[r]
(1)2
1
x x
(2x 1)e
dx
(ĐH Dợc_81 )/4
3
dx
dx
I
J
cos x
cos x
(§HBK TH_82)/
0
sin x cos x 1
dx
sin x 2cos x 3
(Bé§Ị)1
3
(3x 1)dx
(x 3)
(Bé §Ị)1
3
xdx
(x 1)
(Bé §Ị)1
x
1
dx
x
1
(Bé §Ị) 2x0
e sin xdx
(Bé §Ị)/
0
cos xdx
2 cos 2x
(Bé§Ị)2
1
dx
x 1
x 1
b
x ln xdx
(BK_94)/
2
x cos xdx
BK_94)2
2 /
dx
x x
1
(BK_95)0
cos x sin xdx
Cho hàm số:
f(x)
sin x.sin 2x.cos5x
Tìm họ nguyên hàm g(x)Tính tích phân:
2 x
f(x)
I
dx
e
1
(BK_99)ln 2x x
e
dx
e
1
(BK_00)1
0
x
1
dx
x 1
(XD_96)/
0
cos x 2sin x
dx
4cos x 3sin x
(XD_98)1
3dx
1 x
(XD_00)1
4
0
dx
x
4x
3
(§H Má_95)/
2
/
tg x cot g x 2dx
(§H Má_00)/
/
dx
sin x sin(x
/ 6)
(§H Má_00)6
/
x /
sin x
cos x
dx
6
1
(§H Má_01)57
1
3dx
1 x
(§H LuËt _00)
58
1
2 2x
(1 x) e dx
(§H C§_98) 59
2 / /
2 x
0 0
dx
dx
(2x 1)cos xdx
1 sin 2x
e
1
(§H C§_99)
60
1
2x
0
dx
ln(x 1)
dx
e
3
x
(§H C§_00)
61
/ x
2x
/
1 sin 2x cos2x
(1 e )
dx
dx
sin x cos x
1 e
(§H NN I_97)
62
/ /
2x
0
cos xdx
e sin3xdx
1 cos x
(§H NN I_98B)
63
1
19
x(1 x) dx
(§H NN I_99B)
64
2 /
2
1
dx
xtg xdx
x(x
1)
(§H NN I_00) 65
6 /
4 /
cos x
dx
sin x
(§H NN I_01A)
66
2
1
ln(1 x)dx
(ĐH Lâm NghiÖp_97)
67
1
x
sin x
dx
x
1
(ĐH Lâm Nghiệp_98)
68
/
0
dx
2 sin x cos x
(ĐH Lâm Nghiệp_00) 69
1
x sin xdx
(2)2
ln(x 1)
dx
x
(ĐH Hàng Hải_00)/
3
sin xdx
sin x
cos x
(§H GT VT_95)3
5
0
x x dx
(§H GT VT_96A)1/ 3x
2
0
x
1
5
dx
4x 1
sin (2x 1)
(§H GT VT_97)
7 /3
x 1
dx
3x 1
x
4
(10
sin x)dx
(§HGTVT9/
2 /
x cos x
dx
4 sin x
(§H GT VT_00)/
3
5 cos x
4sin x
dx
(cos x
sin x)
(§HGT VT_01)/
4
0
cos x
dx
cos x sin x
(§H GTVT HCM_99)/ /
sin x
dx
cos x
(§H GTVT HCM_00)2 2
x
1
dx
x x
1
(HV BCVT_97)/
2
sin x cos x
dx
1 cos x
(HV BCVT_98)1 x
x
dx
1 2
(HV BCVT_99)2
x sin x cos xdx
(HV NH_98)/
2
0
I
cos x cos 2xdx
/2
0
J
sin x cos 2xdx
HV NH HCM_98)/
x sin x
dx
cos x
1
2
x
dx
x
x
1
70
a
2 2
0
x
a
x dx
(a 0)
(§H SP HN I_00) 71
1
3
0
x
1 x dx
(§H SP HN I_01B)
72
2
xdx
x
2
(ĐH THợp_93)
73
0
x sin xdx
(ĐH THợp_94)
/
0
dx
sin x cos x
74
1
0
dx
1
x
(§H QG_96)
75
/
2
0
sin xdx
dx
x 1
x
1 cos x
(§H QG_97A, B, D)
1
2
0
x dx
xdx
4 x
4 x
76
1 /
3
x
0 0
dx
sin x
x x dx
dx
e
1
cos x
(§H QG_98) 77 TÝnh
2
/ /
0
sin x
cos x
I
