Lista de Exercícios 2

Prévia do material em texto

UNIVERSIDADE FEDERAL DO RIO GRANDE - FURG 
INSTITUTO DE MATEMÁTICA, ESTATÍSTICA E FÍSICA - IMEF 
01352 - CÁLCULO II – TURMA: U 
LISTA DE EXERCÍCIOS N° 2 
 
 
 Resolver as integrais: 
 
1.  dxxxx  4352
23 , R: Cx
xxx
 4
2
3
3
5
2
234
 
2. 

dx
x
xx 24 2
 , R: Cxx  42 2 
3. 
   32bxa
xdx
, R: 
 
C
bxab



224
1
 
4. dttt  32
2 , R: 
 
C
t


6
32
32
 
5.    dxxax
2
, R: C
x
ax
xa

5
2
3
2 52
3
 
6. dy
tgyba
y
 
2sec
, R:   Ctgyba
b
ln
1
 
7. 


d
bae
bae
 

, R:   Cbae  ln2 
8. dx
tgx
x
2
1
sec
 






 , R: C
tgx



1
1
 
9. dx
e
e
x
xarctg
x
x
 







 441
2
2
2
2
, R:     Cexarctg x  4ln
2
1
2
4
1 22 
10. dx
x
xx

 3 1cos
, R:   Cxxsen  3 41
2
3
2 
11. dx
gx
xx
ex x 









cot
seccos
3
1 22 3 , R:     Cgxx
e x
 cotln1
9
2
3
3
3
 
12.   dxx
2
14sec  , R:   Cxxtgxxtg  44secln2
1
4
4
1
 
13. 

dx
x
xx ln
 , R: C
x
x 
2
ln
2
2
 
14. dx
x
xsenx


3 2
3
3
2
 , R: Cx
x

 3cos3
2ln
23
3
 
15.     dgtg
2
cot , R: Cgtg   cot 
16. 
   
 







dx
x
x
x
xxarcsen 2lncos
1 4
2
 , R: 
  
  Cxsen
xarcsen
 2ln
4
22
 
17. 
 
  
dx
xtg
xx
22
22
1
sec
, R:    Cxtgarcsen 2
2
1
 
18. 
  
dx
gx
x
x
xarc
x 






 cot
seclncos
1
sec1
2
 , R:      Cxsenxarc  seclnsec
3
2 3
 
20. 
  
dx
x
xxx
 

4
42
1
1ln1
, R:     Cxxarctg  422 1ln
8
1
2
1
 
 
21. dx
x
tgx
xtgx 





 

2
2
cos
1
sec , R:   Ctgxxtg  32 1
3
2
2
1
 
22. 
 
dx
arctgxx
e xx 







21
1
3 , R: Carctx
e xx


)ln(
3ln1
3
 
23. 
 


dx
ba
ba
xx
xx 2
, R: Cx
ba
a
b
b
a
xx














2
lnln
 
24. 


dx
x
xx
21
arccos
 , R:   Cxx  22 1arccos
2
1
 
25. 
 
 

23
52
2x
dxx
 , R:   C
x
x
x 











63
63
ln
12
65
23ln
3
1 2 
26. 
 



21
2
x
dxx
 , R: Cxarcsenx  212 
27. 
 
 

25
1
2x
dxx
 , R:   Cxarctgx 






55
1
25ln
2
1 2