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FM Ciclo 2023 - 2024 Alumno:
D,(a) = 0 D,(u) =1 D,(utvtw)=du+dvtdw D,(a:u) =a-du D,(u:v) =u:dv+v-du uy v-du—u-dv i 2 v v D,(u") = nut + du uy du D.(=z ; aE ay —a-du BIG Ds () ~ we a > D,.(u) = S (WH) nVurt = du ra D,(Ln u) = — u D,(a") = a“ + du-Ln|a| D,(e") = e" + du D,(w”) = (vu? + du) +Ln |u| + (u? « dv) loge D,,(log u) = a du D,(Senu) = Cosu-du D,.(Cos u) = —Senu: du D,(Tanu) =Sec? u+ du D,(Cot u) = —Csc? u+ du D,(Secu) = Secu: Tanu:du D,(Cscu) = —Cscu-Cotu-du du v1 2 D,(Arc Senu) = D,(Arc Cos u) = d D,(Arc Tanu) = Taw —du D,.(Arc Cot u) = Tae D, (Are Cse u) = re Csc u) = ———— * uvu2 —1 du D,.(Arc Sec u) = ——= uvu2 —1 D,(Senhu) = Coshu: du D,(Coshu) = Senhu: du D,(Tanhu) = Senh?u: du J senu-du= —Cosut+C | cosu:du=Senu+¢ [ sectu:du=Tanw¢ [tan + du =—Ln|Cos u| +C = Ln|Secu|+C i Cotu :du=Ln|Senu|+C f(x + Ax) — f(x) Ax [ secu-du=1n |Secu+Tanu| +C | csew-du = Ln|Cscu— Cot ul +C [ ¢sctu:du=—Cotu+¢ J Secu-Tanw:du = Secut+C J cscw:Cotu-du=~Cscw ¢ Js Zu d 1 ty 2u+C en*u-du = u——Sen2u 2 4 1 1 | costu-du=Fut 3 Sen2u 6 du 1 u | an gare Tan“ atw a a _ 1. ua 3 yqla | 1 po u [Vem au = Fee a +— 2 u J. wta?-du=> uw +a? eZ in(u sy wea) +C [ul =—ArcSec—+C a a b b Area = [> dx Volumen = a) yd la a b Trabajo Mec.=W ={ F(x)dx la iG ch b Long.de Arco = S = i vI+ > Area Sup. de Rev.= anf yvit+ x x)? dy ly poy mt va? — uw? hagase u = aSenz,NI aCosz va? + u? hagase u = aTanz,NI aSecz yu? — a? hagase u = aSecz,NI aTanz fau=wee | adu=af du (du tdv +dw) =fdutfdv+fdwsc nth ™ du = +C -1 Je ene (me —1) fevau =e"+C du [Geintulre u at “du=——+¢ Je “= Inlal & & 2 = 5 2 6 2 a Integral por partes [udv= wf vau Preparatoria 20-30 Albert Einstein FH Ciclo 2023 - 2024 Alumna: 
