Phiếu bài tập về Tích phân Giải tích 12 - Anh Sơn

SCELL 2016 TÍCH PHÂN 
PHIẾU BÀI TẬP TÍCH PHÂN THEO DẠNG 
MÔN: GIẢI TÍCH 12 
DẠNG 1: TÍCH PHÂN CÁC HÀM SỐ HỮU TỈ 
1, 
3
2 3
0
I x (1 x) dx  
3, 
1
2 3
0
I (1 2x)(1 3x 3x ) dx    
5, 
1
0
2x 9
I dx
x 3



 
7, 
21
0
x 3x 2
I dx
x 3
 


 
9, 
2
2
1
5
I dx
x 6x 9

 
 
11, 
21
2
0
x
I dx
4 x


 
13, 
2
2
1
1
I dx
x 2x 2

 
 
15, 
1
2
0
4x 1
I dx
x 5x 6


 
 
17, 
1
42
2
0
x
I dx
x 1


 
19, 
32
2
1
3x
I dx
x 2x 1

 
 
21, 
1
2
0
2x 2)
1
I dx
(x 1) ( 
  
23, 
2
2
1
x 1
I ( ) dx
x 2



 
25, 
3 21
2
0
x 2x 10x 1
I dx
x 2x 9
  

 
 
27, 
1
2
5
1
I dx
2x 8x 26

 
 
2, 
1
3 4 5
0
I x (x 1) dx  
4, 
1
5 3 6
0
I x (1 x ) dx  
6, 
3
0
x 1
I dx
2x 3



 
8, 
1
2
0
3
I dx
x 4x 5

 
 
10, 
1
2
0
x
I dx
4 x


 
12, 
33
2
1
x
I dx
x 16


 
14, 
22
2
1
x
I dx
x 7x 12

 
 
16, 
1
3
2
1
1
I dx
9x 6x 5

 
 
18, 
23
2
0
3x 2
I dx
x 1



 
20, 
3
2
3
1
I dx
x 3


 
22, 
1
3
0
3
I dx
x 1


 
24, 
21
3
0
2 x 5
I dx
x
x
1
 


 
26, 
1
2
0
x 3
I dx
(x 1)(x 3x 2)


  
 
28, 
4
2
1
1
I dx
x (x 1)


 
SCELL 2016 TÍCH PHÂN 
29, 
1
3
0
x
I dx
(2x 1)


 
31, 
2
3
2
1
1
I x
x
x
d
x



 
33, 
5
3
4
2
2
3x
x
1
I dx
x 2 5x 6


  
 
35, 
21
4
0
(x 1)
I dx
(2x 1)



 
37, 
1
2
0
2
5x
I dx
( 4)x


 
39, 
2
10 2
1
1
I dx
x(1 )x


 
41, 
2
3
6
1 x x
1
I dx
(1 )


 
43, 
22
4
1
1 x
I dx
1 x



 
45, 
22
4
1
1 x
I dx
1 x



 
47, 
73
8 4
2
x
I dx
1 x 2x

 
 
49, 
3
23
4
0
x
I dx
x 1


 
51, 
1
3
0
4x
I dx
(x 1)


 
53, 
31
2 3
0
x
I dx
(x 1)


 
55, 
41
6
0
x 1
I dx
x 1



 
30, 
1
3 2
0
4x 1
I dx
x 2x x 2


  
 
32, 
2
5 3
1 x
1
I dx
x


 
34, 
1
3
0
x
I dx
(x 1)


 
36, 
991
101
0
(7x 1)
I dx
(2x 1)



 
38, 
2
71
5
0
I d
x
(1 )x
x

 
40, 
4 3
4
1
1
I dx
x(1 x )


 
42, 
72
7
1
I dx
x(1
x
x )
1



 
44, 
2
20012
1002
1
I dx
(1 )
x
x


 
46, 
41
6
0
x 1
I dx
x 1



 
48, 
2
1
4
0
x
I
x
dx
x 1

 
 
50, 
2
1 5
22
4
1
x 1
I dx
x 1x



 
 
52, 
1
4 2
0
1
I dx
(x 4x 3)

 
 
54, 
2
2 2
0
1
I dx
(4 x )


 
56, 
52
5
1
1 x
I dx
x(1 x )



