How can I add music to my itunes library from my ipad
iDevices are not and have never been backup devices.
Move or copy the content from the old computer to the new computer.
Sync is one way, computer to iDevice.
The only exception being iTunes purchases.
To transfer purchases, with the device connect, select File > Transfer Purchases.
See Recover your iTunes library from your iPod or iOS device.
Retrieving data ...