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Unformatted text preview: 7 TECHNIQUES OF INTEGRATION TECHNIQUES OF INTEGRATION As we have seen, integration is more challenging than differentiation. In finding the derivative of a function, it is obvious which differentiation formula we should apply. However, it may not be obvious which technique we should use to integrate a given function. TECHNIQUES OF INTEGRATION Until now, individual techniques have been applied in each section. For instance, we usually used: Substitution in Exercises 5.5 Integration by parts in Exercises 7.1 Partial fractions in Exercises 7.4 TECHNIQUES OF INTEGRATION 7.5 Strategy for Integration In this section, we will learn about: The techniques to evaluate miscellaneous integrals. TECHNIQUES OF INTEGRATION STRATEGY FOR INTEGRATION In this section, we present a collection of miscellaneous integrals in random order. The main challenge is to recognize which technique or formula to use. STRATEGY FOR INTEGRATION No hard and fast rules can be given as to which method applies in a given situation. However, we give some advice on strategy that you may find useful. STRATEGY FOR INTEGRATION A prerequisite for strategy selection is a knowledge of the basic integration formulas. STRATEGY FOR INTEGRATION In the upcoming table, we have collected: The integrals from our previous list Several additional formulas we have learned in this chapter Most should be memorized. It is useful to know them all. However, the ones marked with an asterisk need not be memorizedthey are easily derived. STRATEGY FOR INTEGRATION TABLE OF INTEGRATION FORMULAS 1 1 1. ( 1) 2. ln   1 3. 4. ln + = = + = = n n x x x x x x dx n dx x n x a e dx e a dx a TABLE OF INTEGRATION FORMULAS 2 2 5. sin cos 6. cos sin 7. sec tan 8. csc cot 9. sec tan sec 10. csc cot csc 11. sec ln sec tan 12. csc ln csc cot xdx x xdx x x dx x x dx x x xdx x x x dx x xdx x x xdx x x =  = = =  = =  = + = 1 1 2 2 2 2 13. tan ln sec 14. cot ln sin 15. sinh cosh 16. cosh sinh 1 17. tan 18. sin x dx x x dx x x dx x x dx x dx x dx x x a a a a a x = = = = = = +  TABLE OF INTEGRATION FORMULAS Formula 19 can be avoided by using partial fractions....
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 Fall '11
 AlanS.Grave
 Derivative

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