It is worth noting that the latest edition now INCLUDES a fully-searchable CD-ROM version of the book. It is amazing how many practical functions actually have closed-form integrals. You will still need to transform a lot of things, but that's just one of the humdrum parts of your job that needs done.
Gradshteyn and Ryzhik is the authoritative mathematical table book. If you want to get a grasp on how special functions relate to each other, and analytic approximations to understand systems, this is a great resource.