The question I was given is
I want to say
I feel that learning Chinese isn't easy, but I can do it.
So far, I've written
but I'm not sure if I should use “可以”，“会”，or “能”.
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In this setting, I would go for:
I think studying Chinese is not easy, but I can do it.
It's a variant on the standard phrase 你能做到的 = "you can do it!" (example sentences), which is encountered regularly.
CC-CEDICT: 做到 (zuòdào) to accomplish / to achieve
You've already said 学 once, so it's somewhat repetitive to say it a second time.
会 = would
能 = able to; can
可以 = willing to; allowed to; can
Both 能 and 可以 can be translated as "can" but "can" itself has different implications.
我觉得学汉语不容易，但是我 （会）学。 I think learning Chinese is not easy, but I (will) learn it -- I will learn it despite the difficulty
我觉得学汉语不容易，但是我 （能）学。 I think learning Chinese is not easy, but I (can) learn it -- I have the ability to overcome the difficulty
我觉得学汉语不容易，但是我 （可以）学。 I think learning Chinese is not easy, but I (can) learn it -- I am willing to learn it
我会幫你修理電脑 - I will repair your computer
我是有执照的电脑维修工, 我能幫你修理電脑 - I am a licensed computer repairman, I can repair your computer (I have the ability)
我是有执照的电脑维修工, 我可以幫你修理電脑 - I am a licensed computer repairman, I can repair your computer (I am allowed/ I have the ability)
To be honest, you can use all these words:
But these words has its own suitable context and indicates different desires. You can try to expand the original sentences, which may help for your understanding. let me show you how to expanding it:
First of all,
我觉得学汉语不容易 shows that learning Chinese is not easy.
但是我会学 shows that you will do it.
会 may have two kinds of meanings:
You will spend your time and effort to do(learn) it, in Chinese is
You have the ability to learn it, which describes you are confident with your self-teaching ability, which in Chinese is
但是我可以学 shows that you can do it, you just won't right now, but you can spend time and effort to learn it, which in Chinese is
但是我能学 shows that you are able to do it, it indicates that you have the confidence to learn it, which in Chinese is
This is my sentence expanding, hoping it can help you understanding.
I'll not explain the meanings, only what each word feels to me as a native speaker.
I would suggest use 但我能办得到 for "but I can do it"
I can learn.
I will learn, but if someone says
I can learn by myself, do not need you to teach me.), the
be able to) here, is identical to
我会做某事 can be translated to either
I can do something or
I will do something in different contexts.
Maybe it is not a problem with usage of "会/能/可以". As a native speaker, I think that it may be much more coherent if you make it explicit whether you are expressing confidence or stating facts. For instance, translating "I feel that learning Chinese isn't easy, but I can do it", my first thoughts are:
All the three sound fine to me: "I feel that learning Chinese isn't easy, but I believe that I can do it."
The difference between translations with "我相信" and those without is that listeners will tend to interpret the latter ones as facts, which may confuse people since you are expressing your confidence.
Also, as is explained by Tang Ho, "可以" expresses your willingness to do something. I want to add a bit to the common phrase "但我可以".
"但我可以……" is very much used to offer a way to compensate for some inability. I feel "我觉得学汉语不容易，但是我可以学" is a bit strange, since I am expecting, for example, "我不会说汉语，但我可以学" (I cannot speak Chinese (the inability), but I am willing to learn (to try to compensate for my inability)).
你觉得学汉语怎么样？- How you feel study Chinese?
会 means "will"; 能 and 可以 both mean "can/able". The choice of which word to use is indicated in the sentences below:
我觉得学汉语不容易，但是我会努力的去学。- It's not easy, but I'll put up the effort to learn.
我觉得学汉语不容易，但是我能堅持的學下去。- It's not easy, but I can continue on learning.
我觉得学汉语不容易，但是我可以慢慢的学。- It's not easy, but I can slowly learn.
Note the compliment word/phrase associated with 会, 能, and 可以.
First of all, I do not think "你觉得学汉语怎么样？" is what I would hear from a native (mainland) mandarin speakers intending to say "do you feel learning Chinese easy?" I would say "你觉得汉语好学吗？" for such meaning. I may hear "你觉得学汉语怎么样？" or "你觉得选(学)汉语怎么样？" for the intended meaning of "What do you think about choosing Chinese to learn".
Secondly, regarding the first half of your proposed answer "我觉得学汉语不容易，但是我 （会/能/可以）学。", it's different from "我觉得学好汉语不容易" or "我觉得学会汉语不容易". The former "学汉语" means "learn", while the latter "学会汉语/学好汉语" means "grasp/master/know well". The difference is similar to the difference between "look/see" or "listen/hear". (is there any such "learn/?" pair in English?)
So the natural conversion will be like:
What do you think about choosing to learn Chinese? -- I think learning Chinese is not easy, but I will take/choose/learn Chinese (anyway).
Do you feel learning/mastering Chinese easy? -- I do not think so, but I believe I can learn it.
For the first case, "能" is not appropriate, since there is not a goal to achieve. Depending on the context, you may use "可以" in this case, but it has a different emphasis/implication (in the sense of may/may not).
For the second case, you may replace "能" by "会" with similar meaning, but using "能" is more clear. Here "会" means "will", and strictly speaking, you cannot tell for sure whether you "will" learn Chinese well or "will not", but you probably can still use "will" to indicate that's your belief. Using "可以" in this case is probably ok, in the sense of "will" showing your belief, but it's probably even less appropriate than "会".
So in summary, you were probably asking about case 2) above, and in this case, all of 能/会/可以 probably will deliver the intended meaning but "能" is probably the best with the least ambiguity.