," from sollicitus "agitated," from sollus "whole, entire" (from PIE root *sol- "whole, well-kept") + citus "aroused," past participle of ciere "shake, excite, set in motion" (from PIE root *keie- "to set in motion"). Related: Solicited; soliciting.
The meaning "entreat, petition" is from 1520s. Meaning "to further (business affairs)" evolved mid-15c. from a French sense of "manage affairs." The sexual sense (often in reference to prostitutes) is attested from 1710, probably from a merger of the business sense and an earlier sense of "to court or beg the favor of" (a woman), attested from 1590s.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit sarvah "uninjured, intact, whole;" Avestan haurva- "uninjured, intact;" Old Persian haruva-; Greek holos "whole;" Latin salvus "uninjured, in good health, safe," salus "good health," solidus "solid;" Armenian olj "whole, healthy."