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# BÀI TẬP NGUYÊN HÀM DT by muoitt9

VIEWS: 19 PAGES: 5

• pg 1
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BT NGUYÊN 26.  3 dx                          x
52. 
dx                                  
81.  tan x tan  x  dx 4. 2
cos x sin 2 x
2
      3     (2 sin x  3cosx  x ) dx
HÀM        1 3                                   x

53. 
dx                                                 3
82.  cot x tan  x  dx 1
x
1.  x dx 5
27. 
2
dx                                              sin x                                          4  5. (e x  x)dx
1              4 1                       x
dx                                                   
2.  dx                                                             54.                                           dx
83.  2
0
x 1
28. 
7
x                                                                     cos x
sin x  2cos x  1
2       1
dx
x 1                                                      cos 2 x                                         6.  ( x3  x x )dx
3.  x dx
5           2
55.                   dx       84.  1  sin 2xdx
29. 
dx                                                   cos 2 x sin 2 x                                       0

4. 
1
dx       x x 1                              4
56.  cos3x sin xdx             85.  cos5 x sin xdx                          2
7.  (x  1)( x  x  1) dx
5                                                                                                                              1
x
x3                   57.  sin 4 x sin xdx                   sin 2 xdx                             
5.  6 dx x                          30.                      dx                                   86.                                          2                   1
x8  1                                                    cos 2 x tan x                         8.  (3 sin x  2cosx  ) dx
1                                                             58.  cos3x sin 2 xdx                                                                            x
6.  x dx                            31. 
dx                                                      sin x cos xdx
87.  6                                       3
2                                       x  x 1              59.  tan 2 xdx                      sin x  cos6 x                            1

1                                                                                                                                    9.  (e x  x 2  1)dx
7.             dx                         ( x  1) dx              60.  cot 2 xdx                                     cos x sin xdx
(2 x  3)5                      32.                                                           88. 
22     2   2
0

5x2 1                                                            a sin x  b cos x                   2 2
dx                                                                          3
8. 
1                                                          61.  cos ln x                                  x  2 x 1
3       2          10.   ( x  x x  x ) dx
dx                           x2 1                                        x           89. 
1
1 x                         33.  4       dx                                                                         dx                   2
x 1                     62. 
4
cos x sin xdx                             x                    11.  ( x  1)( x  x  1) dx
9.  3x5x dx
                        dx
dx                                                                                      2          1
34.                                 cos x                                         2 x  3 3x                     3
2x
10.  x dx                                  x x2  4                63. 
x
dx                90.                    x                         
12. ( x  1).dx
3
7                                          xdx
35.                           64.  3 sin x cos xdx                        2      2
x 1  x 1
1
11.  32 x 1 dx                               x  x2  4
4
91.                    dx                     2 x.dx
sin x                                     4
x 1                        13. 
12. 
dx                            36.  2x (4x 1)5 dx           65.         dx                                                                -1 x 2  2
513 x                                                              cos3 x                 e3 x  1
92.  x      dx
37.  xe1 x dx                                                                                                   e2 7x  2 x  5
2

x                                                          66.  tan(cos x)sin xdx      e 1                                                   
13.         dx                                                                                                                                14.                     dx
1  x2                                  1                     67.  tan3 xdx                         1  2 x  x2
1       x
38.         dx                                                93.                dx
14.  x(1  x2 )10 dx                      e 1                                                                                                        5    dx
1 x
x

2x 1                 68.  cot 4 xdx                                                            15.
39.  2                                                              x2  1                                       2 x2 x2
 x(3x  1) dx                                                                                 94.  4 dx
9
15.                                                    dx
x x2                  69. 
dx                     x 1                       2 ( x  1).dx
dx                                      3x  2                      sin x  6cos 2 x
2                                               16. 
16.                                 40.  2                                                                   dx                    1 x 2  x ln x
x 1    2
4x  4x 1
dx
sin 2 xdx             95. 
70.                                      1  2x 1                  
17. 
dx                       41.  cos 2xdx                      2 cos x  1
2
xdx
2 cos3 x.dx
x  2x
2
97.                             17. 
dx                       42.  cos3 xdx                         1 dx
71.  tan 2 3                           x  1 x  2  x  3      3 sin x
18.                                                                        x x                                                      6
x2  1                                                                           98.  3
xdx                     
43.  cos(3x  )dx                         dx
5        72.  2                                 x  3x  2                   4 tgx .dx
dx                                                      sin x  9cos x    2
18. 
19.              x2  3             44.  cos4 3xdx                   sin x  cos x                                
x 2  1 dx              0 cos2 x
73.                            99. 
dx                           dx                   sin x  cos x
dx
 x  1 x  1
2          1 e x  e x
20.                                 45.                  dx                                                                    19.  x        x dx
x 2  3x  1              cos 2 (3x  1)               sin x  cos x                                               0e e
74.                                             dx
46.  sin 4xdx                    sin x  cos x  2
dx 100.
  x  a  x  b           1      x
e .dx
sin x cos x                                              20. 
21. 
dx                        x              75.                     dx                                          0 e x  e x
47.  sin(  )dx                  sin x  cos x
2 x2  5                                                                              BT TÍNH PHÂN
1                            dx
2 7
                   
