Phrasal verbs in English fall into three classes: a main verb and an adverb particle (‘bring in’), a verb and a preposition which cannot be separated from each other (‘cope with’), a verb and an inseparable particle and preposition (‘catch up with’).
A common exercise in making an English text appear more academic in style is to convert phrasal verbs into more formal single-word alternatives: but does this mean phrasal verbs should be avoided altogether? The usual arguments for doing so are that phrasal verbs are colloquial and may be difficult to understand from their component parts (this applies in particular to the three-part phrasal verbs such as ‘come up with’ and ‘look down on’) and that they often have different meanings in different contexts (for example, ‘turn on’ can be to activate (a TV), attack (a weaker opponent) or arouse, please). Also, the one-word equivalents are often Latin in origin and so possess the patina of ‘academic style’ (‘propose’ rather than ‘put forward’, ‘oppose’ rather than ‘go against’, ‘indicate’ rather than ‘point out’).
But academic writing is about clear communication, and sometimes the phrasal verb more vividly conveys (‘puts across’) the idea and is common enough currency so as to be readily understood. ‘The argument breaks down here’ is just as good as ‘the argument fails here.’ Context usually pins down the meaning of a phrasal verb unambiguously; moreover, the one-word equivalents may also have alternative meanings in other contexts: which of ‘perform’, ‘conduct’ or ‘execute’ would you use for ‘carry out’ in the sense of “carry out a study”?
The adverbial/prepositional particles in a phrasal verb usually convey meanings of relative position, direction or movement (‘with’, ‘between’, ‘in’, ‘away’, ‘off’, ‘toward’) and in this way bring a dynamic sense or directness to the verb that may be lacking in synonyms (‘bring about change’ or ‘effect change’? ‘go on to consider’ or ‘proceed to consider’, ‘take on a role’ or ‘assume a role’?).
But enough puttering on, let the corpus speak: the following phrasal verbs are frequently used in academic texts, primarily with the meaning indicated (definitions courtesy of Merriam-Webster dictionary).
point out to talk about or mention (something that one thinks is important), e.g. ‘we ought to point out that’
go on to continue, proceed, e.g. ‘before we go on to discuss’
take on to begin to perform or deal with, e.g. ‘take on this new challenge’; to assume or acquire as or as if one’s own, e.g. ‘take on the role’
set up to found, inaugurate, e.g. ‘a commission was set up to investigate the disaster’; to put forward or extol as a model, to claim oneself to be, e.g. ‘he set himself up as an authority’; cause, create, bring about, e.g. ‘this sets up a vicious circle’
make up to combine to produce, constitute, compose, e.g. ‘make up a large part of’; to compensate for (something, such as a deficiency or omission), e.g. ‘use contributions to make up one’s basic pension’ level’
turn out to prove to be in the result or end, e.g. ‘these findings turn out to be artifactual’
take up to proceed to consider or deal with, e.g. ‘I shall take up this point shortly’; to occupy entirely or exclusively, e.g. ‘it would take up too much space to treat this here’
carry out to put into execution, e.g. ‘we shall carry out a task analysis’
end up to reach or come to a place, condition, or situation that was not planned or expected, e.g.’are Catholics more likely to end up in prison than Protestants?
open up to make available, accessible or possible, e.g. ‘this opens up a complex range of new questions’
pick up to recover or increase speed, vigor, or activity, e.g. ‘the economy picked up again’; understand, catch. e.g. ‘pick up on non-verbal cues’; to resume after a break, e.g. ‘we will pick up this point later’
find out to learn by study, observation, or search, discover, e.g. ‘if we are to find out what this means’
come up to come to attention or consideration, e.g. ‘the question never came up’; to occur in the course of time, e.g. ‘come up for consideration’
come up with to produce especially in dealing with a problem or challenge, e.g. ‘failed to come up with hard evidence’
To sum up, do not be put off putting to use phrasal verbs in putting down your ideas – no need to put yourself out to put across your meaning in one-word words.
Phrasal verbs in academic writing (Writefull)
Phrasal verbs and multi-word verbs (Cambridge grammar online)