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 sec^{2} 

_{} 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.