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# My arquivo FORMULÁRIO CALCULO II E III

DisciplinaCálculo II31.155 materiais818.949 seguidores
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Universidade Luterana do Brasil
DISCIPLINAS: CÁLCULO II e III \u2013 FORMULÁRIO
Nº FUNÇÕES E DERIVADAS Nº INTEGRAIS
1
0'\uf03d\uf0de\uf03d yky

1
\uf0f2 \uf02b\uf03d cudu

2
'..' 1 uunyuy nn \uf02d\uf03d\uf0de\uf03d
2
1,
1
.
1
\uf02d\uf0b9\uf02b
\uf02b
\uf03d\uf0f2
\uf02b
nc
n
u
duu
n
n

3
)(')).(('))(( xgxgfxgfy \uf0de\uf03d
3
cu
u
du
\uf02b\uf03d\uf0f2 ln

4
\uf0de\uf03d uay )1,0(,'.ln.' \uf0b9\uf03e\uf03d aauaay u
4
1,0,
ln
. \uf0b9\uf03e\uf02b\uf03d\uf0f2 aaca
a
dua
u
u

5
'.' ueyey uu \uf03d\uf0de\uf03d
5
\uf0f2 \uf02b\uf03d cedue
uu .

6
\uf0de\uf03d vuy . '.'.' uvvuy \uf02b\uf03d
6 Integral por partes
\uf0f2 \uf0f2\uf02d\uf03d duvvudvu ...

7
\uf0de\uf03d
v
u
y
2
'.'.
'
v
vuuv
y
\uf02d
\uf03d
7
\uf0f2 \uf02b\uf02d\uf03d cuduusen cos.

8
\uf0de\uf03d uy alog e
u
u
y alog
'
'\uf03d
ou
au
u
y
ln.
'
'\uf03d
8
\uf0f2 \uf02b\uf03d cusenduu .cos

9
\uf0de\uf03d uy ln
u
u
u
u
y
'
'.
1
' \uf03d\uf03d
9
\uf0f2 \uf02b\uf03d cuduu secln.tan

10
\uf0de\uf03d vuy '.)(ln.'..' .1 vuuuuvy vv \uf02b\uf03d \uf02d
10
\uf0f2 \uf02b\uf03d cusenduu ln.cot

11
\uf0de\uf03d useny uuy cos'.'\uf03d
11
\uf0f2 \uf02b\uf02b\uf03d cuuduu tansecln.sec

12
\uf0de\uf03d uy cos usenuy '.' \uf02d\uf03d
12
\uf0f2 \uf02b\uf02d\uf03d cduu ucot ucscln.csc

13
\uf0de\uf03d uy tan uuy
2sec'.'\uf03d
13
\uf0f2 \uf02b\uf02d\uf03d cduu ucsc.ucot. csc

14
uuyy 2csc'.'ucot \uf02d\uf03d\uf0de\uf03d
14
\uf0f2 \uf02b\uf03d cuduu tan.sec
2

15
\uf0de\uf03d uy sec uuuy tan.sec'.'\uf03d
15
\uf0f2 \uf02b\uf03d cuduuu sec.tan.sec

16 \uf0de\uf03d uy csc ucot .u u'.csc' \uf02d\uf03dy

16

\uf0f2 \uf02b\uf02d\uf03d cduu ucot .csc
2

17 \uf0de\uf03d\uf03d
\uf02d usenusenarcy 1
21
'
'
u
u
y
\uf02d
\uf03d

17 22
22
, auc
a
u
senarc
ua
du
\uf03c\uf02b\uf03d
\uf02d
\uf0f2

18 \uf0de\uf03d\uf03d
\uf02d uuarcy 1coscos
21
'
'
u
u
y
\uf02d
\uf02d
\uf03d

18

\uf0f2 \uf02b\uf02d\uf02b\uf03d
\uf02d
cauu
au
du 22
22
ln.

19 \uf0de\uf03d\uf03d \uf02d utguarcy 1tan
21
'
'
u
u
y
\uf02b
\uf03d

19 \uf0f2 \uf02b\uf03d\uf02b ca
u
arc
aua
du
tan.
1
22

20 \uf0de\uf03d uarcy cot
21
'
'
u
u
y
\uf02b
\uf02d
\uf03d

20

\uf0f2 \uf02b\uf02b\uf02b\uf03d
\uf02b
cauu
au
du 22
22
ln

21 \uf0de\uf0b3\uf03d 1,sec uuarcy 1,
1.
'
'
2
\uf03e
\uf02d
\uf03d u
uu
u
y

21 \uf0f2 \uf02b\uf03d
\uf02d
c
a
u
arc
aauu
du
sec
1
. 22

22 \uf0de\uf0b3\uf03d 1,cossec uuarcy 1,
1.
'
'
2
\uf03e
\uf02d
\uf02d
\uf03d u
uu
u
y

22

22
22
,ln.
2
1
auc
au
au
aau
du
\uf03e\uf02b
\uf02b
\uf02d
\uf03d
\uf02d\uf0f2

23
xyxsenhy cosh'\uf03d\uf0de\uf03d 23 \uf0f2 \uf02b\uf03d cuduusenh cosh.

