This free online calculus 2 (multivariable calculus) course teaches several methods of single, double, triple, and numerical integration. The course is currently under development and will consist of around 50 video tutorials which cover the material of a typical multivariable calculus course (calculus II) at the university level.
In order to gain a comprehensive understanding of the subject, you should start at the top and work your way down the list. That way you will start learning the most basic concepts first and build off of those as you progress through the course.
The table of integrals and trigonometric identities from the videos is here.