Edit (May 2019)
This is nearly 5 years old question and as one of the commenter mentioned, I have moved on. I don't want to delete it - cause there is a warning against that. So I'm putting this edit.
I know 14.04 has Kernel 3.13 and is supposed to be better at dynamic power management. My problem is the estimated remaining time keeps changing. But on an average I see 5 hours.
On same machine on Linux mint 15 (based off 13.04) I used vgaswitcharoo method and used to get at least 6 hours.
echo OFF > /sys/kernel/debug/vgaswitcheroo/switch
Does not work any more.
I've tried acpi_call method mentioned here : http://www.noobslab.com/2013/10/enable-laptop-mode-and-other-tweaks-to.html Unfortunately my card isn't listed/supported
Also (unsuccessfully) tried : http://www.webupd8.org/2014/04/prevent-your-laptop-from-overheating.html
In case there are card specific suggestions, I have following cards:
$ lspci -nn | grep VGA 00:02.0 VGA compatible controller : Intel Corporation 3rd Gen Core processor Graphics Controller [8086:0166] (rev 09) 01:00.0 VGA compatible controller : Advanced Micro Devices, Inc. [AMD/ATI] Thames [Radeon HD 7500M/7600M Series] [1002:6840] (rev ff)