No chainRule No Product Rule No Quotient Rule we have learned Infgrationbylarts indefinite integral definite integral Solve by u substitution NEW solve by by parts There are two methods to find integration U sub by parts looks like chain rule looks like product rule FormulaG Sadr ur Sud ex Sxe dx U du dx dr e dx V ex ex Se dx Xe MSxe dx U du dx du e dx 2 ex Sx 5 8d du du 1 518dx v 41 519 5 9d 4 1 51 to1 5 4 1 5 gxxtf to xt5f C 1 2 1 2 e 2 e e dx 2 to 212 4ef ext Sx lnxdx u du Inx dv Rdx dx V X hx 3dx b Rdx 3 3 6 3 3 hx 3 3 nx 31 4 460 ex Sx Inxdx dv x dx U Inx 6 6 dx du 1 6 dx 6 6 nx t Sx5d 6 6 nx xd nx b 6 6 tC t intId ex f HxPe dx e d u Ze du eY1tx Scitx e dx 2 HX dx HR dv It e e Itx e Y1txf Hx e Hx e f 1Hxe I Se dx Ie C e ex FI dx u x du dx du XD dx v 31 17 3 1 17 381 1 dx 3 1 1 3 1 11 3 1 11 41 116 C ex See dx 4 X du 2xdx 2 dv dx v e fox dx u bx du 6dx f dx dy If 2 53 25 e 21 3 2 8 2 dx
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