Tong hop tich phan luyen thi dai hoc
Trang 1*BÀI TẬP LUYỆN THI:
1,
3
0
I= ∫x (1 x) dx−
3,
1
2 3 0
I= ∫(1 2x)(1 3x 3x ) dx+ + +
5,
1
0
2x 9
x 3
+
=
+
∫
7,
2
1
0
x 3x 2
x 3
=
+
∫
9,
2
2
1
5
x 6x 9
=
∫
11,
2 1
2 0
x
4 x
=
−
∫
13,
2
2
1
1
x 2x 2
=
∫
15,
1
2
0
4x 1
x 5x 6
+
=
∫
17,
2
2
0
x
x 1
=
−
∫
19,
3 2
2
1
3x
x 2x 1
=
∫
21,
1
2
1
(x 1) (+ +
= ∫
23,
2
2
x 1
I ( ) dx
x 2
−
=
+
∫
2,
1
0
I =∫x (x −1) dx
4,
1
0
I =∫ x (1 x ) dx−
6,
3
0
x 1
2x 3
+
=
−
∫
8,
1 2 0
3
x 4x 5
=
∫
10,
1
2 0
x
4 x
=
−
∫
12,
3 3 2 1
x
x 16
=
−
∫
14,
2 2
2 1
x
x 7x 12
=
∫
16,
1 3 2 1
1
9x 6x 5
−
=
∫
18,
2 3 2 0
3x 2
x 1
+
=
+
∫
20,
3 2 3
1
x 3
=
+
∫
22,
1 3 0
3
x 1
=
+
∫
24,
2 1 3
2 x 5
I = x + + dx
+
∫
CHUYÊN ĐỀ NÂNG CAO
Giải Tích 12
CHUYÊN ĐỀ NÂNG CAO
Giải Tích 12
* TÍCH PHÂN LUYỆN THI ĐẠI HỌC *
Trang 225,
1
2 0
x 2x 10x 1
x 2x 9
=
∫
27,
1
2 5
1
2x 8x 26
−
=
∫
29,
1
3 0
x
(2x 1)
=
+
∫
31,
2
3
2
1
1
x
x d x
−
=
+
∫
33,
5
3
4
2 2
3x x
1
x 2 5x 6
+
=
∫
35,
2 1
4 0
(x 1)
(2 x 1)
−
=
+
∫
37,
1
2
5x
(x 4)
=
+
∫
39,
2
10 2 1
1
x(1 x )
=
+
∫
1
(1 )
=
+
∫
43,
2 2
4 1
1 x
1 x
+
=
+
∫
45,
2 2
4 1
1 x
1 x
−
=
+
∫
47,
7 3
2
x
1 x 2x
=
∫
49,
3
2 3
4
0
x
x 1
=
−
∫
51,
1
3
0
4x
(x 1)
=
+
∫
53,
3 1
0
x
(x 1)
=
+
∫
26,
1
2 0
x 3
(x 1)(x 3x 2)
−
=
∫
28,
4 2 1
1
x (x 1)
=
+
∫
30,
1
0
4x 1
x 2x x 2
−
=
∫
32,
2
1
x
=
+
∫
34,
1
3 0
x
(x 1)
=
+
∫
36,
99 1
101 0
(7x 1)
(2x 1)
−
=
+
∫
7 1
5 0
(1 x ) x
= +
∫
40,
4 3
4 1
1
x(1 x )
=
+
∫
42,
7 2
7 1
x(1
x
x )
1
=
+
−
∫
2001 2
1002 1
(1 )
x x
= +
∫
46,
4 1 6 0
x 1
x 1
+
=
+
∫
1 4 0
x I
x dx
=
∫
50,
2
1 5
2 2
4 1
x 1
x x 1
+
+
=
∫
52,
1
0
1
(x 4x 3)
=
∫
54,
2
2 2 0
1
(4 x )
=
+
∫
Trang 355,
4
1
6
0
x 1
x 1
−
=
+
5 2
5 1
1 x
x(1 x )
−
=
+
∫
1,
1
0
x 1 x
I= ∫ − dx
3,
1
0
x 1 x
I= ∫ − dx
0
x 1 x
I= ∫ + dx
7,
2
0
I= ∫x (x +4) dx
9,
7
3
3
0
x 1
dx 3x 1
+
= ∫
11,
2
3 1
1 dx
x 1 x
I=
+
∫
13,
2 3
2 5
1
x x 4
=
+
∫
15,
2
2 0
x dx
I
1 x−
= ∫
17,
2
2 2
3
1 dx
x x 1
I
−
