Embed Size (px)
Citation preview
http://www.facebook.com/hoitoanhoc 1
http://www.facebook.com/hoitoanhoc
2
43
1
1x dx
x
4
2
6
sin 2
dx
x
31
20 1
x dx
x
22
0
2sin (sin 1)
1 cos
x x dx
x
21
30 ( 1)
x dx
x
3
22 ( 1)
dx
x x
42
21
2 1 1
1
x x dx
x
21
2 20
3 3
1 3 1
x dx
x x x
3
1
2 lne x xdx
x
2
4
cot 1 ln(sin )x x dx
21
20
ln 1
1
x x xdx
x
3
2 20
sin 2
2sin 3cos
xdx
x x
41
60
( 1)
1
x dx
x
12
20
1 ln 11
xx dx
x
1
0
lnx x x x
x x
e e e edx
e e
1
2
0
1
4dx
x ln
2
0
1
e
x xe e dx 2
2
1
6 5 1 24 10x x x dx
22
2
sin 2 cosx xdx
6
0
1 1
2 cosdx
x
2
0
(1 3 )sin 2x xdx
24
1
2 3xdx
x
ln 3
0
1
1
e x
x
edx
e
4
1
4
4
dx
x x
26
0
os
cos 2
c xdx
x
26
0
sin
cos 2
xdx
x
64 3
1
1 xdx
x
1 2
0
x
x dx
e 2
4
1 sinxdx
0
1 cos2 1 cos2x x dx
1
2 2
1
3 3 2x x dx
4
1
1 2 3x x x dx
x
2
2
0
cosxe x dx
1
20 2 1
dx
x x
2
1
30
4 1
1
x x dx
x
3 21
21
3 9 8
2 5
x x x dx
x x
http://www.facebook.com/hoitoanhoc 2
4
20
1s inx
cosx dx
x
ln
ln21
e xx x x dx
x
2
2
0
sin sin cosx x x dx
2
2 2
0
sin sin 2cosx x x dx
4
2
0
sin 2 sin 4cosx x x dx
1
0
1
3 2 2 1
x dx
x x
1
10
dx
x x
32
21 1 1
xdx
x
3
22 1
dx
x x
33
20 1
x dx
x
4
2 1 2
dx
x x
1
20 4
dx
x
1
20 4
xdx
x
3
21 4
dx
x x
13 2
30 2 1
xdx
x
1
0 12
12ln
dx
x
xxx
2 3
3
ln 1
ln
e
e
xdx
x x
1
21
1 2ln
4 2
xdx
x x
4
2
6
dx
sin x cot x
6
0
sin x cos xdx
1 sin 2x
8
02
tan xdx
tan x 1
333
3
6
sin x sin xdx
sin x
1
0
dx
x 1 x 2
3
4
dx
x 1 x 2
32
4
3tan x dx
42
6
2cot x 5 dx
3 32
3
sin x sin xcot x dx
sin x
2
3
6
tan cotx x dx
2
0
2 2sin os.x c xdx
2
4
0
sin x dx
44
0
cos x dx
23
0
sin x dx
3
2 2
4sin cos
2 2
dx
x x
2
0
1 cos xdx
1 cos x
2
32
0
c2 3sis no x x dx
4
6
cot 2 x dx
41
21
tan
1
x x dx
x
10
1
11
xdx
x
4
2
1 ( )
11
x x dx
x
http://www.facebook.com/hoitoanhoc 3
2
1
ln 1 4 lne x x dx
x
2
0
cos .sinx x xdx
2
0
sin
1 sin
x xdx
x
22
0
cos 2 .sinx xdx
2
0
1 sin cos ( )n
x xdx n N
2
0
3cos (1 sin )
2 1 3sin
x xdx
x
32
21 1 1
xdx
x
1 57 4
0
1x x dx 2
1
1 ln .lne
e
x xdx
x
