DIFFERENTIATION INTEGRATION
(constants of
integration omitted)
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Derivative |
Function |
Integral |
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Note: Calculus involving trig functions assumes you are working in RADIANS |
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similarly for cos and tan |
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similarly for sin and sec2 |
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Product Rule |
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Integration by parts |
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Quotient Rule |
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Use double angle formula
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Parametric differentiation |
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Use double angle formula
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Chain Rule |
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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. |
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Useful Relation |
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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. More than one method may work; which is the easiest? |
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. 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?Warning: You cannot differentiate or integrate the parts of a product or quotient separately: consider multiplying or dividing out first or using another method.