I would approach this a different way. I would connect the UX2 analog outputs directly to my speaker inputs (assuming your speakers are external - i.e. not the built-in laptop speakers), not to the computer Line In. You would use standard audio cables that have the required and connectors: 2x1/4" for the UX2 balanced outputs, and whatever you need on the other end to match your speaker inputs. Alternatively you could use one 1/4" stereo plug from the UX2 headphone output to your speakers.  If necessary you can use adapters on one end or the other. Your local electronics store should have everything you need for this.

For recording, you do need to use the USB connection from the UX2 to your computer. Follow the instructions BigChas52 provided earlier to get your signal from the UX2 into Reaper.

The reason I would connect the UX2 outputs directly to the speakers and not to the computer Line In is that the ASIO driver you need to use for recording demands that the same audio device be used for both input and output. As BigChas52 notes, this has to be the UX2 for your purposes. Which means the audio output will be directed to the UX2 as well - not to your computer soundcard. So if your speakers remain connected to your computer soundcard they won't receive the audio.