= ∫
19,
3 7
0
x d
1 x+
= ∫
21,
1
0
x dx 2x 1
I
+
= ∫
23,
1
2 0
1 x d
I= ∫ − x
25,
3
1
1
x 4 x
=
−
∫
2,
9 3 1
x 1 x
I =∫ − dx
4,
1
0
I=∫x 1 x dx+
6,
1
0
x 1 x
I =∫ + dx
8,
2
3 2 0
(x 3) x 6x 8 d
I=∫ − − + x
10,
2 1
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
3x 2
+
=
+
∫
18,
4
2 7
1
x 9 x
=
+
∫
20,
6
2
2 3
1
dx
x x 9
I
−
= ∫
22,
3 2 0
x 2x
x 1
+
=
+
∫
24,
3 8
1
x 1
x
+
=∫
26,
1
2 3
(1 x )
I =∫ − dx
Trang 427,
1
2 0
1
4 x
=
−
∫
29,
2
2 2
2 0
x
1 x
=
−
∫
31,
1
2
0
x 1
I= ∫ + dx
33,
2
2 1
I 4x x 5 dx
−
= ∫
35,
2
3
0
x 1
x x
1
+ +
= ∫
37,
2 4
4 3
3
d x
I= x −4 x
∫
39,
4
1
2
dx
x 5 4
I
− + +
= ∫
41,
2
0
x
2 x 2 x
=
∫
43,
2
1
x
1 x 1
=
∫
45,
1
0
3
x 9 x
=
+ −
∫
47,
1
3 3
1
x 4 (x 4)
−
=
∫
49,
6
4
x 4 1
dx
x 2 x
I
2
−
= ∫
51,
2 2
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
= ∫
28,
3 2
2 1
2
1 dx
I
x 1 x−
= ∫
30,
2
1
x 4 x d
−
−
= ∫
32,
2
2 0
I =∫ 4 x dx+
34,
1
2 0
3x 6x 1dx
I=∫ − + +
36,
2 1
0
x
(x 1) x 1
=
∫
38,
3 2 2
1
x 1
=
−
∫
40,
1
0
1
dx
x 1 x
I
+ +
=∫
42,
7
2
1
dx
2 x 1
I
+ +
=∫
44,
3 1
2 0
x
x 1 x
=
∫
46,
1
2 1
1
1 x 1 x
−
=
∫
2 1
x 1
dx x
I = +
∫
50,
1 2
2 1
2
1
dx (3 2x) 5 12x
I
4x
= ∫
52,
2 1 2 0
x x
4
+
=∫
54,
2 4 1
x x
dx x
I = −
∫
56,
3
2 1
1
dx 4x x
I
−
=∫
Trang 557,
2
2 2
2x 5
dx
x 4x
I
13
−
−
= ∫
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,
2 5
1
x 1
dx
x 3x 1
+
= ∫
67,
2
3
0
2x x 1
dx x
I
1
+ − +
= ∫
69,
4
I
(1 1 2x
x 1
x ) d
=
+
∫
71,
2
2 0
2 3x x
dx x
x
I
x 1
− +
= ∫
73,
1
2 1
1
dx
1 x 1 x
I
− + + +
= ∫
75,
1 3
4 1
3
x I
x
(x )
dx
−
= ∫
77,
2
27
3 1
I x 2 dx
x+ x
=
∫
81,
1
3
0
1
dx ) 1
I
(1 x x
=
∫
83,
4
2 2
2 3
x
dx 1
(x ) x 1
x
I
= ∫
85,
2 1
6 0
x
dx
4 x
I
−
= ∫
58,
2 1
2 2
2
1 x
dx x
I = −
∫
2
2 5
2
( ) 4 dx
−
= ∫
62,
2 1
0
x x
dx
1 x x
+
=∫
64,
1
0
1 x
dx
1 x
+
=∫
66,
3
0
x 3
dx
3 x 1
I
x 3
− + + +
=∫
68,
2 1
0
x
dx (x 1) x
2
1
I
= ∫
70,
1
3 0
2
(x 1) 2x x
I= ∫ − −x d
72,
8 2 3
x 1
dx
x 1
+
= ∫
74,
2
