Nahin, a prolific writer of popular and semi-poplular books on math and engineering, authored Inside Interesting Integrals which was published a couple of weeks ago. The book is a collection of methods for finding closed form solutions of definite integrals, a once lively area of math that fell into obscurity around 1900. Due to the advent of symbolic computational math a couple of decades ago, this area as well as the solution of indefinite integrals has seen a revival. I have not read this book but it is on my list as well as a related book Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals.
The entire preface and table of contents can be found here (pdf file).
Addendum: The link above is dead.
Addendum 2: I wrote a four part review by example of Nahin’s book: