well,let me tell the answer simply: 毕竟_when you have no way out,this word is ok. 究竟 _when you are confused,you can use this word. 归根结底_when you have stated a lot,and you want to make an with a conclusion,use this

I feel i'm really stupid after all!---- 归根结底，我还是很笨！--- to interpret the english sentence into chinese, better not literally translate the phrase' i feel', or , such as 归根结底，我还是觉得我很笨，it may seem not so chinese. and more worse--- though the above chinese sentence is perfectly correct in grammar, while confusing or odd in meaning, because the 归根结底 in meaning refers to the 很笨， but if we speak verbally 我觉得，the hearers or readers may very likely refer 归根结底 to 我觉得。 a really idiomatical expression to convey the meaning of the english sentence above mentioned is to say 我觉得我真的很笨/真是很笨。 as for the differences between the 3 chinese words, please let their usage speaks for it: 毕竟after all, all in all, when all goes to all------- 她虽然很爱他，可还是嫁给了另一个男人，毕竟他们之间的年龄差距太大了。 究竟 (as an adverb) after all, in the end, finally./in the world/ what,how...ever/ the hell 他究竟是爱我呢， 还是恨我呢？ 你究竟想干什么？（in this sense, 到底is more common than 究竟） 你他妈到底去不去？不去老子宰了你！ 究竟（as a noun) result, outcome/ essence, root, origion 他好奇心很强，对这样的现象总要问个究竟。 归根结底after all,untimately, in the last analysis (note: this idiom is mostly used to modify a whole sentence, and usually come at the first of it). When you use this phrase, you are drawing a conlusion and talking about the ultimate causes, sourses, substance etc. 归根结底，她还是个女人，所以尽管她对自己说：“不要爱他！”但是对于这么一个风度翩翩，又懂女人心的男人，她那平静了很多年的心，也不由得开始摇荡起来了。|| 归根到底，我们还是要到语言内部去找原因，否则很难说明这种现象。

hey i got what you want i Ialways thought I was pretty clever)It turns out Im stupid after all or It seems/would appear Im stupid after all. you should say that like below that makes you more chinese 我一直认为我很聪明，（其实），我不是的我很笨 so 其实 is that you should use in that sentence you mentioned however,if you say 毕竟 in that sentence ,might we chinese understand what you wanna express but it feels something strange it is not as chinese to say chinese secondly ,whats the differance between 毕竟, 究竟 and 归根结底 your friend Polyz explains those very cleverly if any something comfusing ,ok ,take it to me ,[email protected] call me linus

Meanings: 毕竟【bìjìng】 <adv.> after all; all in all; when all is said and done; in the final analysis. 究竟【jiūjìng】 outcome; what actually happened; <adv.> actually; exactly; after all; in the end. 归根结底 chase to the root cause, originally

Ah..it is hard to explain...the differences between them are delicate...and it is really hard to you to undersrand.But when we want to say after all,we use毕竟 often.归根结底...this idiom,you can consider it as.. in the final analysis,it stresses result. ><...Hope it can help.