1
0
ln( 1)x xe e dx 4
2
6
ln(cos )
sin
xdx
x
1
0 212
1dx
x
2
4
4
sin
dx
x
2
2
sin x4
dx
sin x4
22sin x
4
e sin 2x dx
4
6
0cos
dx
x
2
4 4
0
cos2 sin cosx x x dx
tan 24
2
0cos
xe
x
23
0
cos xdx
6
22 3
dx
x x 9
1
2 23
dx
x 4 x
4
22
dx
x 16 x
22 2
1
x 4 x dx
22 3
0
x (x 4) dx
32
0
4sin xdx
1 cosx
13 2
0
x 1 x dx
15 2
0
x 1 x dx
1
0
xdx
2x 1
1
x0
1dx
e 4
2
x1
1dx
1 e
2x2
x0
edx
e 1
x1
x0
edx
e 1
e
21
ln xdx
x(ln x 1)
1 3
2
0
1 2x 1 3x 3x dx
2
3 2
0
x 3 x 6x 8 dx
ln 2x
0
e 1dx
24
4 3
3
x 4dx
x
22
22
x 1dx
x x 1
e
1
sin ln xdx
x
http://www.facebook.com/hoitoanhoc 4
1
0
1dx
3 2x 2
5
0
sin xdx
3
0
1dx
cos x
2x1
x0
edx
e 1
ln 3
x0
1dx
e 1 4
2
6
1dx
sin x cot x
3 2e
1
ln x 2 ln xdx
x
13 4 5
0
x (x 1) dx
7
3
30
x 1dx
3x 1
2
31
1dx
x 1 x 3
2 2
6
tan x cot x 2.dx
12 3
0
(1 x ) dx
1
2x0
1dx
e 3
xln 3
3x0
edx
e 1
02x 3
1
x e x 1 dx
26 3 5
0
1 cos x sin x.cos xdx
2 3
25
1dx
x x 4 4
0
xdx
1 cos2x
2xln 5
xln 2
edx
e 1
2e
1
x 1.ln xdx
x
21
0
xdx
x 1 x 1
2
0
sin x.sin 2x.sin3xdx
24 4
0
cos2x(sin x cos x)dx
2
3 3
0
cos x sin x dx
73
8 42
xdx
1 x 2x 2
0
4cos x 3sin x 1dx
4sin x 3cos x 5
93
1
x. 1 xdx
2
30
x 1dx
3x 2
6
0
xsin dx
2
2
0
xdx
2 x 2 x
33 2
0
x . 1 x dx
1
20
ln(1 x)dx
x 1
2
0
sin xdx
sin x cos x
e
1
cos(ln x)dx
22
0
4 x dx
2
1
xdx
1 x 1
http://www.facebook.com/hoitoanhoc 5
e
1
1 3ln x ln xdx
x
32
2
ln(x x)dx
e2
1
(ln x) dx
2e
e
ln xdx
x
2e
1
ln xdx
ln x
22
1
x ln(x 1)dx
3
23
1dx
x 3
1
20
1dx
4 x
2
4
0
sin xdx
3
2
6
ln(sin x)dx
cos x
2
1
cos(ln x)dx
22
0
ln( 1 x x)dx
3
22
1dx
x 1
38
1
x 1dx
x
33
21
xdx
x 16
6
20
cos xdx
6 5sin x sin x
2e
2e
1 1dx
ln xln x
32
4
x 4 dx
23 2
1
x 2x x 2 dx
3
4
4
cos2x 1dx
0
cos x sin xdx
2
0
1 sin xdx
3
4
4
sin 2x dx
0
1 sin xdx
31
2
1
ln x x 1 dx
2
0
xsin xdx
1 cos x
1
2 x1
1dx
(x 1)(4 1)
41
x1
xdx
1 2
2
4
0
xsin xdx
2
4
0
x cos xdx
62
0
x.sin x cos xdx
2 x1
20
x edx
(x 2)
2x 2
0
e sin xdx
22
1
1x ln 1 dx
x
e
21
e
ln xdx
x 1
1
2
0
1 xx.ln dx
1 x
