It's fairly limited right now, but SwiftKey will allow you to search the web without leaving what you're typing.
Microsoft's SwiftKey keyboard on Android is getting some added functionality, with integrated Bing search implemented into the latest beta version of the application. Anyone can download it from the Play Store right now and take it for a spin.
In the bar above the word suggestions now you'll see a small search box on the left-hand side which, when tapped, pops out and allows you to perform a Bing search. It doesn't matter which app you're currently in as you won't have to leave it.
Full story from the WindowsCentral blog...
Facebook
Twitter
Instagram