sin x.lncos xdx.. sin x.tan xdx..[r]
Trang 1
4
1
2
1
x
2 sin 4
x
1
0 2 1
3
x
dx x
2
0 1 cos
) 1 2
(sin
sin
2
x
dx x
1
0 ( 1 )3
2
x
dx x
3
2x 2 x( 1 )
dx
2
1 1
4
2
x
dx x
1
0 ( 2 1 )( 2 3 1 )
) 3 2 3 (
x x x
dx x
e
dx x
x x
1
ln 2 3
2
4
) ln(sin
1
cot
1
1 2 ln
dx x
x x x
3
0 2sin2 3cos2
2 sin
x x
xdx
1
0 6 1
)
1
4
(
x
dx
1
2 1 ln(
1 1
x
x
1 0
) ln(
) (
dx x
e x e
x e x e x e x e
1
2
0
1
4 x dx
0
1
e
x x
e e dx
2 2 1
(6x 5x 1)(24x 10)dx
2
2
2
sin 2 cosx xdx
6
0
1 1
2 cosx dx
2
0
(1 3 )sin 2x xdx
4 2
1
(2x 3)
dx
x
ln 3
0
1 1
e x x
e dx e
4
1
4 4
dx
2
6
0
os
cos 2
c xdx
x
2 6
0
sin cos 2
xdx x
64 3
1
1 x
dx x
1 2
0
x
x dx
e
2
4
1 sinxdx
0
2 ( 1 cos2x 1 cos2 )x dx
1
2 2
1
3 x 3 x 2dx
1
x
0
cos
x
1
2
dx
1
) 1 2
4 (
x
dx x
2
s inx
2
ln
1
x
Trang 22 2 2
0
1
1
0
dx
3 2
2
x dx x
3 2
dx
x x
3
3
2
x dx
x
4
2
dx
1
2
0 4
dx x
1
2
0 4
xdx
x
3
2
dx
3
x dx x
1
1 2 ln
dx x
x x
x
2 3 ln
1 3 ln
e
e x x dx
1
2 ln 2 4
1
dx x
x x
dx 2
sin x cot x
6
6 sin x cos x
1 sin 2x 0
8 tan x
tan x 1 0
/3 sin x sin x
x 1 x 2 0
x 1 x 2 4
3
2
4
3tan x dx
4
2
6
(2cot x 5) dx
3 3 2
3
sin x sin x
cot x dx sin x
3
6
2
0
sin x c os xdx
0
sin x dx
4
4
0
cos x dx
2 3 0
sin x dx
3
dx
2
0
1 cos x
dx
1 cos x
3
4
6
cot 2 x dx
1
)
tan
4
(
x
dx x
x
1
1x10 1
xdx
1
1 2 1
) 4 (
x
dx x x
Trang 3
e
x
dx x x
1
2 ln 4
1
ln
38)
0 .sin
2 cos x xdx x
0 1 sin2
sin
dx x
x x
2
0cos 2 .sin
2
xdx
0(1 sin ) cos ( )
N n xdx
x n
2
0 2 1 3 sin
) sin 1 ( cos 3
dx x
x x
2
1 1 2 1
3
dx x
e
e
dx x
x x
1
2 ln ln 1
1
0. ln( 1)dx
x
e
x
e
4
6 sin2
) ln(cos
x
1
1 2
1
dx x
2
4
4
sin
dx
x
2
4
2
2 sin x 4
4
6
0 cos
dx
x
2
0
cos 2 (sinx x cos )x dx
4 2
x
e x
2
3
0
cos xdx
6
2
2 3
1
dx
1
3
1
dx
4
2
2
1
dx
x 16 x
2
1
2
0
x (x 4) dx
3
2
0
4sin x dx
1 cosx
1
0
x 1 x dx
1
0
x 1 x dx
1
0
x
dx
2x 1
1 x 0
1 dx
e 4
2
x 1
1 dx
1 e
2x
2
x
0
e
dx
e 1
x 1 x 0
e dx
e
2 1
ln x
dx x(ln x 1)
1
2 3 0
(1 2x)(1 3x 3x ) dx
2
3 2 0
(x 3) x 6x 8 dx
ln 2
x 0
e 1dx
2
4
4 3
3
x
2 2
2 2
dx
e 1
sin(ln x)
dx x
Trang 40
1
dx
3 2x
5 0
sin xdx
3 0
1 dx cos x
2x
1
x
0
e
dx
ln 3
x 0
1 dx
e 1
2 6
1
dx sin x cot x
e
1
ln x 2 ln x
dx x
1
0
x (x 1) dx