76.  cos4 x  sin 4 x dx A-TP CƠ BẢN                                2
21. 
dx
22.                                 48.  2
                   
dx                                                                 1
1 4x 2  8x
77.  cos8 x  sin8 x dx 1. ( x3  x  1)dx
3x 2  2 x                   sin 2 x                                                 
78.   cos10 x  sin10 x  dx
dx                                                                              ln 3
23.  x 2 2 x dx                     49. 
3                                                                            0
.dx
(cos x  3 sin x)  2                                    e
1 1                  22.        x     x
sin x  3cos x  1        2.  ( x   2  x )dx     2
0 e e
 2 x  1dx
2
24.                                            dx               79.                        dx               x x                     
50.                              sin x  cos x  2
1

25.  x(1  x) dx          20              1  sin 2 x                                              2                                2 dx
80.  4
dx               3.  x  1dx                     23.                 24.
51. 
dx
sin x  cos x   4
1
0 1  sin x
1  sin 2 x                                                                           3
 x  2 dx
1                      1
B-PP ĐỔI BIẾN SỐ 2. Nếu hàm số có căn                                          3. hàm số có lũy thừa 8/ I= ln 3                            e
x                          1          3
1. Nếu hàm số có mẫu:đặt t = căn                                               đặt t = biểu thức trong lũy   
0 (e    x                 x
dx   6/I =  2               dx
đặt t = mẫu            22                                                thừa                                                       1) e            1             0 x  4x  5
3                                                                 1                               2x                                          0
3
3 x dx       1 ) I   3 3 x  5dx                                     1 ) I   x3 (1  x 4 )3dx                  2 e
7/I = 
1
1/ I                       1                                                            0                          9/I =  x      dx                                                     dx
02
x 1                              1                                         1 5                               0 e 1                                          1 x 2  2x  9
2x                       2) I   x3                2
2  x dx           2) I      x (1  x3 )6 dx                       x                                        2
ln 5 e                                   0                                         0                                  1 e
8/I =  4x  x 2  5 dx
2/I =             dx                                                                                               10/I =   x      dx
e 1  ln x                                                                                                                  1
ln 2 e x  1                    3) I                        dx                         2    3
0e     1
2
1           x                   3/ I =           cos xdx             5. Hàm số có chứa Ln       1 x
4
3/ I  
1
dx                                    2                                        0                          đặt t = Ln      9/I =    2
dx
1
0 2x  1                                     x
                                                        0                           4x
4/I   =               dx                                                            e sin(ln x)
                                     0 (x  1) x  1                           2                                                                                    1
4/I =
5
 sin xdx
1/I =            dx                                       4
2 sin 2x. cos x                      4                                                                            1     x
2 x
4/ I   =                dx           5) I   
1                                     0                                                                             10/I =  2    dx
dx                                                                    
0 1  cos x                          0 2x  1                                 1 3 4      5
e                                                0 x 1
                                                                      5/I   =  x (x  1) dx                2/I =      cos(ln x)dx
1 xdx
2 sin 2x  sin x              6) I                                           0                                       1
5/I =                   dx                   0 2x  1                                      0                                e 1  3 ln x ln x
sin 2x
0 1  3 cos x                          2 3                             6*/I =                       dx      3/I =                                 dx
dx
                             7) I                                                (2  sin x ) 2                 1            x
2                             5 x x2  4                                 2                                 2
4 1  2 sin x                                                                                                       e        ln x
6/I =                 dx                    4     1                                                                4/I   =                  dx
0 1  sin 2x                  8/I   =            dx                           2               2 3                   e       x
2 x 16  x 2
7/I=     sin 2x(1  sin x) dx
5      3                                                                                                      
3 x  2x                                                                    0
7/I =                 dx                          6                                   1 5                                   3 ln(sin x)
1                                3 6                 5/I =              dx
0      2
x 1                   9*/I =                             dx   8/I   =  x (1  x ) dx                        cos 2 x
                                      2 3 x x2  9                            0
                                     6
3                  tan x                   2 2                                                                         
8/I =                           dx   10/I
2
=  x 4  x dx                    9/ I= 2 sin x cos x(1  cos x) 2 dx

