1. How can I remember all of the formulae for integrating and differentiating trig functions?
Luckily, nowadays, you will be given the formulae for the differentiation of the six basic trig. functions.
Using anti-differentiation you should be able to find the integrals of most of these functions although you may have to use trig. identities to help you in some cases.
2. Do I have to be able to integrate the product of two trig functions such as sin 2x and cos 5x?
Yes, the integration of the product of trig. functions is in most high school prescriptions.