dx; J
dx
sin x
3 cos x
sin x
3 cos x
Từ suy ra:
5 / 3 /
cos2x
dx
cos x
3 sin x
(§H QG HCM_01A)
78
/ /
x
0
2cos xdx
5e sin 2xdx
3 2sin x
(§H SP II _97)
79 Cho f(x) liªn tơc trªn R :
f (x) f ( x)
2 2cos 2x
x R
TÝnh3 /
3 /
f (x)dx
(3)(HV NH HCM_00)
2
0
1 sin xdx
(ĐH NThơng_94)
1
2
0
dx
x
3x 2
dx
x 3
(x
3x 2)
(ĐH NThơng_99)
/
3
cos2x
dx
sin x
cos x
2
(ĐH NThơng_00A)1
2
x
2x
10x 1
dx
x
2x 9
(§H NTh¬ng_00)1 2
x
3x 10
dx
x
2x 9
/
6
0
sin 4x
dx
sin x
cos x
(ĐH NThơng_01A)
2
2
I
ln(x
1 x ) dx
(§H KT_95)1
5
x (1 x ) dx
(§H KT_97)/
4
0
dx
I
dx
cos x
x
1
1
0
x
J =
(§H TM_95)1
0
x xdx
(§H TM_96)7 ln x
x
3
0
x
1 e
I
dx
dx
1 e
1 x
J=
(§H TM_97)ln x
dx
e
5
(§H TM_98A4
dx
x (1 x)
(§H TM_99)/
3
4sin x
dx
(sin x cos x)
(§H TM_00)11
sin xdx
(HV QHQT_96)/
2
0
sin x cos xdx
(§H NN_96)e
2 1/
ln x
dx
(1 x)
80
/
10 10 4
0
(sin x sin x cos x sin x)dx
(§H SP II _00)
81
3
2
1
3x
2
dx
dx
x 4
x 2
x
1
(C§ SP HN_00) 82
1 /
2
0
(sin x 2cos x)
x
1 x dx
dx
3sin x cos x
(C§ SP HN_00)
83 2
0
sin x cos xdx
(C§ SP MGTW_00 )
84
/
0
1 sin x
dx
ln(
)dx
1 cos x
x(1
x )
(C§ SP KT_00)
85
1
2
x
1
1 x
1 x arcsin xdx
dx
1 2
(C§ PCCC_00)
86
2
1
x x
1
(e sin x e x )dx
(§H TN_00)
87
3
2
t
dt
t
2t 1
(§H SP Vinh_98)
88
1
2
1/
1 x
dx
x
1dx
1 x
(§H SP Vinh_99)
89
1 2
(x
x)dx
x
1
(§H H§_99)
90
/
0
dx
sin x cos3xdx
1 tgx
(§H H§_00)
91
2
ln x
dx
x
(§H HuÕ_98)
92
/
6
0
sin x
dx
sin x cos x
(4)(§H NN_97)
2
/
cos x cos 4xdx
(§H NN_98)
3
7 / 3
x 1
dx
3x 1
(§H NN_99)
1
2
(1 x
x ) dx
(§H NN_01D)
5
/
x
e cos xdx
(ĐH Thuỷ Lợi_96)
6
0
1 cos2xdx
(§H Thủ Lỵi_97)
3 2
4
1
x
1
dx
I
dx
x
x
1
J =
x(x
1)
(ĐH Thuỷ Lợi_99)
/
ln tgx dx
(ĐH Thuỷ Lợi_01A)
9
/
2
0
3sin x 4cos x
dx
3sin x 4cos x
(ĐH Thuỷ Lợi_00)
3
3
0
x
2x
xdx
10
/
sin x.cosx
dx
sin 2x
cos2x
(ĐH Văn Hóa_01D) 11
/
2 2
0
sin x cos x
dx a,b 0
a cos x b sin x
;
(HV TCKT_95)
12
2 / 2
x
dx
1 x
(HV TCKT_97)
13
/
2
x(2cos x 1)dx
(HV TCKT_98)
93
2
7
dx
2 x 1
(§H §N_97)
94
/
2
0
cos x
cos xdx
dx
1 sin x
1 cos x
(§H §N_98)
95
/
4
0
dx
x ln xdx
cos x
(§H §N_99)
96
/ /
/
sin x cos x
sin xdx
dx
sin x cos x
1 2cos x
(§H §N_00)
97
1
2
x
x arctgx
dx
1 x
(ĐH Tnguyên_00) 98
2
2 10
0
