I'm a physics student with interests in mathematics and enjoy doing integrals by hand. I have been looking for a workbook or place with lists of difficult integrals I can try and do for practice. I am hoping for integrals with trig substitutions, Fourier transformations, complex analysis, integration by parts, differentiating under the integral, etc. I need practice in advanced techniques in integration and am looking for a book or place with lists of integrals that will allow me to practice.
Take a look at the following:
Inside Interesting Integrals: A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and ..., by Paul J. Nahin. ISBN-13: 978-1493912766
Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, by George Boros. ISBN-13: 978-0521796361
I prefer Thomas Calculus by George V Thomas, Pearson Publications. I suggest its 11'th edition ( Now 12'th edition available ).The book provide a vast number of solved problems and hundreds of exercise questions (Answer keys also available ).These are the section I found, which will help you.
- CHAPTER 5--INTEGRATION
- CHAPTER 6--APPLICATIONS OF DEFINITE INTEGRALS
- CHAPTER 8--TECHNIQUES OF INTEGRATION
- CHAPTER 9--FURTHER APPLICATIONS OF INTEGRATION
- CHAPTER 15--MULTIPLE INTEGRALS
- CHAPTER 16--INTEGRATION IN VECTOR FIELDS