 
SCELL 2016 TÍCH PHÂN 
DẠNG 2: TÍCH PHÂN CÁC HÀM SỐ VÔ TỈ 
1, 
1
0
x 1 xI dx  
3, 
1
3 2
0
x 1 xI dx  
5, 
3
3 2
0
x . 1 xI dx  
7, 
2
2 3
0
I x (x 4) dx  
9, 
7
3
3
0
x 1
dx
3x 1
I


  
11, 
2
3
1
1
dx
x 1 x
I 

 
13, 
2 3
2
5
1
I dx
x x 4


 
15, 
2
32
2
0
x
dxI
1 x
  
17, 
2
2
2
3
1
dx
x x 1
I

  
19, 
37
3 2
0
x
dI x
1 x
  
21, 
1
0
x
dx
2x 1
I

  
23, 
1
2
0
1 x dI x  
25, 
3
2 2
1
1
I dx
x 4 x


 
27, 
1
2
0
1
I dx
4 x


 
2, 
9
3
1
x. 1 xI dx  
4, 
1
15 8
0
I x 1 x dx  
6, 
1
5 2
0
x 1 xI dx  
8, 
2
3 2
0
(x 3) x 6x 8 dI x    
10, 
21
3
0
3x
dx
x 2
I

  
12, 
1
0
1
dx
3 2x
I

  
14, 
4
2
2
1
dx
x 16 x
I

  
16, 
2
3
0
x 1
I dx
3x 2



 
18, 
4
2
7
1
I dx
x 9 x


 
20, 
6
2
2 3
1
dx
x x 9
I

  
22, 
5 33
2
0
x 2x
I dx
x 1



 
24, 
38
1
x 1
I dx
x

  
26, 
1
2 3
0
(1 x )I dx  
28, 
3
2
2
1
2
1
dxI
x 1 x
  
SCELL 2016 TÍCH PHÂN 
29, 
2
22
2
0
x
I dx
1 x


 
31, 
1
2
0
x 1I dx  
33, 
2
2
1
I 4x x 5 dx

   
35, 
23
0
x 1
x
x
I d
1


  
37, 
24
4 3
3
d
x
I
x 4
x

  
39, 
4
1
2
dx
x 5 4
I
  
  
41, 
2
0
x
I dx
2 x 2 x

  
 
43, 
2
1
x
I dx
1 x 1

 
 
45, 
1
0
3
I dx
x 9 x

 
 
47, 
1
3
3
1
I dx
x 4 (x 4)

  
 
49, 
6
4
x 4 1
. dx
x 2 x
I
2

 
  
51, 
22
2
2
x 1
dx
x x 1
I




  
53, 
1
3
1
2
x
dx
x 1
I

  
55, 
0
2
1
1
dx
x 2
I
x 9  
  
57, 
2
2
2
2x 5
dx
x 4x
I
13

 
  
30, 
2
2 2
1
x 4 x dI x

  
32, 
2
2
0
I 4 x dx  
34, 
1
2
0
3x 6x 1dxI     
36, 
21
0
x
I dx
(x 1) x 1

 
 
38, 
3
2
2
1
I dx
x 1


 
40, 
1
0
1
dx
x 1 x
I
 
  
42, 
7
2
1
dx
2 x 1
I
 
  
44, 
31
2
0
x
I dx
x 1 x

 
 
46, 
1
2
1
1
I dx
1 x 1 x

  
 
48, 
23
2
1
x 1
dx
x
I

  
50, 
1
2
2
1
2
1
dx
(3 2x) 5 12x
I
4x   
  
52, 
21
2
0
x
x
I dx
4
  
54, 
3 32
4
1
x x
dx
x
I

  
56, 
3
2
1
1
dx
4x x
I

  
58, 
21
2
2
2
1 x
dx
x
I

  
SCELL 2016 TÍCH PHÂN 
59, 
2
2
1
x
dx
3x 9x 1
I
 
  
61, 
4
0
2x 1
dx
1 2x
I
1

 
  
63, 
6
2
1
dx
2x 1 4x
I
1  
  
65, 
25
1
x 1
dx
x 3x 1
I


  
67, 
23
0
2x x 1
dx
x
I
1
 

  
69, 
0
2
4
I
(1 1 2x
x 1
x
)
d
 

 
71, 
3 22
2
0
2 3x x
dx
x
x
I
x 1
 
 
  
73, 
1
2
1
1
dx
1 x 1 x
I
   
  
75, 
1
31 3
4
1
3
x
I
x
(x )
dx

  
77, 
2
27
3
1
I
x 2
dx
x x


 
79, 
x
I dx
x x
3 2
2 2
0
(1 1 ) (2 1 )

   
 
81, 
1
33 3
0
1
dx
). 1
I
(1 x x

 
 
83, 
42 2
23
x
dx
1
(x ) x 1
x
I
 
  
85, 
21
6
0
x
dx
4 x
I

  
60, 
2
2
25
2
( ) 4 dxI x x x

   
62, 
21
0
x x
dx
1 x x
I


  
64, 
1
0
1 x
dx
1 x
I


  
66, 
3
0
x 3
dx
3 x 1
I
x 3

  
  
68, 
21
0
x
dx
(x 1) x
2
1
I
 
  
70, 
1
3
0
2(x 1) 2x xI x d   
72, 
8
2
3
x 1
dx
x 1
I


  
74, 
2
32
3
0
I
x
x
dx
4


 
76, 
2
2 5
2
2
x
dx
( 1) x 5
I
x  
  
78, 
1
2
0
1
x
x x
I d
1 
  
80, 
x
I dx
x x x x
3 2
0
2( 1) 2 1 1

    
 
82, 
3 32 2
4
1
x 2015x
d
x
I
x
x
 
  
84, 
22
4
1
(3 4 )
d
x
2x
xI
 
  
86, 
21
2
0
x
dx
3 2 x
I
x 
  
SCELL 2016 TÍCH PHÂN 
DẠNG 3: TÍCH PHÂN CÁC HÀM SỐ LƯỢNG GIÁC 
1, 
3
2
4
I 3tan x dx


  
3, 
4
2
6
(2cot xI 5)dx


  
5, 
2
2
0
2I cosin x. dx xs

  
7, 
2
3
0
2I 2cos x 3s( dxin x)

  
9, 
2
4 4
0
I cos2x(sin x cos x)dx

  
11, 
2
0
I sin x.sin 2x.sin 3xdx

  
13, 
2
2
0
cos x.cos4x dxI

  
15, 
2
2 3
0
sin 2x(1 sin x) dxI

  
17, 
2
3
2
cos x cos x cosI xdx



  
19, 
3
4
4
tan xdxI


  
21, 
4
5
0
tan x dxI

  
2, 
2
3
0
I sin x dx

  
4, 
4
4
0
cos x dxI

  
6, 
4
6
I cot 2 x dx


  
8,  
3
6
2
tan x cotxI dx



  
10, 
3
2 2
6
tan x cot xI 2dx


  
12, 
2
6 3 5
0
1 cos x sin x.cos xdI x

  
14, 
3
0
sin x.tan xdxI

  
16, 
2
2
0
sin x cos x(1 cos x)I dx

  
18, 
2
5 4
0
cos xsin xdxI

  
20, 
4
3
6
cot x dxI


  
22, 
3
2
4
tan x
dx
cos x 1 cos x
I

 
  
SCELL 2016 TÍCH PHÂN 
23, 
2
4
4
1
I dx
sin x


  
 25, 
3
0
1
dx
cos x
I

  
27, 
4
6
0
1
I dx
cos x

  
29, 
4
3
0
1
dx
cos x
I

  
31, 
32
0
4sin x
dx
1 cosx
I


  
33, 
2
4
0
sin 2x
dx
1 cos x
I


  
35, 
2
0
sin 2x.cos x
dx
1
I
cos x


  
37, 
2
0
sin 2x sin x
dx
1
I
3cos x



  
39, 
24
0
1 2sin x
dx
1 sin 2x
I



  
41, 
34
2
0
sin x
dx
cos x
I

  
43, 
52
0
sin x
dx
cos 1
I
x


  
45, 
3
2
6
cos 2x
dx
1 cos 2x
I

 
  
24, 
4 44
0
sin x cos x
dx
sin x cos x 1
I


 
  
26, 
2
0
sin x cos x cos x
dx
sin x 2
I



  
28, 
2
0
cos x
dx
2 cos 2x
I


  
30, 
6
2
0
cos x
dx
6 5sin x
I
sin x

 
  