http://www.facebook.com/hoitoanhoc 6
4
0
2014sin 2x.cos xdx
3
0
sin x.ln(cos x)dx
2e2
1
cos (ln x)dx
4
0
1dx
cos x
4
30
1dx
cos x
21
3 x
0
x e dx
22sin x 3
0
e .sin x cos xdx
2
40
sin 2xdx
1 cos x
34
22 5
0
sin xdx
tan x 1 cos x
1
20
3dx
x 4x 5
2
21
5dx
x 6x 9
1
25
1dx
2x 8x 26
1
0
2x 9dx
x 3
4
21
1dx
x (x 1)
0
2
2
sin 2xdx
(2 sin x)
1
20
x 3dx
(x 1)(x 3x 2)
1
30
4xdx
(x 1)
1
4 20
1dx
(x 4x 3)
33
20
sin xdx
(sin x 3)
33
6
4sin xdx
1 cos x
3
2
6
1dx
cos x.sin x
3
0
sin x.tan xdx
3
4
dx
sin 2x
3
2 2
3
1dx
sin x 9cos x
2
2
cos x 1dx
cos x 2
2
0
1 sin xdx
1 3cos x
2
0
cos xdx
sin x cos x 1
4
21
dx
x (x 1)
1
33
dx
x 4 (x 4) 33
0
sin xdx
cos x
1
0
x 1 xdx 6
4
x 4 1. dx
x 2 x 2
0
21
dx
x 2x 9
3
21
1dx
4x x
22
1
4x x 5 dx
2
22
2x 5dx
x 4x 13
http://www.facebook.com/hoitoanhoc 7
1
x0
1dx
3 e
2x 2
0
e sin x dx
2 x1
20
x edx
(x 2)
e
1
(1 x)ln x dx
e2
1
x ln x dx
1
e2
1
ln x dx
1
4x 2x2
2x0
3e edx
1 e
4
27
dx
x 9 x 2
x 2
0
e sin xdx
42
4 40
cos xdx
cos x sin x
1
0
3dx
x 9 x
0
xsin xdx
2 2
0
x cos xdx
1
0
cos x dx
1
0
sin x dx
2
4
0
xsin x dx
2
4
0
x cos x dx
2
0
x cos xsin x dx
62
0
x cos xsin x dx
4x
1
e dx 43x
0
e sin 4x dx
e
1
x(2 ln x)dx
2e
2e
1 1dx
ln xln x
22
1
(x x)ln x dx
22
1
1x ln(1 )dx
x
2
51
ln xdx
x
e
21
e
ln xdx
(x 1)
1
2
0
1 xx ln dx
1 x
2
3
cos x.ln(1 cos x)dx
22
sin x 3
0
e sin x cos x dx
2
40
sin 2xdx
1 sin x
22
1
x 1dx
x 2
4
2
0
x.tan x dx
5
3
x 2 x 2 dx
2
40
sin 2xdx
1 cos x
2
21
5dx
x 6x 9
http://www.facebook.com/hoitoanhoc 8
21
0
x 3x 2dx
x 3
4
21
1dx
x (x 1)
1
20
ln(1 x)dx
x 1
41
60
1 xdx
1 x
115 8
0
x 1 x dx x1
x x0
edx
e e
e
1
e
ln x dx 2sin x
0
(e cos x)cos x dx
2
0
sin 2x.cos xdx
1 cos x
2
0
sin 2x sin xdx
1 3cos x
24
0
1 2sin xdx
1 sin 2x
5 33
20
x 2xdx
x 1
3
2
4
tan xdx
cos x 1 cos x
4
1
2dx
x 5 4
2
1
xdx
x 2 2 x
2
21
ln(1 x)dx
x
2
0
sin 2xdx
1 cos x
20132
2013 20130
sin xdx
sin x cos x
2
0
sin x.ln(1 cos x)dx
23
21
x 1dx
x
34
20
sin xdx
cos x
22
0
cos x.cos4x dx
