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1001_5.2_Lab_22

# 1001_5.2_Lab_22 - CALCULUS 1 LAB 22 NAME_PARTNER 5.2...

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CALCULUS 1 LAB 22 NAME: ___________________PARTNER: _________________ 5.2 Integration of Indefinite Integrals GSA: ______________________Lab Time: ____________ Replace u by x to have Table 5.2.1 on page 324. See also page 489 and the inside book front cover. Linearity property: cf ( u ) " du = c f ( u ) dx " [ f ( u ) ± g ( u )] " du = f ( u ) du ± g ( u ) du " " Differentials: Indefinite Integrals: 1. d [ u ] = du 1. du " = u + C , dx " = x + C , dt " = t + C , dF " = F + C 2. d u n + 1 n + 1 " # \$ % & ' = u n 2. u n " du = d u n + 1 n + 1 # \$ % & ' ( = " u n + 1 n + 1 + C 3. du u u d ) cos( )] [sin( = 3. cos( u ) " du = d [sin( u )] " = sin( u ) + C 4. du u u d ) sin( )] [cos( ! = 4. sin( u ) " du = d [ # cos( u ) " ] = # cos( u ) + C 5. du u u d ) ( sec )] [tan( 2 = 5. sec 2 ( u ) " du = d [tan( u ) " ] = tan( u ) + C 6. )] [cot( u d = du u ) ( csc 2 ! 6. csc 2 ( u ) " du = d [ # cot( u ) " ] = # cot( u ) + C 7. )] [sec( u d = du u u ) tan( ) sec( 7. sec( u )tan( u ) " du = d [sec( u ) " ] = sec( u ) + C 8. )] [csc( u d = du u u ) cot( ) csc( ! 8. csc( u )cot( u ) " du = d [ # csc( u ) " ] = # csc( u ) + C 9. du e e d u u = ] [ 9. e u " du = d [ e u ] " = e u + C 10. du b b b d u u = )] ln( / [ 10. b u " du = d [ b u /ln( b )] " = b u ln( b ) + C 11. d [ln( u )] = 1 u du 11. 1 u " du = d [ln( u )] = " ln( u ) + C 12. d [sin " 1 ( u )] = 1 1 " u 2 du 12. 1 1 " u 2 # du = d [sin " 1 ( u )] = # sin " 1 ( u ) + C 13. d [tan " 1 ( u )] = 1 1 + u 2 du 13. 1 1 + u 2 " du = d [tan # 1 ( u )] = " tan # 1 ( u ) + C 14. d [sec " 1 ( u )] = 1 u u 2 " 1 du 14. 1 u u 2 " 1 # du = d [sec " 1 ( u )] = # sec " 1 ( u ) + C At first, we have some examples where simple formulas in terms of x can be used. By the next lab, we will need to use and KNOW the formulas in terms of u in the above right column.

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