32, 
2
4
cos x sin x
dx
3 sin 2x
I




  
34, 
4
2
6
1
dx
sin x co
I
t x


  
36, 
34
2 2 5
0
sin x
dx
(tan x 1)
I
.cos x


  
38, 
33
0
sin x
dx
cos x
I

  
40, 
2
4
0
sin 2x
dx
1 sin x
I


  
42, 
2
0
sin 2x
dx
1 cos x
I


  
44, 
33
2
0
sin x
dx
(sin x 3)
I


  
46, 
0
2
2
sin 2x
dx
(2 sin x)
I
 
  
SCELL 2016 TÍCH PHÂN 
47, 
2
6
1 sin 2x cos 2x
dx
cos x sin x
I


 

  
49, 
32
2
0
sin x.cos x
dx
co
I
s x 1


  
51, 
3
2 2
3
1
dx
sin x 9cos x
I




  
53, 
3
4
6
1
dx
sin x cos x
I


  
55, 
4
2 2
0
sin 2x
dx
sin x 2cos x
I


  
57, 
36
0
sin x sin x
dI x
cos2x


  
59, 
2
2
0
sin x
dx
cos x 3
I


  
61, 
4
0
1
dx
2 tan x
I


  
63, 
2
2
0
cos x
dx
cos x 1
I


  
65, 
32
4 2
0
cos x
dx
cos x 3c
I
os x 3

 
  
67, 
2
3
1
dx
sin x 1 cos x
I

 
  
69, 
2
0
sin x
dx
1 sin x
I


  
48, 
33
6
4sin x
dx
1 cos x
I

 
  
50, 
3
2
6
1
dx
cos x.sin x
I


  
52, 
2
0
sin3x
dx
cos 1
I
x


  
54, 
3
2
4
tan x
dx
cos x cos 1
I
x

 
  
56, 
4
2
0
tan x 1
( ) dx
tan 1
I
x



  
58, 
2
0
sin 2x sin x
dx
co
I
s3x 1



  
60, 
3
2
0
cos x
dx
1 sin x
I


  
62, 
2
0
4cos x 3sin x 1
dx
4sin x 3cos x 5
I

 
 
  
64, 
2
4
0
sin xdxI

  
66, 
2
0
1 sin x
dx
1 3cos x
I



  
68, 
2
2
cos x 1
dx
cos x 2
I





  
70, 
2
0
cos x
dx
sin x c
I
os x 1

 
  
SCELL 2016 TÍCH PHÂN 
71, 
2
0
cos x
dx
7 cos 2x
I


  
73, 
2
0
sin x
dx
x
I

  
75, 
2
0
1
dx
2 sin x
I


  
77, 
2
0
1
dx
2 cos x
I


  
79, 
2
2
3
cos x
dx
(1 cos x)
I

 
  
81, 
24
3
2
cos x
I
c
sin x 1
d
os x
x




  
83, 
2
2
6
1
I x
2
sin x. sin dx


  
85, 
2
0
1 sin xI dx

  
87, 
2
2
I x.(2 1 cos2x)sin dx


   
89, 
4
6 6
0
I
x cos
sin 4x
dx
si xn



 
91, 
3
1
dx
2 3sin x
I
cos x

  
  
93, 
2
2
0
1 3sin 2x 2 dI xcos x

   
72, 
2
0
cos x
dx
cos x 1
I


  
74, 
2
0
cos x
dx
2 cos x
I


  
76, 
32
0
cos x
dx
cos 1
I
x


  
78, 
23
6
0
sin x
dx
cos x
I

  
80, 
2
0
1
dx
2cos x si
I
n x 3

 
  
82, 
3
8
cot x tan x 2tan2x
dx
sin 4x
I


 
  
84, 
6
0
1
dx
2sin 3
I
x


  
86, 
2
2
3
0
I cos x 1)c( dxos x

  
88, 
22
0
cos x sin 2x 38
dx
sinx co
I
s x


 
  
90, 
2
3
0
sin x
dx
(sinx 3
I
cos x)