                  2
1
0                             6/I = 3 sin x. ln(cos x)dx

cos x 1  cos x                                                                                                  0
4                                                                                     3
2     2    3                            1    x                                
11/I   =  x (x  4) dx                  10/I   = 2         dx
0                                       0 (x  1)
3                          e2    2
1        x                                                                                                   7/I   =  cos (ln x )dx
9/I =                   dx                        4
2
4         11/    1
2 3                  1
04x
2                                      x                          (1 2x)(13x 3x ) dx
12/I =                            dx           0                                            3      2
e ln x 2  ln x
3                     4 3              x                                                    8/I =                                 dx
7    x
10/I =             dx                             3                                                                         1             x
0 31  x 2                                  2                          4. hàm số nằm trên                            e
 2 x 1                                                                                   ln x
2                         13*/I =              dx
hàm e mũ                              9/I =              dx
3 x 1                                                                                                                    2
2 x x 2  1                    t = biểu thức trên mũ                      1 x (ln x  1)
11/I =          dx
                        e2  1       1 
4 e tan x  2
0 x 1                               ln 2 x
14/I =  e  1dx                                                               10/   2           dx
                                                                                                                 e  ln x ln x 
3                              0                                 1/ I = 
4 sin x
12/I =  2 dx                                 1    1
0 cos 2 x                      6.Hàm số có dạng
0 cos x                        15/I   =         dx                                                          a2 + x2 thì đặt x = a tanu
                                      0 3  2x                                  2 sin 2 x                    a2 - x2 thì đặt x = a sinu
2 sin 2x                                 2x                        2/I =     e       sin 2x dx          x2 - a2 thì đặt x = a /sinu
ln 5 e                                    
13/I =                 dx            16/I   =            dx
0 1  cos x                       ln 2 e x  1
4                                     1

1
7                                                                                                        1/I =           dx
3 x 1                               2   x
3/
2 sin 2 x            3                 3 x2 4  x2
14/I   = 3      dx                   17/I =         dx                           e       . sin x cos xdx
0 3x  1                             11 x 1                             0                                      2 2
                                             2
9                                                                 2/I =  x 4  x dx
4

1
18/I =  x.
3
1  xdx             4/I = 2 (esin x  cos x) cos x dx
                                1
15/I =                  dx
7 x x2  9
1                                      0                                2       2
2       x 1                             1 3x 1                  3/I =  4  x dx
2     1                       19/I =                       dx         5*/I =  e          dx                  0
16*/I =           dx                           3
0 3x  2                                 0                               3
1 x 1  x3                                                                 /2 sin 2 x 3
1
2                              6/  e           sin x cos xdx
4/I =  2       dx
7   x
3
4                                  0                                    3 x 3
17/I =           dx                  20/I =      sin xdx                                       x                        3    1
1
0 31  x 2                                0                                             e                 5*/I =            dx
7/ I =                  dx
x
0 e e      x                      2 x2  1
2
BT TỰ LUYỆN                                      
1  3ln x ln x     58/I=  cos3x.sin 8x dx
e                                                                                 1 3
24/ I =                        1  x 2 dx

2                                                                                                                 x
                                                                       37.                       dx
19.  sin xcos xdx
0
2
3         2
x                    π                                            1
25/I =  x5 1  x 2 dx
1.  sin xcos xdx
1
3             2
                                                                  3
e 2ln x 1
e                    59. I =  3tg2x dx                                    0

38. 
3

                                            dx                    π                                 26/I =
1

x
dx
3                                                                                  x                          4                                          0         2x  1
                                           2                                1
π
e
sin x                                                                                                 1           1
20.                    cosxdx          e2
2                                                                               1  ln 2 x                                                      27/I =                         dx
39. 
2    3                                                                                                 4                                                    x
4
2.     sin xcos xdx                                                                            dx        5/I =  (2cotg2x  5) dx
0e
                                                                                  x ln x                                                                 2             1
3
4

e                              π                                   28/I =                    x
dx
11 e
                                               2
e2
1                   6
2
sin x                              21.  ecosx sin xdx                40.                     dx         π                                   29/I = 
2       e 2x
dx
3.                                                                                   cos 2 (1  ln x)      6/I = 1  cos x dx
2                                                          1
x
0e
dx                                                                                                  
1  3cosx
e
0                                              4                                 2
x                           0 1  cos x                       30/I = 
1         e x
dx
41. 
x
                                           1                                            dx                    π                                          0e                1
22.  e x          2
1 1   x 1
2
2
4
xdx                                     7/ I =      sin2 x.cos2xdx                         e               ln x
 cot gxdx
31/I =                                  dx
4.                                               0                                1
0                                          1 x(ln
2
x  1)
x
42. 
π
                                                                                                                                                        7
dx                      3
(2cos2 x-3sin2 x)dx 32/I = 3 x  1 dx
6                                           2                                   2x 1                  8/I =   