1
2x x0
dx
e e
e
21
e
ln xdx
(x 1)
1
0
1dx
x 1 x
21
20
xdx
4 x
1
20
xdx
4 x
1
42
20
xdx
x 1
2
0
sin 3xdx
cos x 1
2
22
20
xdx
1 x
22
41
1 xdx
1 x
37
3 20
xdx
1 x
xln 2
x0
1 edx
1 e
1
0
x 1 x dx
12
0
x 1dx 23 3
0
(cos x sin x)dx
http://www.facebook.com/hoitoanhoc 9
23
0
x 1dx
x 1
12 2x
0
(1 x) .e dx 2
20
cos xdx
cos x 1
7
3
30
x 1dx
3x 1
2
6
1 sin 2x cos2xdx
cos x sin x
x 21
2x0
(1 e )dx
1 e
32 3
0
x (1 x) dx 32
20
sin x.cos xdx
cos x 1
1
2
20
4x 1dx
x 3x 2
2
0
xsin x.cos xdx
2
0
cos xdx
cos2x 7
4
21
1dx
x (x 1)
22 3
0
sin 2x(1 sin x) dx
2
30
x 1dx
3x 2
4
27
1dx
x x 9
3 4
0
xsin x cos xdx
23
2
cos x cos x cos xdx
12
1
ln x a x dx
2
x0
1 sin xdx
(1 cos x)e
2
0
sin 2x sin xdx
cos3x 1
4
2 20
sin 2xdx
sin x 2cos x
2
32
20
xdx
1 x
2
32
20
xdx
1 x
21
22
2
1 xdx
x
21
20
xdx
4 x
2
22
3
1dx
x x 1
15 3 6
0
x (1 x ) dx
2
0
sin xdx
1 sin x
2
0
cos xdx
7 cos2x
4
21
1dx
(1 x)x
2
30
x 1dx
3x 2
3
4
cos x sin xdx
3 sin 2x
23
2
cos x cos x cos xdx
http://www.facebook.com/hoitoanhoc 10
34
4
tan xdx
2x
0
1 sin xe dx
1 cos x
12 3
0
(1 x ) dx
42
0
x.tan xdx
2
2 20
1dx
(4 x )
21
30
3xdx
x 2
52
51
1 xdx
x(1 x )
3
20
cos xdx
1 sin x
23
60
sin xdx
cos x
36
0
sin x sin xdx
cos2x
2
3
1dx
sin x 1 cos x
3
6 21
1dx
x (1 x )
2
20
sin xdx
cos x 3
2
0
sin xdx
x
22
0
sin x cos x(1 cos x) dx
4 44
0
sin x cos xdx
sin x cos x 1
4 44
0
sin x cos xdx
sin x cos x 1
2
0
sin x cos x cos xdx
sin x 2
1
1 x
3a
edx
x
3 21
20
x 2x 10x 1dx
x 2x 9
31
2 30
xdx
(x 1)
1
30
3dx
x 1
41
60
x 1dx
x 1
1
30
xdx
(2x 1)
7
2
1dx
2 x 1
3
2
21
2
1dx
x 1 x
21
20
x ln(x 1 x )dx
1 x
42
1
(x 1) ln x dx
32
0
x ln(x 1)dx
32
21
3xdx
x 2x 1
1
3 20
4x 1dx
x 2x x 2
1
2
21
2
dx
(3 2x) 5 12x 4x
1
0
1dx
x 1 x
http://www.facebook.com/hoitoanhoc 11
2
0
cos xdx
2 cos2x
2
4
cos x sin xdx
3 sin 2x
23 3
0
(cos x sin x)dx
25 4
0
cos xsin xdx
24 4
0
cos2x(sin x cos x)dx
2
0
1dx
2 sin x
2
0
1dx
2 cos x
2
22
3
1dx
x x 1
37
3 20
xdx
1 x
2
31
1dx
x 1 x
31
20
xdx
