How to transfer my music library from my iPhone to my Laptop?

Hi, my laptop broke and had to re-formatted, again. On it I had all of music which is the first time its ever been on one computer with no back up.
I have 4, 807 songs on my iPhone, but only 532 bought through iTunes, most have been through CDs (no longer with me) with a couple of cheeky Youtube conversions.
How am I able to transfer these songs on my iPhone onto my laptop? I've been trying for a few hours, and all I've managed to do is copy a word document listing all the songs onto my laptop.
Any help would be greatly appreciated!

You can't. One of the greater reasons why you shouldn't get an iPhone! I mean you can plug it into your computer and play the songs off of iTunes but that's basically it!

You can't transfer any music that hasn't been bought on iTunes. If you sync your iPhone to your laptop, it will wipe off your music.

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