x 1
dx
(1 3x)(1 2x 3x ) dx
3x 2
(ĐH Quy Nhơn)
99
2
e e
1 1
2 ln x
ln x
dx
sin xdx
dx
2x
x
(ĐH Đà Lạt)
100
2
2
0
x
1
x
x
1dx
dx
x 1
(ĐH Cần Thơ)
/ / /
4
0 0
cos x
sin x
sin 4x
dx
dx
dx
sin x cos x
sin x cos x
sin x cos x
2
e 1
3 x
1 0
ln xdx
x
x e dx
dx
1
x
x(ln x 1)
101
/ /
2
0
sin 2x(1 sin x) dx
sin x cos x(1 cos x) dx
2
/
2
x
0
x
2x
(x
1)sin xdx
dx
(ĐH Thuỷ sản NT)
102
/ /
2
0
sin xdx
dx
x cos xdx
cos x 3
(§H (5)14
/
2 /
cos x sin x
1
dx
dx
3 sin 2x
x
1
1
0
x
(HV TCKT_99)
/
4
0
sin x 7cos x 6
dx
x cos xsin xdx
4sin x 3cos x 5
15
1
4
x
dx
x
x
1
(HV TCKT_00)
16
/ 2
(x
1)sin xdx
(§H Më_97)
17
/
0
4sin x
dx
1 cos x
(§H Y HN_95)
18
1
2
2x x
1/
dx
1 x dx
e
e
(§H Y HN_98)
19
4 /
dx
x
sin
2
(§H Y HN_99) 20
/ 2
4
2
/
x
tg xdx
dx
x
7x 12
(§H Y HN_00) 21
3 2
x
1dx
(§H Y HN_01B) 22
1
x
1dx
(§H Y TB_97B)
23
/
2
dx
2 cos x
(§H Y TB_00)
24
1
2
(1 x ) dx
(§H Y HP_00)
25
2 /
x /
x sin x
I
dx
1 2
(ĐH Dợc_96 )
/
4
3
0
xdx
cos 2xdx
(2x 1)
103
1
0
xsin x
dx
x xdx
9 4cos x
(ĐH Y Dợc HCM) 104
2 x
-sin xdx
1 sin xdx
1 3
(ĐH Ngoại thơng)
e
2
1
x ln xdx
x x dx
105
2
0
x sin xdx
arctg(cos x)dx
1 cos x
(§H SP HCM)
/
4
0 0
sin xdx
4x 11
dx
cos xdx
sin x cos x
x
5x 6
106
1 x
3 x
0 0
e
dx
x sin xdx
x sin xdx
1 e
(§H QG HCM)
1/ /
2
0
x
sin 2xdx
dx
x
1
1 sin x
/ /
4
0 0
sin 2x
xdx
dx
sin xdx
2x 1
1 cos x
/
2 x
0
sin x cos xdx
e sin ( x)dx
107
1
x 2x
2
0
1
e dx
(x 1)e dx
1 x
(§HDL NN Tin Häc)
2
x
0
x dx
e dx
108
1 x
2 20
x
0
(1 e )
1 x dx
x(x 4) dx
dx
e
(DL)
e ln 2x x
2x x
1
1 ln x
e
3e
dx
dx
x
e
3e
2
(6)26
/
x
1 sin x
e dx
1 cos x
(ĐH Dợc_00) 27
10
x lg xdx
(ĐH Dợc_01A)
28
x
ln3
2 x
0
dx
x.e dx
e
1
(HV QY_97) 29
3
3
2
2
dx
sin x
dx
x x
1
4 5x
(HV QY_98)
30
1/
0
dx
1 cos x
(HV QY_99)
31
/
2 /
cos x ln(x
1 x )dx
(HV KT MËt M·_99)
1 /
6
0 /
x
1
dx
dx
x
1
sin x cos x
32
1
xtg xdx
(HV KT MËt M·_00)
33
1
2
xdx
(x 1)
(HV KTQS_95)
34
/ 4
4sin x
dx
1 cos x
(HV KTQS_96)
35
/ 3 /
sin x sin x
cot gxdx
sin x
(HV KTQS_97)
36
1
2
dx
1 x
1 x
(HV KTQS_98)
37
/
0
cos x ln(1 cos x)dx
(HV KTQS_99)
109
3
2
x
dx
x
1
(Dù bÞ_02)
110
x ln
3 x
e
dx
e
1
(Dù bÞ_02) 111
0
2x
1
x e
x dx
(Dù bÞ_02) 112
/
6
0
