As you may know, Ubuntu 12.04 Precise Pangolin is still very popular, because it is a LTS (long term support) version. It has support for 5 years, so it is ideal for production computers.

By default Ubuntu 12.04 Precise Pangolin is released with Kernel 3.2, but both the Kernel 3.5 and Kernel 3.8 have been added to the default repositories, in order to help the users easily update their Linux Kernel.
In this article I will show you how to install both Kernel 3.5 and Kernel 3.8 on Ubuntu 12.04 Precise Pangolin, and derivates like Linux Mint 13 Maya and Elementary OS 0.2 Luna, via the default repositories.
How to install Kernel 3.5 on Ubuntu 12.04 Precise Pangolin, Linux Mint 13 Maya and Elementary OS 0.2 Luna:
$ sudo apt-get install linux-image-generic-lts-quantal linux-headers-generic-lts-quantal
How to install Kernel 3.8 on Ubuntu 12.04 Precise Pangolin, Linux Mint 13 Maya and Elementary OS 0.2 Luna:
$ sudo apt-get install linux-image-generic-lts-raring linux-headers-generic-lts-raring
seen on lffl.org