take up vs undertake

take up

verb
  • To begin doing (an activity) on a regular basis. 

  • To accept (a proposal, offer, request, etc.) from. 

  • To implement, to employ, to put into use. 

  • To review the solutions to a test or other assessment with a class. 

  • To occupy; to consume (space or time). 

  • Synonym of take in (“tighten a belaying rope”) 

  • To resume. 

  • To pick up. 

  • To address (an issue). 

  • To shorten by hemming. 

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 up and undertake occurred in a corpus of books? (source: Google Ngram Viewer )