work out vs integrate

work out and integrate both are verbs.

Word	Noun	Adjective	Verb	Adverb
work out	No	No	Yes	No
integrate	No	No	Yes	No

As verbs, integrate is a hyponym of work out; that is, integrate is a word with a more specific, narrower meaning than work out:

work out (verb)	integrate (verb)
do physical exercise	make into a whole or make part of a whole
give a workout to	become one; become integrated
come up with	calculate the integral of; calculate by integration
work out in detail	open (a place) to members of all races and ethnic groups
find the solution to (a problem or question) or understand the meaning of
make a mathematical calculation or computation
be calculated
happen in a certain way, leading to, producing, or resulting in a certain outcome, often well