If you prefer using other search tools, such as Google, Firefox or Yahoo, there's currently no easy way to make Cortana access them without disabling the AI. Microsoft claims this is so Cortana can deliver personalized search results in an end-to-end environment. It's also required to default to the company's preferred browser, Microsoft Edge.
However, for searching the web, Cortana is hardwired to search using Microsoft's own search engine, Bing. It works with voice commands or as you type.