23.  sin 3 xcos 2 xdx
0                                 0                                 3
0         3x  1
6                                                                              1                                     π       π
sin(  x)
x
2

                                                                                        x  1dx

1  4sin xcosxdx                                                                                                                                  (x  3)                  x 2  6x  8 dx
3
5.                                                                            43.                                         2       4                   33/I =
3
9/ I=         
π
dx                     0
π
0                                                                             0                                         sin(  x)                         1
2       4                                                  1
1                                           2                                  1                                                                 34/I =                                     dx
1                        π                                                   2
4  x2

x
x                                    24.  sin xcos xdx
3
6.                 x  1dx
2                                     2          3
44.                     dx   10 / I =
3
(tgx-cotgx)2 dx
x 1  x                                                         4                 1
                                  0                                     π                           35/I =                                  dx
0                                                                                                                  
6
2   x 16  x 2
1                                           3                                  1
1
x


6                    1
7.                1  x 2 dx                                                  45.                     dx                π
36*/I =                                      dx
2
sin x                                    x 1  x                                                              2 3           x x2  9
25. 
0                                                                              0                                   4
dx                                              11/ I =       cos
4
x dx
1  3cosx
2 2
4  x 2 dx
x 1                                                     37/I =
1                                                                              3                                   0                                         x

x                x  1dx                                                      
3             2                  0                                                                         π                                      1
8.                                                                           46.                 dx                     2                                     2
0                                           4                                  1
x            12 / I =           3
 sin x dx                   38/I =  x (x 2  4)3 dx
26.  tgxdx
0                                     0
1                                                                              e
x2                                                                sin(ln x)                       π
9.                              dx              0                            47.            dx            13*/
2 sin 3 x  sin x
3
39/I =
4

x2  4
dx
                     cot gx dx
0            x 1
3
                                1
x                           π     sin x                                4 3
3
x
3
1  3ln x ln x
1                                      4                                  e
π
 x 1  x dx                            cot gxdx                      
x2  1
3     2                                                                                                                                                2
10.                                        27.                                48.                    dx        2                                      40*/I =                           dx
0                                                                      1
x         14/I =  sin 4 x dx                                         2           x x2  1
2                                      6                                 e 2ln x 1                  0                                      41/I =
ln 2
e x  1dx
1                                                            e                                                                           

49. 
x                                                                                  dx                                                                0
11.                                   dx         6                                                            π
x3  1                                                                        x

1           1
1                                28.           1  4sin xcosxdx          1                               3         1
42/I = 
3  2x
dx
e2                      15/I =                 dx                         0
1  ln x
1                                                                                   2
1                                                                                                         π sin 2 x cos2 x
12.                                                                                
0                                                                                                             π
dx                                                               50.                 dx                       2      2                            2
1  x2
1                                                                 4                                                 5
x ln x                                                       43/I =    sin             xdx
0
1
1
29.   x           x 2  1dx              e
e2
π
4
0
π

1 x2  2 x  2dx
0                                             1           16/I =  cot2x dx

13.                                                                                                                                                                  3     1
1                            51.                       dx         π                                  44*/I =                 dx
cos 2 (1  ln x)                                                                  cos x
x
0
                                30.                1  x 2 dx             e                             6
e 2x
1                                                                                                         π                                          1
1                                                           1 2 3                                                             45/I =                          dx

0                                                                                                                     x
14.            dx                                                                                                   2      2                                   0e                1
x2  1
1                            52.    x x  5dx             17/I =  esin x sin 2x dx
 x x  1dx
ln 3              1
0
31.      3 2
0                               π                                 46/I =                                dx
4                                           0            ex  1
1
1                                                                        
15.                                                                                                                π
0

             
π
dx                                                              2                                   tgx 2
(1  3x 2 ) 2                                                                         4
1
x2              53.     sin x  1 cos xdx 18/I = 4 e
4                      1

47/I =                                       dx
0
32.                         dx                                                                                     π     sin 2 x cot gx
0 cos2 x

0
2                                      0        x 13
4                                π
6
2                                                              e ln x 3              2  ln 2 x
e                                                                         4  x dx
sin x                          1
16.                         cosxdx                                            54.                                    2                                48/I =                                   dx
19/ I =  1
x            1  x 2 dx
3                                                                     dx                                                     x

33.                                      0                                                                          1
π sin 4 x                                 e sin(ln x)
4                                      0                                  4                                4                                49/I =                             dx
                                                                                 2                                                                            x
 4  x dx
1
2
1              55.                                     π
x
2                                                                                                                                                1
34.                           dx         0                                 4                               50/I =  x 3 (x 4  1)5 dx
17.  e            cosx
sin xdx                    x 1    3                                       20/ I =  1          dx                             0


1
1 dx                              0 cos6 x                                 1
 (1  2x)(1  3x  3x ) dx
2 3
51/I =
1  ln x
e
56.                               π


4                                                                                                                                                0
1                                35.
x
dx                0 1  x2               21/
2
 cos 2x(sin x  cos x)dx
4       4
2                 1
18.  e           x2  2
xdx                  1
e                                   e 1  ln x
0
π
52/I = 
1   x 1  x3
dx

sin(ln x)                  57. 

