Counting different words in text using hashing
If you really just want to count the number of distinct words in the document, you don't need to save each instance of the word to the hash table.

So, if you find a words that's already in the table, just don't add it there. This means you don't have to deal with chaining as often, which will speed things up.

But you still have to deal with collisions, because two different words can have the same hash code.

This way, the expected time complexity is $\mathcal{O}(n)$, where $n$ is the total count of characters in the text, assuming a good hash function.