Is there a book which contains just a bunch of integrals to evaluate? I want to learn new integration techniques and I'm open to other suggestions as to how I can go about learning new techniques. Thank you
One I was put onto by Paul Nahin in his Inside Interesting Integrals is the two-volume compendium of 1921 by Joseph Edwards, A Treatise on the Integral Calculus, with applications, examples and problems. It's in the public domain and is available as two files via the University of Toronto:
There are many PDF worksheets you can find on google that come complete with worked out solutions.
Why buy a book when you have the power of the internet? ;)
A good book which contains various single-variable integration techniques together with many (and I mean many!) exercises that accompany each technique can be found in chapters 4 and 5 of Problems in Mathematical Analysis by B. Demidovich. It is an English translation of a Russian (Soviet) text. For example, Ostrogradsky's method is given which one rarely if ever finds in English language texts but apparently is pretty standard fair in Russian texts.
I am assuming that you have already studied Calculus I, II from a book like Stewart's Calculus or something equivalent. There are a lot of good books out there but here are a few that I have found helpful.
If solving problems is your aim I would suggest: Mathematical Methods by Boas http://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269 This text goes into many mathematical methods for solving problems including lots of tips and tricks for integration.
Or if you are interested in an introduction to integration theory I would suggest: Apostols Calculus http://www.amazon.com/Calculus-Vol-One-Variable-Introduction-Algebra/dp/0471000051 This text develops calculus with Integration as the primary motivation and I have found hidden in the exercises many tricks for integration.
Also, if you are near a used book store always check out older books on Calculus. A lot of times books that came out prior to the 1950's will have methods that our modern education system has found too difficult for mass public education, and you might find something interesting leafing through older texts.
Hope this helps.
Here is a book of advanced integration if you interested
This is more or less the purpose of an integral calculus book. If you own one, there should be exercises in the back. Alternatively, you can google "integral practice problems" and many many problems will come up.