0
36.               dx                                 dx         22/ I =
2    3
 cos xdx
π

x                             1     x                            0                             53/I =
3
         tg 2 x  cot g 2 x  2dx
1                                                                      π                                      π
58. / 
dx .                            2 4sin 3 x                             6
23/ I =                  dx
x 2 1                           0 1  cosx
3
1                                                        3             1                                               1                                                       π                                                         1
54/I =  (1  x 2 )3 dx                                  85/I =
114/I =  x.ln 1  x dx
                       dx                                    2                                                       2           cos x                                         e
0                                                         3        x2  3                                                                                            141/I =                          dx                      171/I =  ln 2 x dx
0            1 x                                       0     sin x  cos x  1                                   1
1        1                                           1             1
55*/I =                    dx                           86/I =                          dx                                    t  ln x  2                                              4            1                                          e
0e
2x
3                                                                                                                                                  142/I =                          dx                      172/I =    x(2  ln x) dx
0         4  x2                                    115/I =                      dx  I  2
x                                                                                                 1 x                                                     1     x 2 (x  1)                                       1
ln 3             e                                       π2                                                                                                                                                                              e2
56/I =                                 dx                                                                                      π                                                       1                        1                                           1

1
0          (ex  1)3                                      4                                                                                                         143/I =                                             dx   173/I =       (                      )dx
87/I =            sin xdx
116/I =
3
 sin x.ln(cos x)dx                                     3         x  4  (x  4)             3                  e        ln 2 x        ln x
0
0                                                                                                                      0                                                                                                                 2
57/I =  x(e2x  3 x  1)dx                                       π
π
π                                               174/I =  (x 2  x) ln x dx
1                                                       3     ln(sin x)                                                                                                       3       sin3 x                                            1
π                                               88/I =                           dx                                   e2     2
144/I =                 dx
26
π         cos 2 x                                   117/I =      cos (ln x)dx                                        0        cos x                                            2
175/I =  x 2 ln(1  1 ) dx
 1  cos x sin x.cos xdx
3           5                                                                                                  1
58/I =                                                            6                                                                                                                     1                                                         1                    x
0                                                        2                                                             π                                             145/I =  x 1  xdx                                                 2 ln x
89/I =    cos(ln x)dx                                                 4 1                                                     0
176/I =                dx
2 3                  1                               1                                                   118/I =           dx                                                                                                           5
59*/I =                                                                                                                                                                                                                                                x
146/I =  x  4 . 1 dx
                          dx                                                                                     0 cos x                                               6                                                           1
5      x x 4      2                                   2
90*/I =       ln(          1  x 2  x)dx                                 π                                                   4        x2 x2                                        e
177/I =  ln x 2 dx
π                                                            0
119*/I =
4

1
dx                                  0          1                                            1   (x  1)
4      x                                                                                                                                                             147/I =                                    dx
60/I =               dx                                 91*/I =
3             1                                             0   cos3 x                                                                                                    e
0 1  cos 2x                                                                            dx                                                                                      1         x  2x  9
2
1
2          x2 1                                       1            2
120/I =  x3ex dx                                                                                                 178/I =  x ln 1  x dx
2x                                                                                                                                                            3            1                                            2
ln 5        e
61/I =                    dx                                     83        x 1                                                0                                             148/I =                          dx
1 x
ln 2        ex  1
92/I =                 dx                                             π
1        4x  x 2                                         0
1          x                                                                                                                                                                    π
2 sin 2 x                                                 2
e       2
1                                                                                                  121/I =   e        .sin x cos3 xdx                     149/I =             4x  x 2  5 dx                                2
62/I =  x           .ln xdx                             93/I = 
3         x3
dx                                    0                                                         1
179/I =    cos x.ln(1  cos x) dx
π
1       x                                                1x
2
 16                                            π                                                         2                2x  5                                 3
1       x2                                               π                                                             2 sin 2x                                      150/I =                                    dx
π
63/I =                  dx                                                                                           122/I =              dx                                            2         x 2  4x  13
0 (x  1) x  1                                                               cos x
6
0 1  cos x
4                                                                                                    2       2
94/I =                                             dx                                                                                                                         180/  esin x sin x cos3 x dx
π                                                        0     6  5sin x  sin 2 x                                    1             3                               151/I = 
1          1
dx                             0
2                                                            e2
123/I =                             dx                           0        3  ex                                           π
64/I =    sin x.sin 2x.sin 3xdx                                           1

