DIFFERENTIATION                                                                               INTEGRATION

(constants of integration omitted)

 Function Derivative Function Integral 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.