compete vs do one’s utmost

compete

verb
  • To be in a position in which it is possible to win or triumph. 

  • To take part in a contest, game or similar event 

  • To be in battle or in a rivalry with another for the same thing, position, or reward; to contend 

do one’s utmost

How often have the words compete and do one’s utmost occurred in a corpus of books? (source: Google Ngram Viewer )