Regras de Integração Completa (2)

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REGRAS DE DERIVAÇÃO E INTEGRAÇÃO 
Sejam u e v funções deriváveis De x e n as constantes
	
	Função
	Derivada
	
	
	
	R1
	Y=c
	Y’= 0
	
	
	
	R2
	Y=x
	Y’=1
	
	
	
	R3
	Y=ax+b
	Y’= a
	
	
	
	R4
	Y=u+v
	Y=u’+ v’
	
	
	
	R5
	Y=u.v
	Y’= u’.v + u.v’
	
	
	
	R6
	Y=
	Y’= 
	
	
	
	R7
	Y=un y=xn
	Y’= n.un-1.u’ y=n.xn-1
	
	
	
	R8
	Y=au
	Y’= au.lna.u’
	
	
	
	R9
	Y=eu y=ex
	Y’= eu.u’ y’ = ex
	
	
	
	R10
	Y=
	Y’= 
	
	
	
	R11
	Y=ln u
	Y’= 
	
	
	
	R12
	Y=uv
	Y’= v.uv-1 + uv. ln u .v’
	
	
	
	R13
	Y=sen u
	Y’= u’.cos u
	
	
	
	R14
	Y= cos u
	Y’= - u’.sen u
	
	
	
	R15
	Y = tg u
	Y’= u’. sec2u
	
	
	
	R16
	Y= cot u
	Y’= -u’. csc2 u
	
	
	
	R17
	Y= sec u
	Y’= u’.sec u . tg u
	
	
	
	R18
	Y= csc u
	Y’= -u’.csc u . ctg u
	
	
	
	R19
	Y= arc sen u
	Y’= 
	
	
	
	R20
	Y= arc cos u
	Y’= 
	
	
	
	R21
	Y= arc tg u
	Y’= 
	
	
	
	R22
	Y= arc ctg u
	Y’= 
	
	
	
	R23
	Y=arc sec u
	Y’= 
	
	
	
	R24
	Y= arc csc u
	Y’= 
	
	
	
�
REGRAS DE DERIVAÇÃO E INTEGRAÇÃO Sejam u e v funções deriváveis de x e n as constantes.
	
	Função
	Integral
	
	Função
	Integral 
	R1
	
	dx+c
	R20
	
�� EMBED Equation.3 
	
+C
	R2
	
a dx
	ax + c
	R21
	
	
	R3
	
xn
	
	R22
	
	
	R4
	
�� EMBED Equation.3 
	ln
 + c
	R23
	
	
	R5
	
audu
	
	R24
	
	
	R6
	
eudu
	eu + c
	R25
	
	
	R7
	
senu du
	-cos u + c
	R26
	
	
	R8
	
cos u du
	sen u + c
	R27
	
	
	R9
	
tg u du
	ln sec u + c
	R28
	
	
	R10
	
co tg u du
	ln sen u + c
	R29
	
	
	R11
	
sec u du
	Ln (secu + tgu) +C
	R30
	
	
	R12
	
sec2 u du
	tgu + c
	R31
	
	
	R13
	
csc u du
	ln (cscu – cotgu)+C
	R32
	
	
	R14
	
csc2 u du
	-ctg u + c
	R33
	
	
	R15
	
sec u . tg u du
	sec u + c
	R34
	
	
	R16
	
cscu.ctgu du
	-csc u + c
	R35
	
�� EMBED Equation.DSMT4 
	
	R17
	
eax 
	
	R36
	
	
	R18
	
ln(ax)dx
	
	R37
	
	
	R19
	
�� EMBED Equation.3 
	
	R38
	
	
	R39
	
	
	R59
	
	
	R40
	
	
	R60
	
	
	R41
	
	
	R61
	
	
	R42
	
	
	R62
	
	
	R43
	
	
	R63
	
	
	R44
	
	
	R64
	
	
	R45
	
	
	R65
	
	
	R46
	
	
	R66
	
	
	R47
	
	
	R67
	
	
	R48
	
	
	R68
	
	
	R49
	
	
	R69
	
	
	R50
	
	
	R70
	
	
	R51
	
	
	R71
	
	
	R52
	
	
	R72
	
	
	R53
	
	
	R73
	
sen(wx)dx
	
	R54
	
�� EMBED Equation.DSMT4 
	
	R74
	
cos(wx)dx
	
	R55
	
	
	R75
	
	
	R56
	
	
	R76
	
	
	R57
	
	
	R77
	
	
	R58
	
	
	R78
	
	
	INTEGRAÇÃO POR PARTES
	R79
	
u.dv
	u.v-
v.du
	
	FÓRMULAS DE RECORRÊNCIA
	R80
	
sennau du
	
	R12
	
cosnau du
	
	R82
	
tgnau du
	
	R83
	
cotgnau du
	
	R84
	
secnau du
	
	R85
	
cosecnau du
	
	IDENTIDADES TRIGONOMÉTRICAS
	
	sen2x + cos2x = 1
	1 + tg2x = sec2x
	
	1+cotg2x = csc2x
	
	
	
	sen2x = 2senx.cosx
	
	2senx.cosy = sen(x-y)+sen(x+y)
	2senx.seny = cos(x-y) – cos(x+y)
	
	2cosx.cosy = cos(x-y)+cos(x+y)
	
	
	
	
	Integração por Substituições Trigonométricas
	
	
 a 
u 
 
 
	
u = a sen (
du = a cos( d(
= a.cos(
	
	
 
u 
 
 
 a 
	
u = a tg (
du = a sec2 ( d(
= a.sec(
	
	
 
 u 
 
 a
	
u = a sec (
du = a sec ( tg ( d(
= a. tg (
	
	
	
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