take on vs undertake

take on

verb
  • To assume or take responsibility for. 

  • To (attempt to) dribble round (an opposition player). 

  • To catch on, do well; to become popular. 

  • To obtain the services of (a person) in exchange for remuneration; to give someone a job. 

  • To begin to have or exhibit. 

  • To attempt to fight, compete with, or engage with. 

  • To acquire, bring in, or introduce. 

  • To grieve or be concerned (about something or someone). 

undertake

verb
  • To take upon oneself; to start, to embark on (a specific task etc.). 

  • To commit oneself (to an obligation, activity etc.). 

  • To pass a slower moving vehicle on the curbside rather than on the side closest to oncoming traffic. 

noun
  • The passing of slower traffic on the curbside rather than on the side closest to oncoming traffic. 

How often have the words take on and undertake occurred in a corpus of books? (source: Google Ngram Viewer )