3 2 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
1
+ +
=∫
=
∫
82,
2 2
4 1
x 2015x
d
x I
= ∫
1
(3 4 )
d
x
I = − −
∫
86,
2 1
2 0
x
dx
3 2 x
I
x
= ∫
Trang 6Dạng 3: Tích phân các hàm số lượng giác
4
I 3tan x dx
π
π
= ∫
6
(2cot x
π
0
2
I sin x.cos x xd
π
= ∫
0
2
I (2cos x 3sin x)dx
π
0
I cos2x(sin x cos x)dx
π
11, 2
0
I sin x.sin 2x.sin 3xdx
π
= ∫
0
cos x.cos 4x dx
I
π
= ∫
0
sin 2x(1 sin x) dx
I
π
+
= ∫
2
cos x cos x cos
π
π
−
−
= ∫
4
tan xdx
I
π
π
= ∫
0
tan x dx
I
π
= ∫
0
I sin x dx
π
= ∫
0
cos x dx I
π
6,
4
6
I cot 2 x dx
π π
= ∫
6
2
tan x cotx
π
π
−
−
= ∫
6
tan x cot x
π
0
1 cos x sin x.cos xd
π
−
= ∫
14, 3
0
sin x.tan xdx I
π
= ∫
0
sin x cos x(1 cos x)
π
+
= ∫
0
cos x sin xdx I
π
= ∫
20,
4 3
6
cot x dx I
π π
= ∫
22, 3
2 4
tan x
dx cos x 1 cos x I
π
= ∫
Trang 723, 2 4
4
1
sin x
π
π
= ∫
25, 3
0
1
dx cos x
I
π
= ∫
27, 4
6 0
1
cos x
π
= ∫
29, 4
3 0
1
dx cos x
I
π
= ∫
0
4sin x
dx
1 cosx
I
π
+
= ∫
33, 2
4 0
sin 2x
dx
1 cos x
I
π
+
= ∫
35, 2
0
sin 2x.cos x
dx 1
I
cos x
π
+
= ∫
37, 2
0
sin 2x sin x
dx 1
I
3cos x
π
+ +
= ∫
0
1 2sin x
dx
1 sin 2x
I
π
−
+
= ∫
2 0
sin x
dx cos x
I
π
= ∫
0
sin x
dx cos 1
I
x
π
+
= ∫
6
cos 2x
dx
1 cos 2x
I
π
π −
= ∫
0
sin x cos x
dx sin x cos x 1 I
π
−
= ∫
26, 2
0
sin x cos x cos x
dx sin x 2
I
π
+ +
= ∫
28, 2
0
cos x
dx
2 cos 2x I
π
+
= ∫
30, 6
2 0
cos x
dx
6 5sin x
I
sin x
π
= ∫
32, 2
4
cos x sin x
dx
3 sin 2x I
π π
+ +
= ∫
6
1
dx sin x co
I
t x
π π
= ∫
0
sin x
dx (tan x 1)
I
.cos x
π
+
= ∫
0
sin x
dx cos x I
π
= ∫
40, 2
4 0
sin 2x
dx
1 sin x I
π
+
= ∫
42, 2
0
sin 2x
dx
1 cos x I
π
+
= ∫
2 0
sin x
dx (sin x 3) I
π
+
= ∫
46,
0
2 2
sin 2x
dx (2 sin x)
I
−π +
= ∫
Trang 847, 2
6
1 sin 2x cos 2x
dx cos x sin x
I
π
π
+
= ∫
2 0
sin x.cos x
dx co
I
s x 1
π
+
= ∫
51,
3
3
1
dx sin x 9cos x
I
π
π
= ∫
6
1
dx sin x cos x
I
π
π
= ∫
55, 4
0
sin 2x
dx sin x 2cos x
I
π
+
= ∫
0
sin x sin x
d
cos 2x
π
+
= ∫
59, 2
2 0
sin x
dx cos x 3
I
π
+
= ∫