1                            0 x 2  4x  5
0
95*/I =        (
2
)dx                                                                                  1                                                     2 sin 2x
e ln x                     ln x                          2       5                                                            4x
e   2x                      181/I=                          dx
124/I =                                                                                                                    0 1  sin x
dx                               2   3e                                                         4
π
3                                                             1 x 2  6x  9                                152/I =                               dx
2                                               96/I =            x  4 dx
2
0        1  e 2x                                     π
65/I =    cos 2x(sin
4
x  cos 4 x)dx            4                                                            1         1                                                                                                       2 sin 2x
0                                                                                                            125/I =                                      dx                    4                1                            182/I =              dx
π                                           97/I =
2 3
 x  2x  x  2
2
dx                   5 2x  8x  26
2                                       153/I =                               dx                           0 1  cos x
4
2 3                                                  1                                                           1 2x  9
7     x 9  x2
66*/I =       ( cos x                 3 sin x )dx               3π                                                  126/I   =        dx                                                  π                                           183/I = 
2             5
dx
0                                                                                                                 0 x3                                                        2 x                                                   1   x 2  6x  9
4
3            x    7                             98/I =      cos 2x  1dx                                              4            1                                154/I =       e       sin 2 xdx
67/I =                                 dx                         π                                                  127/I =                         dx                                   0                                                     1 x 2  3x  2
21 x
8
 2x 4                                                                                                   x 2 (x  1)                                                                                         184/I =                 dx
4                                                            1                                                           π                                                     0     x3
π                                                    π                                                                  0           sin 2x                                     2            cos4 x
4cos x  3sin x  1                     99/I =  cos x sin xdx                                       128*/I =                                   dx          155/I =                                    dx                      4          1
2
cos x  sin 4 x
4                                185/I =                         dx
68*/I =                             dx                           0                                                                 π   (2  sin x)            2                           0
x 2 (x  1)
0   4sin x  3cos x  5                                  2π                                                             2                                                  1           3
1

9                                               100/I =                   1  sin xdx                                           x 3
156/I =                      dx                                    1 ln(1  x)
69/I =  x.3 1  xdx                                                   0                                              129/I =
1
                     dx                                0        x 9  x                               186/I =                      dx
1                                                                                                                      0 (x  1)(x  3x  2)
2                                                                                                      0       x2  1
3π                                                                                                                  π
2       x 1                                                  4                                                        1
157/I =      x sin xdx                                          11     x4
70/I =  3              dx                               101/I =               sin 2x dx                                                4x                                               0                                             187/I               dx
3x  2                                                π
130/I =                        dx                                                                                       01     x6
0                                                                                                                      0 (x
3
 1)                                       π 2     2
π x
4                                                                                                      158/I =    x cos                xdx                                1
71*/I =  sin 6 dx                                                    π
131/I = 
1                 1
dx
0                                               188/I =  x15 1  x8 dx
0             2                             102/I =               1  sin xdx                                     0 (x
4
 4x  3)2                                 1                                                         0
2           x
0                                                                                                       159/I =  cos x dx
72*/I =                       dx                                                                                3              π                                                       0                                                         1             ex
2x  2x                           103/I =  ln(x  x 2  1)  dx
1
3        sin 3 x                                                                                        189/I =                           dx
e  e x
0
  1                                           132/I =                                 dx                       1
160/I =  sin x dx
0         x
3 3                                                                                                                  0   (sin x  3)
2
73/I =     x .           1  x 2 dx                                        π       x sin x                                                                                             0                                                         e
0                                              104*/I =                                    dx                        π                                                                                                       190/I=     ln x dx
0 1  cos
2
x                             3 4sin 3 x                                                  π2                                                    1
1 ln(1  x)                                                                                          133/I =              dx                                               4                                                    e
74**/I =                              dx                                   1                     1                             π 1  cos x                                   161/I =           x sin x dx                                       π
0    x 12                              105*/I =                                               dx                                                                          0
1 (x
2
 1)(4 x  1)                         6                                                                                                                 2 sin x
π                                                                                                                      π                                                       π2                                              191/I =    (e     cos x) cos x dx
2       sin x                                                      1 x4                                                3       1                                                                                                         0
75/I =                    dx                            106*/I =                             dx                     134/I =                  dx                            162/I =
4
0   sin x  cos x                                                  1 1  2
x
π cos x.sin 2 x
      x cos x dx                                        π
0
192/I = sin 2x.cos x dx
2
eπ                                                             π2
6
π                                                         
76/I =       cos(ln x)dx                                                                                                       π                                             163/I =           2                                                 0        1  cos x
4                                                                                                               x cos            x sin x dx
1
107/I =               x sin xdx
135/I =
3
 sin x.tgxdx
0                                                         π
2                                                           0                                                                                                                  π                                                     2   sin 2x  sin x
77*/I =  4  x 2 dx                                                                                                            0                                                                                                       193/I =                     dx
0                                                          π2                                                          π
6
164/I = x cos x sin x dx

