Is it possible to put music from my iPhone onto my new computer?

So basically my computer that I had used for iTunes with all of my music on it broke and I got a new one this past Christmas. I want to take pretty much my whole library on my iPhone 4S into the iTunes library on my new computer. Is there a way to do this or am I going to have to be re-downloading all of my music again? Thanks!

PS, my phone and iTunes are all updated to the most up-to-date versions.

Sorry, apple does not support this basic function.
you will have to re-download everything again.

As your other answer has said this is one of the problems with Iphone is that some basic operations available with other smart phones is not supported by apple.
First be careful with Itunes because is sync is set you will transfer to your iphone and if your libraries are empty which they will be then so will your Iphone.
If you google the problem then you will get quite a few solutions none of which I have tried so its up to you.
The only one I have tried is from cnet called imobile. It works but as I understand it is a trial but so far has worked for me a few times.look at the link below and try

http://download.cnet.com/...36709.html

If you have been using or you can use the cloud via your phone and once music is in the cloud, use iTunes on the computer to download. Keep in mind Apple ONLY handles music purchased via iTunes store. So if you have music from other sources it may NOT load to the cloud. (Check the information about what will be loaded to the cloud to be certain.)

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