A question about the term "in a nutshell"?

I asked the question that I wrote below from two Moderators but I could not get any answer. Now I would like to ask it from all people in here. Please help me.

The question is about the term "in a nutshell". Longman Advanced American Dictionary reveals that this phrase is informal. I also searched this term in various websites and, almost, in all of them the phrase have been defined as an informal one. However, my sister (she has got an M.A degree in Applied Linguistic) told me that this sentence is commonly used in academic papers and articles and it is a formal one. I was wandering if you would mind helping me in this respect and I really need to know your views about this term. Is it an informal/formal sentence?

Thanks in advance
Ahmad

I also have had the same question with you for a long time. Some of my teachers say this's an informal phrase and should not be used in academic writing. However, others hold the opposing view. Till now, I haven't find out the answer. In my opinion, the safest way is to disregard it when writing a conclusion :)

I think the term is informal, because we cannot ignore Longman dictionary which is one of the best dictionaries. But, there is still this question that why some academics use this phrase in their articles????