61, 4
0
1 dx
2 tan x
I
π
+
= ∫
63, 2
2 0
cos x
dx cos x 1
I
π
+
= ∫
0
cos x
dx cos x 3c
I
os x 3
π
= ∫
67, 2
3
1
dx sin x 1 cos x
I
π
= ∫
69, 2
0
sin x
dx
1 sin x
I
π
+
= ∫
48,
3 3
6
4sin x
dx
1 cos x I
π
π −
= ∫
50,
3
2 6
1
dx cos x.sin x I
π π
= ∫
52, 2
0
sin 3x
dx cos 1
I
x
π
+
= ∫
54, 3
2 4
tan x
dx cos x cos 1
I
x
π
= ∫
0
tan x 1 ( ) dx tan 1
I
x
π
− +
= ∫
58, 2
0
sin 2x sin x
dx co
I
s3x 1
π
+ +
= ∫
60, 3
2 0
cos x
dx
1 sin x I
π
−
= ∫
62, 2
0
4cos x 3sin x 1
dx 4sin x 3cos x 5 I
π
= ∫
64,
2
4
0
sin xdx I
π
= ∫
66, 2
0
1 sin x
dx
1 3cos x I
π
+ +
= ∫
2
cos x 1
dx cos x 2 I
π
π
−
− +
= ∫
70, 2
0
cos x
dx sin x c
I
os x 1
π
= ∫
Trang 971, 2
0
cos x
dx
7 cos 2x
I
π
+
= ∫
73,
2
0
sin x
dx x
I= π∫
75, 2
0
1 dx
2 sin x
I
π
+
= ∫
77, 2
0
1 dx
2 cos x
I
π
−
= ∫
3
cos x
dx (1 cos x)
I
π
π −
= ∫
81,
2 4
3
2
cos x I
c
sin x 1
d
os x x
π
π
−
−
= ∫
6
1
2 sin x sin dx
π
π
85,
2
0
1 sin x
I= ∫π + dx
2
I πsin x.(2 1 cos2x )dx
π
89, 4
0
I
x cos
sin 4x
dx
sin x
π
=
+
∫
91,
3
1
dx
2 3 sin x
I
cos x
π
= ∫
0
1 3 sin 2x 2 d
π
= ∫
72, 2
0
cos x
dx cos x 1 I
π
+
= ∫
74, 2
0
cos x
dx
2 cos x I
π
−
= ∫
0
cos x
dx cos 1
I
x
π
+
= ∫
6 0
sin x
dx cos x I
π
= ∫
80, 2
0
1
dx 2cos x si
I
n x 3
π
= ∫
82, 3
8
cot x tan x 2tan2x
dx sin 4x
I
π π
= ∫
84, 6
0
1
dx 2sin 3
I
x
π
−
= ∫
0
I (cos x 1)cos xdx
π
0
cos x sin 2x 3 8
dx sinx co
I
s x
π
−
= ∫
90, 2
3 0
sin x
dx (sinx 3
I
cos x)
π
+
= ∫
92, 6
0
1
dx sinx 3 cos x I
π
+
= ∫
94, 4
0
cos x sin x
dx
3 sin 2x I
π
−
−
= ∫
Trang 1095,
2
3
0
sin x
dx cos x sin
I
x 3
π
+
= ∫
97, 6
0
tan(x )
4 dx cos 2x
I
π −π
= ∫
99,
2
4
0
tan x
dx cosx
I
cos x 1
π
+
= ∫
3sin x 4cos x
dx 3sin
I
x 4cos x
π
+
+
= ∫
4
sin(x )
4 dx 2sin
I
x cos x 3
π
π
π +
−
= ∫
3
cos x
dx (1 cos x)
I
π
π −
= ∫
96,
2
2
I
cos x 4sin x
sin 2x
dx
π
=
+
∫
98,
2 4
0
I
cos
sin x
dx 5sin x x 2cos x
π
=
+
∫
0
tan
dx cos 2x
x I
π
= ∫
3 0
cos 2x
dx (cos x si
I
n x 3)
π
= ∫
4
I
x.cos
1
