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「Vて＋しまう」 to express an action that has taken place unintentionally often with unsatisfactory results (guidetojapanese.org). I have a sentence below and I don't know what the 「しまう」 for.
試験が終わった！今日は飲んじゃおう！（～のんでしまおう）
meaning: Oh, the exam is over! I am going to have a drink!
Sometimes ~んでしまう means some of actions that you do without too much thinking about the responsibility or afterwards. Such as: 飲んでしまう やってしまう いってしまう, etc. This may be quite similar to "unintentional behavior", but it is also slightly different.
In this case rather than expressing that the action is unintentional and perhaps unsatisfactory, in this case it means something like:
"The exam is over! Today, let's drink!"
(Normally I would refrain from drinking today, but since today is the day that we completed the test it's OK to let myself have a little fun and not worry about the result so much)
I found a paper about the Vて+しまう form.
https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/45277/1/15thIlbonyongu_Ms.Isshiki.PDF
本稿では -てしまう の主観的意味として<一掃><遺憾>を挙げる。<一掃> は 動作主体が意志を持って行為を行って負担感などを一掃し、その結果、話し 手が爽快感を感じること を表し、<遺憾>は 動作主体が意志を持って行為を行い、あるいはコントロール不可能な状況下で行為を行い、その結果話し手が残念 な気持ちになること を表すが、これらは両形式に固定的な意味というよりは、 発話状況を含めた文脈によってその都度実現する語用論的意味である。
I think this 一掃(sweep) exactly explain the nuance of しまう。
動作主体が意志を持って行為を行って負担感などを一掃し、その結果、話し手が爽快感を感じることを表す (The agent does something by own will and sweep the sense of burden, as a result the speaker feels a sense of exhilaration.)