7 3 3 0
x 1
dx 3x 1
2
3
1
1
dx
x 1 x
6
tan x cot x 2.dx
1
2 3 0
(1 x ) dx
1
2x
0
1
dx
x
ln 3
0
e
dx (e 1)
0 2x 3 1
2
0
1 cos x sin x.cos xdx
2 3
2 5
1 dx
0
x dx
1 cos 2x
2x
ln 5
x
ln 2
e
dx
e 1
2 e 1
.ln xdx x
2 1
0
x
dx (x 1) x 1
2
0
sin x.sin 2x.sin 3xdx
2
0
cos 2x(sin x cos x)dx
2
0
( cos x sin x )dx
7
3
2
x
dx
1 x 2x
0
4cos x 3sin x 1
dx 4sin x 3cos x 5
9 3 1
x 1 xdx
2
3
0
x 1
dx
3x 2
0
x
2
2 0
x
dx
2 x 2 x
3
0
x 1 x dx
1 2 0
ln(1 x)
dx
0
sin x
dx sin x cos x
e
1
cos(ln x)dx
2
2 0
4 x dx
2 1
x
dx
1 x 1
Trang 51
1 3ln x ln x
dx x
3 2 2
ln(x x)dx
e
2 1
(ln x) dx
2
e
e
ln x
dx
x
2
e 1
ln x dx
ln x
2
2 1
x ln(x 1)dx
3
2
3
1
dx
x 3
1
2 0
1 dx
4 x
2
4 0
sin xdx
3
2
6
ln(sin x)
dx
cos x
2 1
cos(ln x)dx
2
2 0
ln( 1 x x)dx
3
2
2
1
dx
x 1
3 8 1
x 1 dx x
3 3 2 1
x dx
x 16
6
2 0
6 5sin x sin x
2
e 2 e
ln x
ln x
3 2 4
2
1
3 4
4
cos 2x 1dx
cos x sin xdx
2
0
1 sin xdx
3 4
4
sin 2x dx
1 sin xdx
2 1
0
x sin x
dx
1 cos x
1
1
1
dx
4
1
x
1
x
dx
1 2
2
4 0
x sin xdx
2
4 0
x cos xdx
6
2 0
x.sin x cos xdx
2 x 1
2 0
x e
dx (x 2)
0
e sin xdx
2
2
1
1
x
e
2 1
e
ln x
dx (x 1)
1 2 0
1 x
1 x
Trang 6/4 2014
0
0
sin x.ln(cos x)dx
2
e
2 1
cos (ln x)dx
4
0
cos x
4 3 0
cos x
2
1
3 x 0
x e dx
2
2
0
e sin x cos xdx
2
4 0
sin 2x
dx
1 cos x
3 4
0
sin x
dx (tan x 1) cos x
1
2
0
3
dx
x 4x 5
2 2 1
5
dx
x 6x 9
1 2 5
1
dx
1
0
2x 9
dx
x 3
4 2 1
1 dx
x (x 1)
0
2 2
sin 2x
dx (2 sin x)
1
2
0
x 3
dx
1 3 0
4x dx (x 1)
1
0
1
dx (x 4x 3)
3
3
2
0
sin x
dx (sin x 3)
3 3
6
4sin x
dx
1 cos x
3
2 6
1
dx cos x.sin x
3
0
sin x.tan xdx
3
4
1 dx sin 2x
3
3
1
dx sin x 9cos x
2
2
cos x 1
dx cos x 2
2 0
1 sin x
dx
1 3cos x
2 0
cos x
dx sin x cos x 1
4
2
1
1
dx
x (x 1)
1
3 3
1
dx
0
sin x
dx cos x
1
0
x 1 xdx
6 4
x 2 x 2
0 2 1
1
dx
3
2
1
1
dx 4x x
2
2 1
2 2 2
2x 5
dx
Trang 7x
0
1
dx
3 e
0
e sin x dx
2 x 1
2 0
x e
dx (x 2)
e
1
(1 x)ln x dx
e 2 1
x ln x dx
1 e 2 1
ln x dx
1
4x 2x
2
2x
0
dx
1 e
4
2 7
1
dx
x 9 x
0
e sin xdx
4
2
0
cos x sin x
1 0
3
dx
x 9 x
0
x sin xdx
0
x cos xdx
1 0
cos x dx
1 0
sin x dx
2
4
0
x sin x dx
2
4 0
x cos x dx
2 0
x cos x sin x dx
6
2
0
x cos x sin x dx
4 x 1