  
92, 
6
0
1
dx
sinx 3 cos x
I


  
94, 
4
0
cos x sin x
dx
3 sin 2x
I



  
SCELL 2016 TÍCH PHÂN 
95, 
2
3
0
sin x
dx
cos x. sin
I
x3


  
97, 
6
0
tan(x )
4 dx
cos 2x
I
 

  
99, 
2
4
0
tan x
dx
cosx.
I
cos x1


  
101, 
2
0
2 2
3sin x 4cos x
dx
3sin
I
x 4cos x



  
103, 
2
4
sin(x )
4 dx
2sin
I
x cos x 3





  
105, 
2
2
3
cos x
dx
(1 cos x)
I

 
  
96, 
2
0
2
2
I
cos x 4sin x
sin 2x
dx



 
98, 
2
4
0
I
cos
sin x
dx
5sin x. 2x cos x



 
100, 
36
0
tan
dx
cos2x
x
I

  
102, 
2
3
0
cos 2x
dx
(cos x si
I
n x 3)

 
  
104, 
3
4 3 5
4
I
x.cos
1
dx
s xin


  
106, 
3
6
cot x
dx
sin x.sin(
I
x )
4

 
  
DẠNG 4: TÍCH PHÂN CÁC HÀM SỐ SIÊU VIỆT 
1, 
xln 2
x
0
1 e
I dx
1 e



 
3, 
2x1
x
0
e
dx
e 1
I

 
  
5, 
ln 3
x
0
1
dI x
e 1
  
7, 
2
x
1
x
1 e
I
1
d

  
9, 
2x2
x
0
e
dx
e 1
I

  
11, 
x1
x
0
e
I dx
e 1




 
13, 
1
3x 1
0
I e dx  
2, 
ln 2
x
0
e 1dxI   
4, 
1
x
0
1
dx
e 4
I

  
6, 
xln 3
x 3
0
e
dx
(e 1)
I

  
8, 
1
x
0
1
I dx
3 e


 
10, 
1
2x x
0
1
I dx
e e


 
12, 
x 21
2x
0
(1 e )
I dx
1 e



 
14, 
4
x
1
I e dx  
SCELL 2016 TÍCH PHÂN 
15, 
2xln 5
x
ln 2
e
dx
e 1
I

  
17, 
x1
x x
0
e
I dx
e e


 
19, 
xln 3
x x
0
e
I dx
(e 1) e 1

 
 
21, 
tan x 24
2
0
e
dx
cos x
I


  
23, 
2e
2
e
1 1
I ( )dx
ln xln x
  
25, 
3 2e
1
ln x 2 ln x
I dx
x

  
27, 
e
2
1
ln x
I dx
x(ln x 1)


 
29, 
2e
1
ln x
I dx
ln x
  
31, 
2
2
0
I ln( 1 x x)dx   
33, 
3ln 2
x3 2
0 ( 2)
1
I dx
e 
  
35, 
e
1
3 2ln x
I dx
x 1 2ln x



 
37, 
5
2
ln( x 1 1)
I dx
x 1 x 1
 

  
 
39, 
xx2
x x
1
2 2
I dx
4 4 2


 
 
41, 
2
0
I sin x.ln(1 cos x)dx

  
43, 
4
0
I ln(1 tan x)dx

  
16, 
1
4x 2x2
2x
0
3e e
I dx
1 e



 
18, 
1
2x
1
1
I dx
3 e


 
20, 
e
1
1 3ln x ln x
I dx
x

  
22, 
22 sin x
4
I e sin 2x dx


  
24, 
3
2
2
I ln(x x)dx  
26, 
e
2
1
I ln xdx  
28, 
2e
e
ln x
I dx
x
  
30, 
1 3
2
1
I ln(x x 1) dx

   
  
32, 
22 sin x 3
0
I e .sin x cos xdx

  
34, 
ln 3
x x
l
x
n
2
2
e
I dx
e 1 e 2

  
 
36, 
3 3e
1
ln x
I dx
x 1 ln x


 
38, 
23xln 3
x x
0
xe
I dx
e 4e
e
3 1
2 

 
 
40, 
x1
x x x
0
6
I dx
9 3.6 2.4

 
 
42, 
3
0
I sin x.ln(cos x)dx

  
44, 
1
2
1
I ln( x a x)dx

   
SCELL 2016 TÍCH PHÂN 
DẠNG 5: TÍCH PHÂN TỪNG PHẦN 
1, 
e
2
1
I ln xdx  
3, 
0
I x sin xdx

