TL;DR: It is not possible.

Basically Rust has made it so that the stable version of the compiler will not allow you to use APIs marked unstable.  Looking at the documentation and the code it seems like it should be possible using attributes like #!allow(unstable).  Unfortunately, if you stumble across this attribute and try to use it, you will get the following warning:

warning: unknown 'allow' attribute: 'unstable', #[warn(unknown_lints)] on by default

And of course, the unstable library feature will cause an error:

error: use of unstable library feature 'path_ext': the precise set of methods exposed on this trait may change and some methods may be removed

If you want to call these APIs you must use the Nightly build of the compiler which allows you to opt-in to these features. 

Unfortunately, these unstable APIs are littered throughout the “stable” documentation.  This makes it frustrating to see something you need, only to realize it has been arbitrarily disabled.  Fortunately, since Rust is open source, you can always grab the code for the feature you want and create a “stable” version locally.