I have got to do sth.與I have to do sth.是同樣的意思,不得不做某事.
口語中經(jīng)常使用I've got to do sth.的說法,一般不怎么使用正式的I have to do sth.書面語一般用I have to do sth.
e.g.I've got to do some shopping now.我得去購物了.
至于include的意思,是包括 包含 使成為...的一部分,
你的這個句子中include的用法似乎沒見過,可能你記錯了,也可能是口語中的說法,我不太清楚.include的例句：
You should include some examples in your passage.你應(yīng)該在文章里舉一些例子.
We all went to see the show,me included.我們都去看表演了,連我在內(nèi).
這句話就是我我得花些精力include新朋友了,可能是多交朋友的意思吧.