How to back up music on my iPhone to my laptop?

Before iCloud, I used to never buy music directly on my iPhone from the iTune's app because I could never get it to back up on my laptop. For example, I once decided to buy a few songs through my iPhone, but when I upgraded to a newer phone and transferred all my information to the newer phone (via my computer where the info was stored), I was unable to retrieve the songs I had bought on my old phone.

Fortunately, I didn't seem to have this problem anymore after iCloud was introduced. I hadn't really bought that many songs on my iPhone, but whenever I did, there never seemed to be a problem backing them up on my laptop.

Anyways, for Christmas I received a $20 iTunes gift card from a friend and used it to buy a bunch of songs (about 15 or so) directly from my phone since I was going on a long trip and would have access to my laptop. Now, I'm about to get a new phone because the screen on mine is very damaged and not easily repairable.

Here is my problem (sorry for the boring background details): I'm currently trying to backup the music on my phone to my laptop so I'll have everything on my new phone. I've ran an iCloud backup, so all my photos, contacts, notes, etc. Are covered, but for some reason it will not let me back up my music! I've connected it to my laptop and tried to sync it, but that doesn't work either.

I know I could buy the iTunes Match thing, which I probably will have to do if I can't find another solution, but I'm just confused as to why I've never had this problem before.

Again, sorry for the long backstory, but I wanted to give any details needed. Does anyone have any solutions or ideas as to what is wrong? Any advice is appreciated!

ITunes is not something you have to buy! ITunes is completely free, and you can get it right here: http://www.apple.com/.../download/ You don't need to fill in the email address or any of that, and just press download. As soon as you got it installed and you have it running, plug in your iPod and it will ask you if you want to backup your apple product. Or it might not even ask and just do it for you. Once you're done, you're done!

Itune are free.backup to laptop then transfer to iphone