dx
sin x
π π
= ∫
106,
3
6
cot x
dx sin x.sin(
I
x ) 4
π
= ∫
1,
x
ln 2
x 0
1 e
1 e
−
=
+
∫
3,
2x
1
x
0
e
dx
e 1
I −−
+
= ∫
5,
ln 3
x 0
1 d
e +1
= ∫
7,
2
x 1
x
1 e
I 1− d
−
= ∫
9,
2x
2
x
0
e
dx
e 1
I
+
= ∫
11,
x 1
x
0
e
e 1
−
−
=
+
∫
13,
1
3x 1
0
I= ∫e + dx
2,
ln 2 x 0
e 1dx
I = ∫ −
4,
1 x 0
1 dx
e 4
I
+
=∫
6,
x
ln 3
0
e
dx (e 1)
I
+
= ∫
8,
1
x 0
1
3 e
=
+
∫
10,
1
0
1
e e
=
+
∫
12,
x 2 1
2x 0
(1 e )
1 e
+
= +
∫
14,
4 x 1
I=∫e dx
Trang 1115,
2x
ln 5
x
ln 2
e dx
e 1
I
−
= ∫
17,
x 1
0
e
e e−
=
+
∫
19,
x
ln 3
0
e
(e 1) e 1
=
∫
21, 4 tan x 2
2 0
e
dx cos x
π
= ∫
23,
2
e
2 e
1 1
ln x
ln x
25,
e
1
ln x 2 ln x
x
+
= ∫
27,
e
2 1
ln x
x(ln x 1)
=
+
∫
29,
2
e
1
ln x
ln x
= ∫
31,
2
2 0
I= ∫ln( 1 x+ −x)dx
33,
3ln 2
x
1
e +
= ∫
35,
e
1
3 2ln x
x 1 2ln x
−
=
+
∫
37,
5
2
ln( x 1 1)
x 1 x 1
− +
=
∫
39,
x x
2
1
2 2
4 4 2
−
−
=
∫
41, 2
0
I sin x.ln(1 cos x)dx
π
43, I 4ln(1 tan x)dx
π
16,
1
2
2x 0
3e e
1 e
+
=
+
∫
18,
1
2x 1
1
3 e
−
= +
∫
20,
e
1
1 3ln x ln x
x
+
=∫
22, 2 sin x2
4
I e sin 2x dx
π π
= ∫
24,
3 2 2
I =∫ln(x −x)dx
26,
e 2 1
I=∫ln xdx
28,
2
e
e
ln x
x
= ∫
30,
2 1
I ln(x x 1) dx
−
= ∫ + +
0
I e sin x cos xdx
π
= ∫
34,
ln 3
l
x
n
2
2
e
e 1 e 2
=
∫
36,
3 3 e
1
ln x
x 1 ln x
=
+
∫
38,
2 3x
ln 3
0
x
e
e 4e
e
3 1
2 −
=
− +
∫
40,
x 1
0
6
9 3.6 2.4
=
∫
42, 3
0
I sin x.ln(cos x)dx
π
= ∫
1
Trang 12Dạng 5: Tích phân từng phần
1,
e
2
1
I= ∫ln xdx
3,
0
I= π∫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−
0
I e sin xdx
π
= ∫
13,
3
2
0
I= ∫x ln(x 1)dx+
15,
2
4
0
I x sin x dx
π
= ∫
0
I x.tan xdx
π
= ∫
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
(x 1)
=
+
∫
25,
1
2
0
1 x
I x.ln dx
1 x
+
=
−
∫
27,
2 x
1
2 0
x e
(x 2)
=
+
∫
2,
3 2 2
I =∫ln(x −x)dx
0
I=π∫e sin xdx
1
3 x 0
I =∫x e dx
0
I=π∫ x sin x.cos xdx
10,
2 2 1
I =∫(x +x)ln x dx
0
I e sin 4x dx
π
= ∫
14,
4
2 1
I=∫(x 1) ln x dx−
16,
2
4
0
I x cos x dx
π
= ∫
18, 4
0
x
1 cos 2x
π
= +
∫
0
I =π∫x cos xdx
22,
0 2x 3 1
