For me, the first one is much more natural. I don't think that 'You must learn things that make you happy no matter what is going on in your life right now.' sounds very natural. I don't believe that any native speaker would use 'must' in this situation. It sounds awkward and formal, and is out of keeping with the rest of the sentence - 'going on in your life right now - which is relatively informal. By contrast, 'You've got learn things that make you happy no matter what is going on in your life right now', flows much better. The register (level of formality) is consistent throughout the sentence. In my view, this is definitely the more authentic native-speaker sentence.

I would rewrite the sentence, "You must learn to do things that make you happy no matter what is going on in your life right now". I would not use "You have got...". Apparently in BrE it can be used, but in AmE, it's considered poor grammar. We use it in America yes, but it is grammatically incorrect. I'm including two websites that address this issue. There are four (if I remember correctly), grammatically approved ways to use 'got', but when using it as 'have' or as an action verb, in AmE, no. http://www.englishteachermelanie.com/grammar-have-or-have-got/ http://english.stackexchange.com/questions/5531/difference-between-i-have-got-and-i-have-gotten

They are both correct! Each sentence gives off a little bit of a different feeling, and which sentence you would choose to use would be based on the situation I suppose. Saying "you've got to learn" is more suggestive, depending on how you emphasize. Saying "you must learn" is more demanding. For all intents and purposes they mean the same thing, and you wouldn't be wrong choosing one over the other. :)

In the first sentence, I meant to write, "You've got to learn....."