My arquivo FORMULÁRIO CALCULO II E III
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My arquivo FORMULÁRIO CALCULO II E III

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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 
Regra da cadeia: 
 )(')).(('))(( 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
 
 
 
Universidade Luterana do Brasil 
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
 
IDENTIDADES TRIGONOMÉTRICAS 
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 
DERIVADAS DAS FUNÇÕES HIPERBÓLICAS INVERSAS 
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