 


I. 
 !"#$ %&'#$ 
#$%()*+ +(++!,+(++-.% +(++!
/+012
3!-'4#$% #$% %5678'4$+(++
!-9:#$%2
-;!<=6 #-;>?@4%(A6B#$CD -; %'4
E4FE:+GEA "-(H>H!#$4IE4-)% /-J:K%$
4$I DJL-JJ+%$4<M;2
(6:(6>4 >G+>G*N D>4'E4FE:%?2
  
a. !"#$%&!'&E: HO D"-+ D"-K
( )$%'!*$(+
- C4D4 % (AP +" QRI% DO 677IG+ Q
 ,-./0
a. 1$2+$!34&5+S
( /674
8 9:8;<= 9:>8;<? 
T2UCVWXURYZ[Y\UR]R^2
_2U

`]4%<-aE2R%
b,<1-(HI>#$
%c,<1Ebd,<1ec,<1DA
I<;f

`Ub,<1>;#$
c,<1E:DAgh%]


p2q#$;%
%()*+
R4'-;r
RM4%$
R4'-;_RM:%
b,<1%$44bd,<1ec,<12q
$sc,<1el<

sc,<1e

_
4%c x
DA<∈
t
 
π π
 
−
 ÷
 
CDADAR%;
6-a?$%$
CDA4R%D6
_,C E$l1-9R%9
Eu-a?$D/$2
R4'-;
vM:L
#$
%-ME4D!67_2

%
$sc,<1el<

sc,<1e

_
4%c x
DA<
∈
t
 
π π
 
−
 ÷
 
-9bd,<1ec,<12
%jDB4!
"
bd,<1ec,<12
?6$D4!"bd,<1ec,<1
O4'-;D/$>OE-9
-a>oD/$2
?!"D/$2
?-94
-M42
prd
_rd
cd,<1 c,<1i]


∫
dx x C= +
∫
4% %xdx x C= +
∫
_
, _1
_
x
x dx C
α
α
α
α
+
= + ≠ −
+
∫
% 4%xdx x C= − +
∫
> , 1
dx
x C x
x
= + ≠
∫

4%
dx
tgx C

k
, , 11 , 1 , , 11f u x u x dx F u x C= +
∫
f
2ƒ(++!/+0

`U$%e,<1DDeD,<1J-'4
>7E:
k k
, 1 , 1 , 1 , 1 , 1 , 1u x v x dx u x v x u x v x dx= −
∫ ∫
f
[:Dd,<16<e6D d,<16<e68
E†-(HD6(A6'
u dv uv v du= −
∫ ∫
R4'-;‡
]4ƒ,<1>-$#$<2{$D!67 @
M4%$
ˆ*
, 1
x
P x e dx
∫
, 14%P x xdx
∫
, 1>P x xdx
∫
e ƒ,<1
6De @

-a>op%$
CDADAR%;6
-a>op,C 
E$‡1-9R%9Eu-a>o
D/$2
CDA4R%D6y ‡
,C E$‡ 1-9R%9
Eu+(++!
D/$2
R4'-;y
RM!
%<x dx
∫
iR6$J,<4%<1de4%<
‰<%<
R$<%<e
,<4%<1d‰4%<2
!
k
, 4% 1x x dx
∫

D
4% x dx
∫
⇒
%<x dx
∫
CDADAR%;
6-a>or%$

dx
x
@4
D62
?-9!
%<x dx
∫
@4(A
6B#$CD2
?-94
E4+IG+
@4(A6B#$CD2
pd
GIJ=K
IV. 
 !"#$ %&'#$ 
#$%()*+ +(++!,+(++-.% +(++!
/+012
3!-'4#$% #$% %5678'4$+(++
!-9:#$%2
-;!<=6 #-;>?@4%(A6B#$CD -; %'4
E4FE:+GEA "-(H>H!#$4IE4-)% /-J:K%$
4$I DJL-JJ+%$4<M;2
(6:(6>4 >G+>G*N D>4'E4FE:%?2
=  
a. !"#$%&!'&E: HO D"-+ D"-K
( )$%'!*$(+
- C4D4 % (AP +" QRI% DO 677IG+ Q
= ,-./0
a. 1$2+$!34&5+S

4
1 .
x
e
x


ữ

2. Tìm nguyên hàm của các hàm số
sau :
a) f(x) =
3
1x x
x
+ +
;
b) f(x) =
2 1
x
x
e

;
c) f(x) =
2 2
1
sin .cosx x
;
d) f(x) =

(đặt
= 1 )u x
;
b)
3
2
2
(1 ) dx x x+

(đặt
2
1 )u x= +
;
c)
3
cos sin dx x x

(đặt
cos )t x=
;
d)

+ +

d
2
x x
x
e e
(đặt

a

=
W0%>E:

W0%>E:

R%%?>
$1
( )
L
x
e


e
x
e


x
e

>
;#$
x
e

D
( )







N
5
>;
#$
x
e
x
C
C
5







/6C
$1
dxxxxdx
x
xx



x
x
5C
e









dxedx
e
x
x
C
e
> _
,> _1
x
x
C
e
+
+

61
ECM$QBM$

e C

+
1
_ _ _
, 1
,_ 1,_ 1 l _ _ x x x x
= +
+ +
[G$J
_ _
, 1 >
l _
x
F x C
x
+
= +

qlR%%?>
$1
_
,_ 1
t
_
x
C

+
1

$%
d
d
d