DIFFERENTIATION                                                                               INTEGRATION

                                                                                                                                 (constants of integration omitted)




















Note: Calculus involving trig functions assumes you are working in RADIANS




similarly for cos and tan


similarly for sin and sec2



Product Rule

Integration by parts

Quotient Rule



Use double angle formula


Parametric differentiation




Use double angle formula

Chain Rule

Method of substitution: 1. substitute for dx in terms of du

2. substitute for x in terms of u 3. change limits to u

Always look for simplifications before the next stage.



Useful Relation


General method: 1.  Is it a standard integral? 2.  Is it a reverse chain rule?(can you spot a function and its derivative?) 3. Can you split it up into two or more easier integrals? e.g. . 4 Can you use partial fractions? 5. Can you use a trig formula? 6. Can you do it by parts? 7. Can you use a substitution?

More than one method may work; which is the easiest?

Warning: You cannot differentiate or integrate the parts of a product or quotient separately: consider multiplying or dividing out first or using another method.