24
xsenhyxy \uf03d\uf0de\uf03d 'cosh 24 \uf0f2 \uf02b\uf03d cusenhduu.cosh

25
xhyxy 2sec'tanh \uf03d\uf0de\uf03d 25 \uf0f2 \uf02b\uf03d cuduu coshln.tanh

DISCIPLINAS: CÁLCULO II e III \u2013 FORMULÁRIO
26
xyxy 2csc'coth \uf02d\uf03d\uf0de\uf03d 26 \uf0f2 \uf02b\uf03d cusenhduu ln.coth

27

xxsyxy tanh.ech'sech \uf02d\uf03d\uf0de\uf03d
27 \uf0f2
\uf02b\uf03d cuduu tanh.sech 2
\uf0f2 \uf02b\uf03d
\uf02d cusenhduu 1tan.sech

28

xxyxy coth.csch'csch \uf02d\uf03d\uf0de\uf03d
28
\uf0f2 \uf02b\uf02d\uf03d cuduu coth.csch
2
\uf0f2 \uf02b\uf03d cuduu 2
1
tanhln.csch

1
1cos22 \uf03d\uf02b xxsen
2
xx 22 tan1sec \uf02b\uf03d
3 xx 22 cot1csc \uf02b\uf03d
4
x
xsen
x
cos
tan \uf03d
5
xsen
x
x
x
cos
tan
1
cot \uf03d\uf03d
6

x
x
cos
1
sec \uf03d

7
xsen
x
1
csc \uf03d

8
xxsenxsen cos..22 \uf03d 9
2
2cos12 xxsen
\uf02d
\uf03d
10
2
2cos1
cos 2
x
x
\uf02b
\uf03d
11
)()(cos.2 yxsenyxsenyxsen \uf02b\uf02b\uf02d\uf03d 12 )cos()cos(.2 yxyxysenxsen \uf02b\uf02d\uf02d\uf03d
13
)cos()cos(cos.cos2 yxyxyx \uf02b\uf02b\uf02d\uf03d 14 )
2
(cos11 xxsen \uf02d\uf0b1\uf03d\uf0b1
\uf070
FUNÇÕES HIPERBÓLICAS
1
2
xx ee
xsenh
\uf02d\uf02d
\uf03d

2 2cosh
xx ee
x
\uf02d\uf02b
\uf03d
3
x
xsenh
x
cosh
tanh \uf03d
4
x
x
tanh
1
coth \uf03d

5 xx cosh
1
sech \uf03d
6
xsenh
x
1
csch \uf03d

FUNÇÕES HIPERBÓLICAS INVERSAS
1
xysenhxsenhy \uf03d\uf0db\uf03d \uf02d1
2
0,coshcosh 1 \uf0b3\uf03d\uf0db\uf03d \uf02d yxyxy
3
xyxy \uf03d\uf0db\uf03d \uf02d tanhtanh 1
4
\uf0c2\uf0ce\uf02b\uf02b\uf03d\uf02d xxxxsenh ),1ln( 21
1
2
1
1
1
'
x
yxsenhy
\uf02b
\uf03d\uf0de\uf03d \uf02d
2
1
1
'cosh
2
1
\uf02d
\uf03d\uf0de\uf03d \uf02d
x
yxy

3
2
1
1
1
'tanh
x
yxy
\uf02d
\uf03d\uf0de\uf03d \uf02d
4
2
1
1
1
'coth
x
yxy
\uf02d
\uf02d\uf03d\uf0de\uf03d \uf02d

5
2
1
1.
1
'sech
xx
yxy
\uf02d
\uf02d\uf03d\uf0de\uf03d \uf02d
6
1.
1
'csch
2
1
\uf02b
\uf02d\uf03d\uf0de\uf03d \uf02d
xx
yxy

5
1),1(lncosh 21 \uf0b3\uf02d\uf02b\uf03d\uf02d xxxx
6
11,
1
1
ln
2
1
tanh 1 \uf03c\uf03c\uf02d\uf0f7
\uf0f8
\uf0f6
\uf0e7
\uf0e8
\uf0e6
\uf02d
\uf02b
\uf03d\uf02d x
x
x
x

FÓRMULAS DE RECORRÊNCIA

1
\uf0f2\uf0f2
\uf02d
\uf02d
\uf0f7
\uf0f8
\uf0f6
\uf0e7
\uf0e8
\uf0e6 \uf02d
\uf02b\uf02d\uf03d duausen
n
n
an
auausen
duausen n
n
n .
1cos.
. 2
1 2
\uf0f2\uf0f2
\uf02d
\uf02d
\uf0f7
\uf0f8
\uf0f6
\uf0e7
\uf0e8
\uf0e6 \uf02d
\uf02b\uf03d duau
n
n
an
auausen
duau n
n
n .cos
1cos.
.cos 2
1

3
\uf0f2\uf0f2
\uf02d
\uf02d
\uf02d
\uf02d
\uf03d duau
na
au
duau n
n
n .tan
)1(
tan
.tan 2
1 4
\uf0f2\uf0f2
\uf02d
\uf02d
\uf02d
\uf02d
\uf02d\uf03d duau
na
au
duau n
n
n .cot
)1(
cot
.cot 2
1

5
\uf0f2\uf0f2
\uf02d
\uf02d
\uf0f7
\uf0f8
\uf0f6
\uf0e7
\uf0e8
\uf0e6
\uf02d
\uf02d
\uf02b
\uf02d
\uf03d duau
n
n
na
autgau
duau n
n
n .sec
1
2
)1(
.sec
.sec 2
2 6
\uf0f2\uf0f2
\uf02d
\uf02d
\uf0f7
\uf0f8
\uf0f6
\uf0e7
\uf0e8
\uf0e6
\uf02d
\uf02d
\uf02b
\uf02d
\uf02d\uf03d duau
n
n
na
auau
duau n
n
n .csc.
1
2
)1(
cot.csc
.csc 2
2

SUBSTITUIÇAO TRIGONOMÉTRICA
1
\uf071senaxxa .22 \uf03d\uf0ae\uf02d
2
\uf071tan.22 axxa \uf03d\uf0ae\uf02b
3
\uf071sec.22 axax \uf03d\uf0ae\uf02d