Having worked at a successful sales tax startup, I can tell you "it depends". Local laws vary on whether you calculate sales tax at the line item or invoice level. For some discussion on the topic see:
I can also tell you that US sales tax is extremely complicated. There are over 10,000 jurisdictions that can levy a tax (state, county, city, and special districts such as stadium districts, metropolitan transport districts, water districts, etc.). The boundaries of those districts are not well defined an a readily available public source, and certainly do not conform to ZIP code boundaries.
If you want to get it right, your best bet is to use a sales tax calculation service. There are several SAAS solutions that are well-suited for web apps.