3x 0
e sin 4x dx
e
1
x(2 ln x)dx
2
e 2 e
ln x
ln x
2 2 1
(x x)ln x dx
2
2
1
1
x
2 5 1
ln x dx x
e
2 1
e
ln x
dx (x 1)
1
2
0
1 x
1 x
2
3
cos x.ln(1 cos x)dx
2
2
0
e sin x cos x dx
2
4
0
sin 2x
dx
1 sin x
2
2 1
x 1
x 2
2 0
x.tan x dx
5
3
4 0
sin 2x
dx
1 cos x
2 2 1
5
dx
x 6x 9
Trang 81
0
dx
x 3
4 2 1
1 dx
x (x 1)
1 2 0
ln(1 x)
dx
4
1
6
0
1 x
1
0
0
e
dx
e e
e
1
e
ln x dx
sin x 0
(e cos x)cos x dx
2 0
sin 2x.cos x
dx
1 cos x
2
0
sin 2x sin xdx
1 3cos x
2 4
0
1 2sin xdx
1 sin 2x
3 2 0
3
2 4
tan x
dx cos x 1 cos x
4 1
2
dx
x 5 4
2 1
x
dx
x 2 2 x
2
2
1
ln(1 x)
dx
x
0
sin 2x
dx
1 cos x
2013 2
0
dx
2
0
sin x.ln(1 cos x)dx
2 3 2 1
dx x
2 0
sin x
dx cos x
2
2
0
cos x.cos 4x dx
1 2x x 0
1 dx
e
2 1
e
ln x
dx (x 1)
1
0
1
dx
x 1 x
2 1
2 0
x dx
4 x
1
2 0
x dx
4 x
1
4
2
2
0
x
dx
x 1
2 0
sin 3x
dx cos x 1
2 2 2
2 0
x dx
1 x
2
2
4
1
1 x
dx
1 x
3 7
0
x dx
1 x
x
ln 2
x 0
1 e
dx
1 e
1
0
x 1 x dx
1 2 0
x 1dx
0
(cos x sin x)dx
Trang 93
0
dx
x 1
1
2 2x 0
(1 x) e dx
2 0
cos x
dx cos x 1
7
3
3
0
x 1
dx
3x 1
2
6
1 sin 2x cos 2x
dx cos x sin x
x 2 1
2x 0
(1 e )
dx
1 e
3
0
x (1 x) dx
2 0
sin x.cos x
dx cos x 1
1 2 2 0
4x 1
dx
2
0
x sin x.cos xdx
0
cos x
dx cos 2x 7
4 2 1
1 dx
x (x 1)
2
2 3 0
sin 2x(1 sin x) dx
2 3 0
x 1
dx 3x 2
4
2 7
1
dx
0
x sin x cos xdx
3 2
cos x cos x cos xdx
1
2 1
2
x 0
1 sin x
dx (1 cos x)e
2 0
sin 2x sin x
dx cos3x 1
4
0
sin 2x
dx sin x 2cos x
2
3
2
2
0
x
dx
1 x
2 3 2
2 0
x dx
1 x
2 1
2 2 2
1 x
dx x
2
1
2
0
x
dx
4 x
2
2 2
3
1 dx
x x 1
1
0
x (1 x ) dx
2
0
sin x
dx
1 sin x
2 0
cos x
dx
7 cos 2x
4
2 1
1 dx (1 x)x
2
3
0
x 1
dx
3x 2
4
cos x sin x
dx
3 sin 2x
2
3 2
cos x cos x cos xdx
Trang 104
4
tan xdx
2
x 0
1 sin x
e dx
1 cos x
1
2 3 0
(1 x ) dx
4
2
0
x.tan xdx
2
2 2 0
1 dx (4 x )
2 1
3 0
x 2
5
2
5
1
1 x
dx
x(1 x )
2 0
cos x
dx
1 sin x
2 3 6 0
sin x
dx cos x
3 6
0
sin x sin x
dx cos 2x
2
3
1
dx sin x 1 cos x
3
1
1
dx
x (1 x )
2
2
0
sin x
dx cos x 3
2
0
sin x
dx x
0
sin x cos x(1 cos x) dx
4
0
sin x cos x
dx sin x cos x 1
4 0
sin x cos x
dx sin x cos x 1
2 0
sin x cos x cos x
dx sin x 2
1
1 x
3
a
e
dx
x
1
2 0
dx
3 1
0
x
dx (x 1)
1
3
0
3
dx