2                                      0     1  3cos x
2                                                              4                                                           3      1                                                0                                                     π
x                                         108/I =               x cos xdx                             136/I =                 dx
78/I =             dx
sin 2x                                                                                                    4 1  2sin 2 x
1 1  x 1                                                                                                                 π
0                                                                                                               4 x
165/I =   e   dx                                         194/I =                           dx
π                                                           4                                                                                                             0 1  sin 2x
e       1  3ln x ln x                                         6                                                           π
1
79/I =                         dx                       109/I = x.sin x cos2 xdx
                                                                                                               π                                                              3   x5  2x 3
1            x                                                                                                             4             sin 3 x                                                                               195/I =                           dx
0                                             137/I =                                           dx
166/I =
4 3x
3                                                                                                                          0   (tg x  1) .cos x
2             2         5                   e sin 4x dx                                                 0         x2  1
80/I =  ln(x 2  x)dx                                                      1 x 2e x                                                                                                    0
π
2                                               110*/I =                                dx                             π
π
0 (x  2)
2
3           1                                167/I =  e2x sin 2 x dx                                            3                  tgx
e
81/I =  (ln x)2 dx                                                                                                   138/I =                                           dx                                                             196/I =                                    dx
π sin 2 x  9 cos 2                                                                                                 cos x 1  cos 2 x
π 2x                                                                                                              0                                                         π
2                                                                         x
1                                               111/I =      e             sin xdx                                                                                                                                                      4
0
3                                                     1        x 2e x
e2          ln x                                                                                                        π                                            168/I =                         dx                                 2        x 1
82/I =                   dx                                          2                        1                                 2 cos x  1
0 (x       2) 2                                197/I =  (                  )2 dx
e            x                                  112/I =  x 2 ln(1  )dx                                     139/I =                 dx                                                                                                 1 x  2
1                        x                                  π cos x  2
e
e2      ln x                                                                                                                                                        169/I =  (1  x) ln x dx                                           π
83/I =                dx
113/I =
e         ln x                                              2                                                     1                                                         4     2
1       ln x                                                                       dx                                 π                                                                                                      198/I =    x.tg x dx
1     (x  1) 2                                                                                                   e                                                         0
2                                                            e                                                          2 1  sin x                                  170/I =  x ln 2 x dx
84/I =    x ln(x
2
 1)dx                                                                                 140/I =                 dx                                       1                                                         5
1                                                                                                                       0 1  3cos x                                                                                           199/I =  ( x  2  x  2 ) dx
3
4
π                                                                                                                π
200/I =
4

