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For Mozilla Firefox, several translator addons/plugins exist ; a popular one is Google Translator for Firefox by nobzol which can be used to translate highlighted text using the Google Translate service or entire pages via the icon it installs on the menu bar. This tool can also be used by using the contextual menus via the mouse. Another useful one is ImTranslator for Firefox  which can translate selected portions of selected text on a webpage using Google Translate or Microsoft translate or entire webpages with Google Translate.

If you're looking for a browser plugin that uses Microsoft Translate service, Microsoft has a cross-browser plugin called "Translator bookmarklet" at http://labs.microsofttranslator.com/bookmarklet/ which translates a webpage in place without leaving the page. Works in Mozilla Firefox, Google Chrome and Internet Explorer.

Microsoft Edge

Microsoft has Translator for Microsoft Edge

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