I x(e x 1)dx
−
24,
2 e
1
x 1
I ln xdx
x
+
26,
3
2 6
ln(sin x)
cos x
π π
= ∫
28,
2
1
I =∫cos(ln x)dx
Trang 1329, 2 sin x
0
I e sin 2xdx
π
= ∫
31, e
1
I cos(ln x)dx
π
= ∫
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
x 1
=
+
∫
0
1 sin x
1 cosx
π
+
=
+
∫
41,
1
3x 1
0
I= ∫e + dx
0
I e sin x cos x dx
π
= ∫
32,
2 5 1
ln x
x
=∫
34,
2
3
I cos x.ln(1 cos x)dx
π π
36,
2
3 2
1
ln( 1)
I x dx
x
+
=∫
38,
4
0
2
I=∫ln( x + −9 x)dx
40,
2
1x ln(x 1 )
1
x x
=
+
∫
42,
2 2
1
0
x 1dx
=
+
∫
1,
4
1
x 1
x
1 2
−
=
+
∫
3,
2 2x
cos x
e 1
π
−π
=
+
∫
5,
1
2 1
I ln(x x 1)dx
−
1
1
2 x
I ln( )dx
2 x
x
−
−
=
+
∫
9,
1
1
1
(x 1)(4 1)
−
=
∫
11, I 2 cosx ln(x x2 1)dx
π
2,
1
1
1
(e 1)(x 1)
−
=
∫
4,
2 x
sin x
3 1
π
−π
=
+
∫
6,
1
2 1
I ln( x a x)dx
−
8,
4 1
sinx x
1 x
−
+
=
+
∫
10,
3
3
1
(e 1)(x 3)
−
=
∫
12, 4 sin x
π
= ∫
Trang 1413, 2
3 3
x
I ( 1)ln( )dx
x x
π
−π
π −
π +
∫
0
x sin x
1 sin x
π
=
+
∫
0
I= π∫x sinxcos xdx
19, 2
0
sin x
sin x cos x
π
=
+
∫
21, 2
3 0
4sin x
(sin x cos x)
π
=
+
∫
0
I ( cos x sin x )dx
π
25, 2
0
sin x
cos x sin x
π
=
+
∫
0
3cos x
sin x cos x
π
=
+
∫
29, 4
3 0
2cos 2x
(sin 2x cos2x)
π
=
+
∫
0
4sin 4x
sin 4x cos 4x
π
=
+
∫
0
cos x sin x
sin x cos x
π
=
+
∫
35,
2
3
3
I x sinx dx
π
π
= ∫
0
x sin x
1 cos x
π
= +
∫
16,
3 2 0
x sin x
cos x
π
=∫
18,
4 2 0
x tan x
4cos x
π
=∫
0
cos x
cos x sin x
π
=
+
∫
22, 2
3 0
5sin x 4cosx
(sin x cos x)
π
−
=
+
∫
0
I (cos x sin x)dx
π
0
14
I (cos x sin x)dx
π
0
sin x
sin x cos x
π
=
+
∫
6
0
sin 3x
sin 3x cos 3x
π
=
+
∫
32,
2
x 1 0
1 x 3 x
1 2 −
=
+
∫
2 0
1
I tan (cosx) dx
cos (sinx)
π
∫
36, 4
0
I ln(1 tan x)dx
π
Trang 15(*) Tổng hợp Tích phân- Các Bài toán thi:
1,
2
1
I x 2x x 2 dx
−
3,
5
3
I ( x 2 x 2 )dx
−
5,
1
2
2
0
4x 1
x 3x 2
−
=
∫
0
sin 2 x sin x
1 3cosx
π
+
=
+
0
sin 2x.cosx
1 cos x
π
=
+
11,
3
1
ln x
x ln x 1
=
+
13,
10
5
1
x 2 x 1
=
15,
4
0
2x 1
1 2x 1
+
=
0
tan x
cos 2x
π
= ∫ (A-2008)
19,
2
3
1
l x
x
n
I= ∫ dx (D-2008)
