I have got to do sth.与I have to do sth.是同样的意思,不得不做某事.
口语中经常使用I've got to do sth.的说法,一般不怎么使用正式的I have to do sth.书面语一般用I have to do sth.
e.g.I've got to do some shopping now.我得去购物了.
至于include的意思,是包括 包含 使成为...的一部分,
你的这个句子中include的用法似乎没见过,可能你记错了,也可能是口语中的说法,我不太清楚.include的例句:
You should include some examples in your passage.你应该在文章里举一些例子.
We all went to see the show,me included.我们都去看表演了,连我在内.
这句话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.