In this part we cover integration. The main focus is on the ability to integrate a given integral, from this then applications follow. We also try to explain what this integral thing is actually about.
If you are using these pages to master the techniques of integration, we recommend the following procedure. First, the mechanics of basic integration methods must be mastered (substitution, integration by parts, partial fractions decomposition). They are explained in the Theory part and can be tried out in Exercises - Basic methods.
When you are sufficiently familiar with the techniques (for instance, you can easily do substitution), it is time to check out the Methods Survey, which is a sort of integration manual. It helps to answer the familiar question: What should I do with the integral I was just given? All methods and a bunch of useful tricks are then shown in detail in Solved Problems, which should be read only after you get some knowledge of integration.
Then it is time to check out Exercises. "Simple" problems are about as easy as those in Exercises - Basic methods, but now you also have to decide on the right method. The problems marked "intermediate" are of the usual difficulty.