1 cos x.sin x.cos xdx
(Dù bÞ_02)
113
2
dx
x x
4
(§Ị chung_03A ) 114
/
xdx
1 cos2x
(Dù bÞ_03) 115
1
3
0
x
1 x dx
(Dù bÞ_03) 116
2 /
0
1 2sin x
dx
1 sin 2x
(§Ị chung_03B) 117
2x ln
x ln
e
dx
e
1
(Dự bị_03)
118 Cho hàm số: x
3
a
f(x)
bxe
(x 1)
, t×m a, b biÕtr»ng:
f '(0)
22
vµ1
f(x)dx
5
(Dù bÞ_03) 119
2
x
x dx
(§Ị chung_03D) 120
2
1 x
x e dx
(Dù bÞ_03) 121
2 e
x
1
ln xdx
x
(7)
1/
2
0
dx
(2x
1) x
1
38
2 b
2
a
x
dx
a
x
(a, b số thực dơng cho trớc) (HV KTQS_01A)39
a
2 2
0
x
x
a dx
,
a 0
(§H AN_96)
40
2
x sin xdx
2 cos x
(§H AN_97)
41
/
2
(2x 1) cos xdx
(Dù bÞ_05)
42
/
3
4
0
dx
(cos x sin x)dx
cos x
(§H AN_98)
1
2x
0
xe dx
x sin xdx
0
43
4
2
dx
x x
9
(§H AN_99) 44
2
2
0
3sin xdx
x x
1dx
(§H TD TT_00)
45
2
2
(x ln x) dx
(PV BC TT_98)
46
3
e
1
ln ln x
dx
x
(PV BC TT_98)
47
/
2
1 sin 2x
dx
cos x
(PV BC TT_00)
48
1
xtg xdx
(HV KT MËt M·_00)
122
2
x
dx
1
x 1
(§Ị chung_04A) 123
e
1 3ln x.ln x
dx
x
(§Ị chung_04B) 124
3 2
ln x
x dx
(§Ị chung_04D) 125
/
sin 2x
sin x
dx
1 3cos x
(§Ị chung_05A) 126
/
sin 2x.cos x
dx
1 cos x
(§Ị chung_05B) 127
/ sin x
e
cos x cosxdx
(§Ị chung_05D) 128
7
x
2
dx
x 1
(Dù bÞ_05) 129
/ 2
sin xtgxdx
(Dù bÞ_05) 130
/ cos x
e
sin 2xdx
(Dù bÞ_04) 131
4
2
x
x
1
dx
x
4
(Dù bÞ_05) 132
/
sin x
tgx
e
cos x dx
(Dù bÞ_05) 133
e
x ln xdx
(Dù bÞ_05) 134
/
2
0
sin 2x
dx
cos x
4sin x
(Dù bÞ_05) 135
6
dx
2x 1
4x 1
(Dù bÞ_06) 136
1
2x
x
2 e dx
(8)49
1
2
xdx
(x 1)
(HV KTQS_95)
50
/ 4
4sin x
dx
1 cos x
(HV KTQS_96)
51
/ 3 /
sin x sin x
cot gxdx
sin x
(HV KTQS_97)
52
1
2
dx
1 x
1 x
(HV KTQS_98)
53
/
0
cos x ln(1 cos x)dx
(HV KTQS_99)
1/
2
0
dx
(2x
1) x
1
54
2 b
2
a
x
dx
a
x
(a, b lµ sè thùc d¬ng cho tríc) (HV KTQS_01A)55
a
2 2
0
x
x
a dx
,
a 0
(§H AN_96)
56
2
x sin xdx
2 cos x
(§H AN_97)
(§Ị chung_06D) 137
/
(x 1)sin 2xdx
(Dù bÞ_06) 138
2
x
2 ln xdx
(Dù bÞ_06) 139
ln5
x x
ln3
dx
dx
e
2e
3
(Dù bÞ_06) 140
10
dx
x
2 x 1
(Dù bÞ_06) 141
e
3 ln x
dx
x ln x
(Dù bÞ_06)
142
5
3
x
2x
dx
x
1
(C§ SP_04A) 143
3
x
2
x
2
(C§ GTVT_04) 144
4
5
x
dx
x
1
(C§ KTKT_04A)
145
3
3
dx
x
x
(Dù bÞ_04)
146
ln
x 2x
ln
e
1.e dx
(Dù bÞ_04)
147
2
0
x.sin xdx
(Dù bÞ_05)
148
1
x xdx
(Dù bÞ_04)
149
3
e
1