  
5, 
e
1
I (1 x)ln x dx  
7, 
e
2
1
I x ln x dx  
9, 
e
1
I x(2 ln x)dx  
11, 
2
x 2
0
I e sin xdx

  
13, 
3
2
0
I x ln(x 1)dx  
15, 
2
4
0
I x sin x dx

  
17, 
4
2
0
I x.tan xdx

  
19, 
1
2 2x
0
I (1 x) .e dx  
21, 
2
2
1
1
I x ln(1 )dx
x
  
23, 
e
2
1
e
ln x
I dx
(x 1)


 
25, 
1
2
0
1 x
I x.ln dx
1 x



 
27, 
2 x1
2
0
x e
I dx
(x 2)


 
2, 
3
2
2
I ln(x x)dx  
4, 
2x 2
0
I e sin xdx

  
6, 
2
1
3 x
0
I x e dx  
8, 
2
0
I xsin x.cos xdx

  
10, 
2
2
1
I (x x)ln x dx  
12, 
4
3x
0
I e sin 4x dx

  
14, 
4
2
1
I (x 1) ln x dx  
16, 
2
4
0
I x cos x dx

  
18, 
4
0
x
I dx
1 cos 2x



 
20, 
2 2
0
I x cos xdx

  
22, 
0
2x 3
1
I x(e x 1)dx

   
24, 
2e
1
x 1
I .ln xdx
x

  = 
26, 
3
2
6
ln(sin x)
I dx
cos x


  
28, 
2
1
I cos(ln x)dx  
SCELL 2016 TÍCH PHÂN 
29, 
2
sin x
0
I e .sin 2xdx

  
31, 
e
1
I cos(ln x)dx

  
33, 
1
1 x
3
a
e
I dx
x
  
35, 
1
2
0
1 x
I x ln dx
1 x



 
37, 
8
3
lnx
I dx
x 1


 
39, 
2
x
0
1 sin x
I e dx
1 cosx




 
41, 
1
3x 1
0
I e dx  
30, 
22 sin x 3
0
I e sin x cos x dx

  
32, 
2
5
1
ln x
I dx
x
  
34, 
2
3
I cos x.ln(1 cos x)dx


  
36, 
2
3
2
1
ln( 1)
I d
x
x
x

  
38, 
4
0
2I ln( 9 x)dxx   
40, 
2
0
2
1 x ln(x 1 )
I dx
1
x
x
 


 
42, 
2
2
1
0
I
x
x
dx
1


 
DẠNG 6: LỚP TÍCH PHÂN ĐẶC BIỆT 
1, 
41
x
1
x
I dx
1 2


 
3, 
2
2x
cos x
I dx
e 1




 
5, 
1
2
1
I ln(x x 1)dx

   
7, 
2
1
1
2 x
I ln( )dx
2 x
x




 
9, 
1
2 x
1
1
I dx
(x 1)(4 1)

 
 
11, 
2
2
2
I cosx ln(x x 1)dx



   
13, 
2
3
3
x
I ( 1) ln( )dx
x
x



 

 
2, 
1
x 2
1
1
I dx
(e 1)(x 1)

 
 
4, 
2
x
sin x
I dx
3 1




 
6, 
1
2
1
I ln( x a x)dx

   
8, 
41
1
2
sinx x
I dx
1 x



 
10, 
3
x 2
3
1
I dx
(e 1)(x 3)

 
 
12, 
2
4
4
sin x
I dx
x1 x




 
 
14, 
2
0
xsin x
I dx
1 cos x



 
SCELL 2016 TÍCH PHÂN 
15, 
2
0
xsin x
I dx
1 sin x



 
17, 
2
0
I xsinxcos xdx

  
19, 
2
0
sin x
I dx
sin x cos x



 
21, 
2
3
0
4sin x
I dx
(sin x cos x)



 
23, 
2
3 3
0
I ( cos x sin x)dx

  
25, 
2
0
sin x
I dx
cos x sin x



 
27, 
32
3 3
0
3cos x
I dx
sin x cos x



 
29, 
4
3
0
2cos 2x
I dx
(sin 2x 2x)cos



 
31, 
48
4 4
0
4sin 4x
I dx
sin 4x cos 4x



 
33, 
42
3 3
0
cos x sin x
I dx
sin x cos x



 
35, 
2
3
3
I x sinx dx


  
16, 
3
2
0
xsin x
I dx
cos x

  
18, 
4
2
0
x tan x
I dx
4cos x

  
20, 
42
4 4
0
cos x
I dx
cos x sin x



 
22, 
2
3
0
5sin x 4cosx
I dx
(sin x cos x)