x 1
4 1 6 0
dx
1
3 0
x dx (2x 1)
7
2
1
dx
2 x 1
3 2
2 1
2
1 dx
x 1 x
2 1
2 0
dx
1 x
4
2
1
(x 1) ln x dx
3 2 0
x ln(x 1)dx
3 2
2 1
3x
dx
x 2x 1
1
0
4x 1
dx
1 2
2 1
2
1
dx (3 2x) 5 12x 4x
1 0
1
dx
x 1 x
Trang 110
cos x
dx
2 cos 2x
2
4
cos x sin x
dx
3 sin 2x
2
0
(cos x sin x)dx
2
0
cos x sin xdx
2
0
cos 2x(sin x cos x)dx
2 0
1 dx
2 sin x
2
0
1
dx
2 cos x
2
2 2
3
1 dx
x x 1
3 7
0
x dx
1 x
2
3
1
1
dx
x 1 x
3 1
2 0
x
dx
x 1 x
1
2 1
1
dx
3
4
6
1
dx sin x cos x
2 0
cos x
dx cos x 1
2 0
cos x
dx
2 cos x
2
0
sin x
dx
sin x 2
3 2
0
cos x
dx cos x 1
2 0
1
dx 2cos x sin x 3
2
2 3
cos x
dx (1 cos x)
4 3 0
tan x dx
1
2x 1
1 dx
3 e
2
x
sin x
dx
0
sin x
dx cos x sin x
4 2
0
sin x
dx cos x sin x
4
2
0
tan x
dx
1 ln (cos x)
2 0
sin x
dx cos x sin x
1
1
1
dx
1
3x 1
0
2 1 2 0
x dx
x 4
0
cos x
dx
3
2 4
tan x
dx cos x cos x 1
1
2 0
5 0
tan x dx
Trang 123
6
cot x dx
3 4 4
tan x dx
4 0
1 dx
2 tan x
5
2
0
sin x
dx
cos x 1
3
2 6
cos 2x
dx
1 cos 2x
2 4
0
tan x 1
dx tan x 1
1
3
1
2
x
dx
x 1
2 4 1
x x
dx x
x
ln 3
0
e
dx (e 1) e 1
1
4
e
2
1
e
1
dx
x cos (ln x 1)
4 0
ln(1 tan x)dx
1 1 dx x
1 2 0
x
dx
x x
2 2 1 1
0
x
1 16 1
dx
x x
2 1 2 1 log2 3
3 cos2x
dx
sin x.cos x 4
dx 2
0 sinx 2cosx
4
dx
4x 42 x
0
2 4 /2 cos x cos x
dx
1 sin x cos x 0
2
(x 1).sin 2xdx
0
e 3 2ln x
dx
x 1 2 ln x 1
dx
x 2 x 1
dx 2x 1 4x 1
sin x.tan xdx 0
7 x 2
3 x 1 0
e 2x ln xdx
0
3 2
e ln x
dx
x ln x 1
1
(2x 1).cos xdx
0
dx 3
0 x x
4
dx 2
4 2x 1
dx
1 2x 1
0
1 cos x 0
3 x.sin x
dx 2 cos x 3
Trang 13
3
0 cos x sin x
0 3sin x 4 cos x
x.tan xdx 0
dx
0
dx
1 2 0
x dx
4
01 cos2
2
sin
dx
x
x
x
4
6
) ln(tan cos
0 cos sin
cos 1 sin
Z n x n x
n
3
1
2
4
2
1
)
1
(
x
x
dx
x
4
0 cos 1 sin2
sin
dx x x
07 cos2
sin
dx x
x x
2
sin
3
1
xdx x
x
2 4
3
4
sin
ln tan cos
x
x dx x
3
1 1 2
dx x
x e x
dx x x
x x
x x
x
2
2 (5 1) 1 2
) 2 1 ln(
0 ,
;
0( 2)2
2
b a
b
dx x
a
x a
0
a a x dx
x
a
; với a > 0
1
0(1 2) 2
1 2
dx m x
m x
m N
1
1
2n x n m dx x
m n N,
2
0
5 2 cos
3
2
sin
dx x
6
0 (1 sin3 )2
cos ) 3 2 cos 4 (
x
xdx x
4
6 1 3cos
sin 2 cot
x
x x
2
0(1 sin ) cos ( )
N n xdx
x n
2
1
0 1 2
2 1 ln
x
x
4 ln 0
2
2e x e x xdx
.