0
2
I (cos x 1)cos xdx
π
23,
3
3 ln x
I
x 1)+ dx
+
= ∫ (B-2009)
25,
1
x 2
0
1 2e
x + + x
=
+
2,
0
I= π∫ cos x sin xdx
4,
2
0
I= ∫π 1 sin xdx+
6,
e
1 e
I= ∫ ln x dx
0
I sin x.tanxdx
π
0
I (tanx e cosx)dx
π
12,
6
2
1
2x 1 4x 1
=
14,
2
2
sin 2x
cos x 4sin x
π
=
+
16,
ln 5
ln 3
1
e 2e− 3
=
18,
1
0
2x
I= ∫(x 2)e dx− (D-2006)
e 3 1
I= ∫x ln xdx (D-2007)
0
sin(x )
4
sin 2 x 2(1 sin x cos x)
=
∫
24,
3 x 1
1
e 1
=
−
∫ (D-2009)
26,
e
ln x
x(2 l x)n
=
+
Trang 1627,
e
1
2
I (2x )ln xdx
x
29,
31 x sin x
cos x
π
+
= ∫ (B-2011)
3
1
1 ln(x 1)
d x
I= + + x
3 1
4
0
x
x x
3 2
=
1
0
I= ∫x 2−x dx (B-2013)
0
e sin x
1 sin 2x
π
=
+
∫
39,
1
1
2 x x
2x e e
1 e
x
−
=
+
∫
0
(1 sinx)
1 cos x
π
+
+
=
+
∫
3
1
1 x(2ln x 1)
x 1)
x(
+
=
+
−
∫
45,
1
0
2
1
x 1
x
+
∫
47,
e
1
(x 1)ln x 2
1 x ln x
=
+
∫
49,
2
4
0
sin 4x
5 4sin x cos x cos x
π
=
∫
2
e
1
1
x 4 ln x
−
∫
53,
1
3 0
1
(x 1+ ) (3x 1)+
= ∫
0
x sin x (x 1)cosx
x sin x cos x
π
+ +
=
+
30,
4
0
4x 1
2x 1 2
−
=
+ +
32, 4
0
I x(1 sin 2x)dx
π
2
1
2 1
I x ln x x
−
= ∫ (A-2013)
1
0
2
(x 1) x
1
+
+
= ∫ (D-2013)
38,
x 1
x 0
2
( x)e
x
x
e−
+
=
+
∫
40,
x 1
0
xe
1 (e )
=
+
∫
42, 4
ln(sin x cosx)
cos x
π
+
= ∫
44,
e
1
(x 1)lnx
x ln x 1
−
=
+
∫
46,
x 1
0
2
(2 9) 3.2 2
=
∫
0
2 1
2
x
2 4
(sin x cos
cos x(sin 2x cos x
x
) )
π
+
=
+
∫
e
1
ln x
ln x dx
x 1 x
+
∫
1
2 2
x
x
∫
Trang 1755, 4
0
tan x.ln(cosx)
cos x
π
= ∫
57, 2
0
sin x cosx 1
sin x 2cos x 3
π
=
∫
59,
2 e
x
x
ln
I= ∫ dx
61,
3
6
cot x
sin x.sin(x )
4
π
π
+
∫
63,
1
1
2
2
x x
x
∫
65,
2
2
1
x 1
x x 1
+
=
∫
67,
2 3
1
2
ln 1
I
x
d
+
= ∫
1
0
I= ∫(e− +x)e dx
71, 2
0
sin 2x
3 4sin x cos 2x
π
=
∫
4
xcos x
sin x
π
π
= ∫
75,
2
3
0
sin x
cos x 3 sin x
π
=
+
∫
77, 4
3 0
3cosx sin x
(sin x 2cos x)
π
−
=
+
∫
56,
2
1
4 2
4 0
x
x x
2
2 1
=
∫
0
I sin 2x.e dx
π
−
= ∫
60,
2 3
1
ln(1 ln x)
x
+
= ∫
4
1
cos x(1 e )
π
− π
−
=
+
∫
0
I cos3x.e dx
π
= ∫
66,
3 4
ln(5 x) x 5 x
= ∫
1
0
1
(2x 1) (x 2)+ +
2
+ =
x
t
70, 2