 
24, 
2
3 3
0
I (cos x sin x)dx

  
26, 
2014 20
2
0
14I (cos x sin x)dx

  
28, 
20142
2014 2014
0
sin x
I dx
sin x cos x



 
30, 
2014
2014 2014
6
0
sin 3x
I dx
sin 3x cos 3x



 
32, 
2
x 1
0
1 x 3 x
I dx
1 2 
  


 
34, 
2
2
2
0
1
I tan (cosx) dx
cos (sinx)

 
  
 
 
36, 
4
0
I ln(1 tan x)dx

  
SCELL 2016 TÍCH PHÂN 
TỔNG HỢP TÍCH PHÂN – CÁC BÀI TOÁN THI 
1, 
2
3 2
1
I x 2x x 2 dx

    
3, 
5
3
I ( x 2 x 2 )dx

    
5, 
1
2
2
0
4x 1
I dx
x 3x 2


 
 
7, 
2
0
sin 2x sin x
I dx
1 3cosx




 (A-2005) 
9, 
2
0
sin 2x.cosx
I dx
1 cos x



 (B-2005) 
11, 
3e 2
1
ln x
I dx
x ln x 1


 (D-2005.DB) 
13, 
10
5
1
I dx
x 2 x 1

 
 (B-2006.DB) 
15, 
4
0
2x 1
I dx
1 2x 1


 
 (A-2007.DB) 
17, 
46
0
tan x
I dx
cos 2x

  (A-2008) 
19, 
2
3
1
l x
x
n
I dx  (D-2008) 
21, 
2
3
0
2I (cos x 1)cos xdx

  (A-2009) 
23, 
3
1
2(
3 ln x
I
x 1)
dx


  (B-2009) 
25, 
x x1
x
2
0
2 e 2 e
I dx
1 2e
x x 


 (A-2010) 
2, 
0
I cos x sin xdx

  
4, 
2
0
I 1 sin xdx

  
6, 
e
1
e
I ln x dx  
8, 
2
3
0
I sin x.tanxdx

  (A-2005.DB) 
10, 
4
sin x
0
I (tanx e cosx)dx

  (B-2005) 
12, 
6
2
1
I dx
2x 1 4x 1

  
 (A-2006) 
14, 
0
2
2
2
sin 2x
I dx
cos x 4sin x



 (A-2006) 
16, 
ln 5
x x
ln 3
1
I dx
e 2e 3

 
 (B-2006) 
18, 
1
0
2xI (x 2)e dx  (D-2006) 
20, 
2
e
3
1
I ln xdx x  (D-2007) 
22,
4
0
sin(x )
4I dx
sin 2x 2(1 sin x cos x)
 


  
 
24, 
3
x
1
1
I dx
e 1


 (D-2009) 
26, 
e
1
2
ln x
I dx
x(2 l x)n


 (B-2010) 
SCELL 2016 TÍCH PHÂN 
27, 
e
1
2
I (2x )ln xdx
x
  (D-2010) 
29, 
0
2
3 1 xsin x
I dx
cos x


  (B-2011) 
31, 
2
3
1
1 ln(x 1)
d
x
I x
 
  (A-2012) 
33, 
2
31
4
0
x
x x
I dx
3 2

 
 (B-2012) 
35, 
2
1
0
I dxx 2 x  (B-2013) 
37, 
x2
0
e sin x
I dx
1 sin 2x



 
39, 
2 x1
1
2 x
x
2 e ex
I dx
1 e
x

 


 
41, 
1 cosx2
0
(1 sinx)
I ln dx
1 cos x




 
43, 
2
3
1
1 x(2ln x 1)
x 1)
I dx
x(




 
45, 
1
0
21
I x 1 dx
x 1
x 
   
 
 
 
47, 
e
1
(x 1)ln x 2
I dx
1 x ln x
 


 
49,
2
4
0
sin 4x
I dx