If you want to refer to sections of Survey of integrating methods while working the exercises, you can click here and it will appear in a separate full-size window. Similarly, here we offer Theory - Integration.
Note: Problems marked "basic methods" and "simple" are of similar difficulty. The ones from basic methods are for initial practicing of techniques. The aim is not to solve the integrals, but just do the specified step. The "simple" problems are genuine, you are supposed not only to solve them, but most of all decide on the right approach.
Both simple and intermediate integrals can be considered "normal" integrals and a student should be able to handle them. The difference is that the simple integrals have one-step solutions, which makes them ideal for practicing basic integration techniques; also their hints are more detailed.
"Tough integrals" include integrals with a standard solution that happens to be longer and/or more difficult to actually do. There are also integrals that may have an easy or a short solution - provided you have the right idea; these would be "tricky" integrals that don't exactly fit any "box".