How to put non purchased music from iPhone to my computer?

So my harddrive died and I have to get it replaced. The majority of the music on my phone is downloaded off the Internet mostly from YouTube to mp3 but some are from livemixtapes and other sites. Is their anyway to put these onto my iTunes once I get it redownloaded in a couple of days or will it not work because the mp3 tracks are not in my music on my computer. Or is there a way I can put them straight into my my music from my phone

Add Music to iTunes
1. Open the iTunes software.
2. Click on "File" at the top of iTunes, and the "File Menu" opens.
3. Select "Add File to Library" in the "File Menu." A window labeled "Add to Library" opens.
4. Press and hold "CTRL" on the keyboard (the "Command" key if using a Mac). Then, click the non-iTunes music in the window that you're putting on the iPhone.
5. Click "Open" in the "Add to Library" window. The music is added to iTunes. Change iPhone Sync Settings
6. Connect your iPhone to the computer via the iPhone's USB cable.
7. Click the iPhone's name or the word "iPhone" on the left side of iTunes.
8. Click "Summary" in the middle panel of the program.
9. Click the box next to the iPhone setting that reads "Manually Manage Music and Videos," near the bottom of the middle iTunes panel. The box becomes checked.
10. Click the "Apply" option at the bottom of the program to change the iPhone sync setting. You can now add single songs to the iPhone from iTunes. Add Music to iPhone
11. Click the "Music" heading located under the "Library" category on the left part of iTunes. All of the iTunes music becomes visible in the middle iTunes panel.
12. Press and hold "CTRL" on the keyboard (the "Command" key if using a Mac).
13. Click every iTunes song in the middle iTunes panel that you're putting onto the iPhone.
14. Drag the chosen songs to the iPhone name or iPhone word on the left part of iTunes. The music is added to your iPhone.

You can find some iPhone transfer to transfer your music from iPhone to pc, then add them to iTunes. There are lots of iPhone transfer. Some of them are free. Just find one you like, they can do it with ease. I'm using free iPhone transfer Syncios to do it. Follow the steps:

1. Download and install Syncios on your pc.
2. Connect your iPhone with pc.
3. With Syncios, transfer music from iphone to pc. Then add them to itunes according to your need.

This tutorial may be helpful for you.
http://www.syncios.com/how-to-transfer-music-from-iphone-4s-to-computer.html

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