0
2
1
I= ∫(x 1) 1 2x dx+ −
6 0
cosx cos x
c so x x
π
−
= ∫
0
x x
I cos( )dx
π
= ∫
2 4
0
1 sin x
cos x
π
+
= ∫
78, 2
0
5sin x 4cosx
1 sin 2x
π
−
=
+
∫
Trang 1881, 2
2 2
1
2
0
x (1 x )
−
= ∫
83,
9
4
ln(x x )
x
−
= ∫
2
I cosx cosx cos xdx
π
π
−
87,
2
e
2 1
I= ∫ x ln xdx
89, 3
3 0
x tan( ).sinx(1 sinx)
4 2
cos x
= ∫
91,
5
1
2x 2x 1
2x 1 1
=
− +
∫
93, 2
0
I ln(1 cosx).sin 2 xdx
π
95,
1
4 1
2
2
I= ∫ln(3x +x ) 2− ln x dx
97,
l
2
n
x 0
e
1)
e 3
=
+
∫
99, 2
0
sin 2x
8sin x cos 2x 9
π
=
∫
101,
e
3 1
1
x 7ln x 1
+
∫
2 0
tan x
1 ln (cos x)
π
=
−
∫
x
0
cosx
e (1 sin 2x)
π
=
+
∫
82,
1 2
0
1 x
I x ln dx
1 x
+
=
−
∫
0
sin 2x
1 cos x
π
= +
∫
2
x cos x
4 sin x
π
π
−
+
=
−
∫
88,
2
3
1
x
x x 1 x
=
∫
90,
3
3
x
1 (1 x ) x
=
∫
92,
10
5
(x 2) x 1
x 2
=
−
∫
94, 2
3 0
2sin x cosx
(sin x cos x)
π
+
=
+
∫
96, 4
xcos 2x
(1 sin 2x)
π
=
+
∫
98,
3
cos x cosx sinx
1 cos x
+
∫
100,
(xsi n x c
x osx)
π
=
+
∫
102,
e
1
x (x 2)ln x
x(1 ln x)
+ +
=
+
∫
2 3
3 3
x (x sin x)sin x
sin x sin x
π π
+ +
=
+
∫
106, 2 x sin x2
1 sin 2x
π
+
= +
∫
Trang 19107,
2
e
e
1
x ln x.ln ex
= ∫
1
x
ln x ln 1
d x
∫
111,
x
5
x
2
e (3x 2) x 1
e (x 1) x 1
=
∫
113,
x e
x 1
xe 1
x(e ln x)
+
=
+
∫
115,
e
x 1
2 x ln x 1
x
x
dx
= ∫
2 0
x ln(x 1 x )
1 x
=
+
∫
119,
2 1 3
2
3
0
x
x
x
e
1
+
=
+
∫
2
0
I= ∫ x(2 x) ln(4− + +x ) xd
123,
1
2 0
ln(1 x)
x 1
+
=
+
∫
125,
e
0
(1 2x)ln x 3
1 x ln x
=
+
∫
0
sin 2x cos 2x
sin x cos x
π
+
=
+
∫
129,
2
2 0
1
2x 3x 4
=
∫
4 1
3 4 x
x
= ∫
133,
x
ln 6
x 0
e 1
e 3
+
=
+
∫
108,
2
3
e
2
2 xln x x ln 3
x(1 ln x)
x
=
−
∫
110,
x x e
x 1
ln x e (e ln x)
1 e
=
+
∫
1
0
1 x x
+
∫
0
2 2
(x 1)
x +
=
+
∫
116,
1x ln(x 1 x
x
)
1
+ +
=
+
∫
118,
2 3
e
1
( 1)ln x 2 1
2 x l x
n
=
+
∫
120,
3
0
2 2
x
) 3
9
=
+
∫
122,
3
0
I= ∫ x 1.sin x 1dx+ +
1
ln(x 3) x
I= + dx
∫
126,
2
3 1
x 2ln x
(x 1)
+
=
+
∫
0
I sin 4x ln(1 cos x)dx
π
130,
4
0
x 2
(x 1) 3x 4
+
=
∫
132,
2 5
1
x 1
x 3x 1
+
=
+
∫
134,
ln 2
0
x
e e− 2
=
∫
3