Argthtjtr

I have been thinking about other ways to say "I believe" in an essay and I came across "cogitate". Do you think it would be appropriate to use this word in an essay's conclusion? For instance, does this sound all right?

In conclusion, I cogitate that success solely relies on hard work.

No, that sounds kind of pretentious and just wrong, as though you looked through a thesaurus to find a synonym. What is wrong with just using “believe”? You wouldn’t use “cogitate” exactly this way either. This word means “to meditate (on)”: https://www.merriam-webster.com/dictionary/cogitate - you would use this to describe thinking about something deeply and intently. Not to describe something you think or know to be true. “Cogitating” is more of an active process, and “believing” might be the result of “cogitating”. In any case the word “cogitate” is not very common, and does sound pretentious to me. “Meditate on” or “ponder” are preferable and more common (but still, none of these words are appropriate in this context).

I agree with Mixolydian, "cogitate" sounds pretentious and doesn't fullfil exactly your intention.

I don't know where you have found that word but what about checking the Oxford Thesaurus?

Let me suggest some alternatives

In conclusion, I think that success solely relies on hard work.

In conclusion, I consider that success solely relies on hard work.

In conclusion, I'm of the opinion that success solely relies on hard work.

Firstly, it's pretty rare to use cogitate at all. Using any word related to it, the most common is "cogitation", the action noun for the acting of cogitating.

Second, think has two main senses in English. Most of us native speakers don't even necessarily realise it, but if we learn a language that has separate words for the two, like French, it kind of clicks. In French, their is penser, the active sense of think, where we might say think about, and croire, the stative sense of think, which is closely matched in sense to believe (though clearly with some difference).

Cogitate is a close match to penser, not to croire. It means the act of thinking, pondering, and so on. You might, if you wished to be pretentious, say:

Let me cogitate on that a minute.

You can't say what you want to say. It doesn't make sense.

If you're looking to be the opposite of pretentious, you could say

I reckon that success solely relies on hard work.

As Mixolydian states, cogitate is more about meditation or consideration of something. However, you could use it by rearranging your sentence a bit:

After some cogitation, I conclude that success solely relies on hard work.

This implies that the conclusion was reached after the cogitation.

I think you are trying to suggest that your conclusion is based on some careful consideration. So you might try:
In conclusion, I determine (or have determined) that success solely relies on hard work.

From the OED.

Verb

Ascertain or establish exactly by research or calculation.
‘the inquest is entrusted with the task of determining the cause of death’
with clause ‘the point of our study was to determine what is true, not what is practicable’