x 1 x
1
21
1dx
1 x 1 x
3
4
6
1dx
sin x cos x
2
0
cos xdx
cos x 1
2
0
cos xdx
2 cos x
2
0
sin xdx
sin x 2
32
0
cos xdx
cos x 1
2
0
1dx
2cos x sin x 3
2
2
3
cos xdx
(1 cos x)
43
0
tan x dx
1
2x1
1dx
3 e
2
x
sin xdx
3 1
2
0
sin xdx
cos x sin x
42
4 40
sin xdx
cos x sin x
4
20
tan xdx
1 ln (cos x)
2
0
sin xdx
cos x sin x
1
x 21
1dx
(e 1)(x 1)
13x 1
0
e dx
21
20
xdx
x 4 32
4 20
cos xdx
cos 3cos x 3
3
2
4
tan xdx
cos x cos x 1
12
0
3x 6x 1dx 45
0
tan x dx
http://www.facebook.com/hoitoanhoc 12
43
6
cot x dx
34
4
tan x dx
4
0
1dx
2 tan x
52
0
sin xdx
cos x 1
3
2
6
cos 2xdx
1 cos 2x
24
0
tan x 1dx
tan x 1
1
31
2
xdx
x 1
3 32
41
x xdx
x
xln 3
x x0
edx
(e 1) e 1
14e
21
e
1dx
x cos (ln x 1)
4
0
ln(1 tan x)dx
1
0 1 2x
dx
x1
x x0
8 1dx
2 2 1 1
1 x16 1
dxx x2 1 2 1log 32
3
2 2
4
cos 2
sin .cos
xdx
x x
4
20 sin 2cos
dx
x x
42
4 40
dxx
x 2 x
2 42
4 40
cos x cos xdx
1 sin x cos x
2
0
(x 1).sin 2xdx
e
1
3 2ln xdx
x 1 2ln x
10
5
1dx
x 2 x 1
6
2
1dx
2x 1 4x 1
3
2
0
sin x.tan xdx
7
30
x 2dx
x 1
e2
0
x .ln xdx 4
0
sin xtan x e .cos x dx
3 2e
1
ln xdx
x. ln x 1
22
0
(2x 1).cos xdx
3
30
1dx
x x
42
20
x x 1dx
x 4
4
0
2x 1dx
1 2x 1
2
0
1 cosx1 sin x
ln dx1 cos x
3
2
3
x.sin xdx
cos x
2
30
5cos x 4sin xdx
cos x sin x
2
2 20
3sin 4cos
3sin 4cos
x xdx
x x
42
0
. tanx xdx
http://www.facebook.com/hoitoanhoc 13
1
0
x 1dx
3x 2 2x 1
1
0
2xdx
1 1 x
1
2
0
( 4)
3 2
x dx
x x
4
0
sin 2
1 cos 2
x xdx
x
4
6
cos .ln(tan )x x dx
2
0
1sin cos;( )
cos sin
n x xdxn Zn nx x
3
1
24
2
1
)1(
xx
dxx 4
20
sin
cos 1 sin
xdx
x x
0
sin
7 cos 2
x xdx
x
2
0
1 3sin cosxe x xdx
2
3
4
4
sinln tan
cos
xx dx
x
23
0
11
1
xx e dxx
2 21 sinx x x dx
dx
xx
xxx
2
2 21)15(
)21ln(
2
220
; , 0b a x
dx a ba x
0
a
a xdx
a x
; với a > 0
2 11
220 1
m
m
xdx
x
m N 1
2 1
0
1m
n nx x dx
,m n N
2 5
2
0
sin 2 3 cosx x dx
26
20
(4cos 3)cos
(1 sin 3 )
x xdx
x
4
6
2sincot
1 3cos
xx dx
x
2
0)(cos)sin1(
Nnxdxx n
12
2
20
1.ln
1
xx dx
x
2
ln 42
0
x xe e xdx
