This detailed guide is taken from http://askubuntu.com/questions/205112/how-do-i-get-amd-intel-hybrid-graphics-drivers-to-work. Thanks a lot for finding the solution.
Let’s install all the required packages
sudo apt-get install build-essential cdbs fakeroot dh-make debhelper debconf libstdc++6
sudo apt-get install dkms libqtgui4 wget execstack libelfg0 dh-modaliases
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sudo apt-get install linux-headers-generic xserver-xorg-core libgcc1
Being VPCSB1V9E a 64bits system, the following steps are also required:
sudo apt-get install ia32-libs lib32gcc1 libc6-i386
cd /usr ; sudo ln -svT lib /usr/lib64
The following deb packages have to be downloaded from the links
http://www.mirrorservice.org/sites/archive.ubuntu.com/ubuntu//pool/main/u/udev/libudev0_175-0ubuntu13_amd64.deb
https://docs.google.com/file/d/0B0tTaH4qTIIXdDF3NThFWUtrYlU/edit?usp=sharing
Next step consists in the removal of old intel and fglrx drivers
sudo apt-get remove fglrx*
sudo apt-get remove xserver-xorg-video-intel
and the installation of previously downloaded deb files
sudo dpkg -i libudev*
sudo dpkg -i xserver-xorg-video-intel_2.21.6-0ubuntu4_amd64.deb
The xserver driver have to be prevented from any upgrade with the following command
sudo apt-mark hold xserver-xorg-video-intel
Eventually we are ready for the installation of the ATI Catalysts driver (13.4); we have to download the zip file from the official website: www.amd.com/drivers, and then run the executable to build a deb package and to install it
sudo sh ./amd-catalyst-XX.X-linux-x86.x86_64.run --buildpkg Ubuntu/raring
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sudo dpkg -i fglrx*.deb
There are at the end few post-installation steps to be executed:
sudo mv /etc/X11/xorg.conf /etc/X11/xorg.conf.backup (if present)
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sudo aticonfig --initial -f
Then, to switch to the discrete (ATI HD6470) gpu, you need to execute the following command
sudo aticonfig --px-dgpu
and then reboot the computer. Once started it again, it should use the ATI gpu. To switch back to the integrated one (INTEL HD3000), run the following command
sudo aticonfig --px-igpu
and reboot again