Tính tích phân bằng ph ơng pháp đổi biến1.
Trang 1A Tính tích phân bằng ph ơng pháp đổi biến
1.
2
x
dx
x
2 3
2
dx
x x
1
0
1
x x dx
2
x dx x
5.
7
3
0
2
1
x
dx
x
10
dx
x x
6
dx
x x
2 0
2 1
x x
dx x
9.
5
x
dx
x
1
3
xdx
x
3
1
3
x
dx
x x
5
0
1
x x dx
13
1 2
2
0
3 10
x x
dx
x x
2 0
x x x
dx
x x
2 0
3
x dx
x x
1
01
dx x
17.
3
1
3
x
dx
x x
9 3 1
1
x xdx
2
xdx
x x
4
1
2
5 4
dx x
21.
1 5
2
2
1
1 1
x
dx
x x
x dx
x x
1
dx
x x
1
x dx x
1.
1
3 2ln
1 2ln
e
x
dx
1
1 3ln ln
e
x x dx x
1
ln x 2007 x dx
e
dx
x x
5.
3
2
1
ln
ln 1
e
x
dx
x x
2
1
ln 2 ln
e
x x
dx x
1
ln
e
x dx
x x
8. 3ln x exlnx dx
9.
ln 5 2
x
x
e
dx
e
2 2 0
(1 ) 1
e x
x
e dx e
ln 3
3
x
x
e dx
e
1
dx e
13.
3
0
1
x x dx
ln5
dx
e e
ln8
2
ln 3
1
x x
e e dx
ln 2
dx
e
17. x 4 x
dx
e e
1
5 2
dx x
dx e
1 2
dx
e
21 e xex2dx 22.
1 2 0
x x
dx
e e
1
x x
e dx e
1
0
x
x e
e dx
B-Tích phân hàm l ợng giác
1 2
01 sin 2
dx
x
cot
1 sin
gx dx x
2 0
cos
6 5sin sin
x
dx
x x
2
0
sin sin 2 sin 3x x xdx
4.
2
4
sin 1 cos
dx
x x
2002 3 2006 6
sin cos
x dx x
0
cos 2 sinx x cos x dx
2
0
3sin 4cos 3sin 4cos
x x
dx
x x
8 4
2
0
sin 4
1 cos
x
dx x
2 4
0
1 2sin
1 sin 2
x dx x
10. sin x xsin 2cosx x dx 11
2 5
0
cos xdx
12 2 3
0
4sin
1 cos
x
dx x
2
0
sin 2
1 cos
x dx x
4
0
cos 2 sin cos 2
x dx
x x
3 2
2 0
sin cos
1 cos
x x
dx x
16.
4
2 0
cos 2
sin cos 2
x
dx
x x
2
0
cosn xdx
(n Z ) 18. 2
2
0
sin cos
x
e x xdx
1
Trang 219.
4
0
ln 1 tgx dx
2
2 0
cos
7 5sin cos
x
dx
x x
dx
x x
1 sin cos
x dx
x x
22.
2
3 0
cos 2
sin cos 3
x
dx
x x
4
0
cos 2
1 2sin 2
x dx x
24. tg x tg x dx2 4 25 4
cos
dx x
cos xdx4
26. 1 sin
1 cos
x
dx
x
sin
dx x
28.
3 4
cos sin
x dx x
2
0
sin 2 cos 4sin
x dx
x x
31.2
0
sin 2 sin
1 3cos
x x
dx x
2
0
sin 2 cos
1 cos
x x dx x
2
0
sin 2 cos
1 cos
x x dx x
2 4
0
1 2sin
1 sin 2
x dx x
0
1 cos xsin cosx xdx
2
4
sin
1 sin 2
x cosx
dx x
0
4sin
1 cos
x x
38. 3ln x exlnx dx 39.
3
2 4
cos 1 cos
tgx
dx
2 2 6
cot
gx dx x
0
2cos
3 2sin
x dx x
42 sin 2 sin
cos
a x b x
dx
c x d
3 4 6
sin cos
dx
x x
44. tgx 2x 11 2x 1dx
2
4
sin 1 cos
dx
x x
cot
1 sin
gx
dx x
0
sin 2 1 sinx x dx
2
0
sin 7 cos 6 4sin 3cos 5
x x
dx
x x
2
0
sin sin x nx dx
50 2 2006 2006 2006
0
sin
x dx
0
sin
x dx
52 2 4
0
sin 2
1 cos
x
dx x
2
2
sin
4 5
x dx x
0
cos x sin x dx
4 4
0 cos
dx x
56.2
0
cosx sinxdx
2
2 0
cos
1 cos
x dx x
3
6
1 sin 2 cos 2 sin cos
x x
dx
x x
2 4 2
10 sin
x
x dx
60 2 2
0
cos xcos 4xdx
3 2
2 0
sin cos
x x
dx x
2
0
cos xcos 2xdx
2
0
sin xcos xdx
64.2 6 6 6
0
sin
sin cos
x dx
x x
0
cos x sin x cos xsin x dx
2
3 0
4sin sin cos
x dx
x x
67 6 2
0
sin
sin 3 cos
x dx
2 6
0
cos sin 3 cos
x dx
5 3
3 2
cos 2 cos 3 sin
x dx
70
3
6
tg x g x dx
3
6
1 sin sin
6
dx
x x
0
1 sin ln
1 cos
x
x
dx x
2