The Collaborative International Dictionary of English v.0.48:

Inexhaustible \In`ex*haust"i*ble\, a.
   Incapable of being exhausted, emptied, or used up; unfailing;
   not to be wasted or spent; as, inexhaustible stores of
   provisions; an inexhaustible stock of elegant words.
   --Dryden.
   [1913 Webster]

         An inexhaustible store of anecdotes.     --Macaulay.
   -- In`ex*haust"i*ble*ness, n. -- In`ex*haust"i*bly, adv.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inexhaustibly
    adv 1: with indefatigable energy; "she watched the show
           indefatigably" [syn: indefatigably, tirelessly,
           inexhaustibly]