2
dx
3
229/I =  x 2 (1  x)3 dx                                                                                                   2            3x 3
1     x 5 4
3
256/I =  tg 4 xdx                                           284/I =                             dx
310*/I =
2       sin x
0                                                                                                                 1    x  2x  1
2                                                             dx
π
π                                                                                                                0   cos x  sin x
201/I = 
2          x                                                                                                 4                                                          1                4x  1
dx                                       2   sin x.cos3 x                                                                                   285/I =                                      dx             π
1      x2  2x                            230/I =                                  dx                         π                                                      0x
3
 2x 2  x  2                       2         sin 4 x
2 ln(1  x)
0    cos x  1
2
2 1  sin x x                                                                                  311/I =                          dx
202/I =              dx                                                                                  257*/I =                    e                     dx        286/I =                                                      0   cos x  sin 4 x
4
0 1  cos x
1
1    x2                                               2           4x  1                                                                                     1                                                                π
π                                           231/I =                              dx                       1                                                 2                       1                                        2          tgx
0   x  3x  2
2
258/I =             (1  x ) dx     2 3
                                            dx   312*/I =                               dx
2 sin 2x                                                                                                                                                     1 (3  2x)
203/I =                             dx                             π
0                                                                     5  12x  4x          2                      0    1  ln 2 (cos x)
0 1  cos x
2
232*/I = x sin x.cos xdx
                                                  π                                               2
π
π                                                         0                                                  4                                                          1                1
2008                       π                                         259/I =  x.tg 2 xdx                                         287/I =                              dx
313*/I =
2         sin x
2                  sin            x                                                                                                                                     0        x  1 x                                                       dx
204/I =                                         dx             2        cos x
0
0    cos x  sin x
0   sin 2008 x  cos 2008 x                 233/I =                     dx                              2               1                                               π
0       cos 2x  7                        260/I=                                dx                                2         cos x
1             1
π
0 (4  x
2 2
)                          288/I =                       dx                  314*/I =                               dx
2                                                     4           1                                                                                                              2  cos 2x                                   1 (e
x
 1)(x 2  1)
 sin x.ln(1  cos x) dx
0
205/I =                                               234/I =                         dx
0                                                     1   x 2 (x  1)                                        1           3x 2                                            π                                                    1    3x 1
261/I =                                  dx
2 cos x  sin x                        315*/I =  e               dx
3         x 12                                      π                                                      0           x3  2                              289/I =                    dx                                   0
206/I =                              dx                        2                                                                                                                  π 3  sin 2x
1          x2                               235/I = sin 2x(1  sin 2 x)3 dx
                                                                  2       1  x5
0                                         262*/I =                                          dx                    4
π                                                                                                                        1    x(1  x 5 )                                π
3                                          2 x 1
207/I = sin 2 x dx
4                                                                                                                                                                        2
                                           236/I =                        dx                               π                                               290/I =      (cos x  sin x)dx
3         3
0 3x  2
3
0   cos x                                                                                                    3 cos x                                                     0
263/I =                                  dx
0 1  sin
π                                                      4               1                                               2                                                 π
237/I =                              dx                                                  x
2                                                                                                                                                                        2
208/I =    cos
2
x.cos 4x dx                              7     x x2  9                                     2
π                                               291/I =  cos5 x sin 4 xdx
264/I = sin 6 x dx
0                                                                                                            3                                                           0
π                                                      
1     1                                     238/I =  x sin 3 x cos 4 xdx                                    0   cos x                                       292/I
209/I =                          dx                            0
0e
2x
 ex                                             π
π                                                   π
6   sin x  sin 3 x                                 2
e      ln x                                            2                                        265/I =                         dx                          =    cos 2x(sin
4
x  cos 4 x)dx
210/I =                          dx                  239/I =     cos x              cos x  cos3 xdx                 0       cos 2x                                      0
1   (x  1)        2

π
e                                                                                                             3                  1                                       π
2
266/I =                                       dx                        2       1
1         1                                               1                                                  1       x (1  x )
6                2                  293/I =                  dx
211/I =                  dx                          240*/I =        ln(           x 2  a  x)dx                                                                                0   2  sin x
0      x 1  x                                           1                                                 π
π
2                                          π                                                      2           sin x
1      x                                                       1  sin x                        267/I =                                      dx                         2       1
212/I =                         dx                   241/I =
2
0   cos x  3   2                               294/I =                  dx
04x
2                                                                     dx                                                                                 0   2  cos x
0   (1  cos x)e            x
π2
1      x                                                                                                             sin x
213/I =                   dx                                   π                                         268/I =                   dx
295/I =     
2              1
dx
04x
2
sin 2x  sin x                                    0           x
242/I =
2
                  dx                                  π
2       x x2 1
1                                                     0      cos 3x  1                                      2
3
2      x4                                                                                       269/I =  sin x cos x(1  cos x)2 dx
214/I =                     dx                                 π                                                                                                                   7   x3
0   x2 1                                             4                sin 2x                                0                                               296/I =                         dx
243/I =                                                                                                                         3
0 1  x2
                                    dx                π
π                                                     0   sin x  2cos x
2                    2

270/I = sin x  cos x dx
4 4     4
2    sin 3x                                                                                                                                                                  2           1
215/I =                                                                                                                                                               297*/I =                            dx
             dx                                         2
sin x  cos x  1
0   cos x  1                                           2          x   3                                     0                                                               1   x 1  x3
244/I =                          dx                             π
2
1  x2                                                                                                                 x3
271/I = sin x  cos x dx
0                                                  4 4     4                                                    1
2                                                                                                                                         298/I = 
2            x                                                                                                                                                                                 dx
216/I =                              dx                           2                                                   0   sin x  cos x  1                                      0x              1  x2
0        1 x        2
2          x3                                        π
245/I =                          dx
sin x cos x  cos x                         299/I =
1

1
dx
2 1  x2                                                                                                     2
0         1  x2                        272/I =                             dx                                 1 1  x 
217/I =                     dx
sin x  2                                                               1  x2
11 x
4                                                                                                     0
1         1  x2                                                                                                 π
7   x3
246/I =                          dx                                     1
3               1
218/I =                              dx                           2         x2                                      1 ex                                              300/I =                              dx
0 3 1  x2                                            2                                       273/I =    
3
dx                                              π   sin 4 x cos x
a     x                                                       6
ln 2 1  e x                                          1           x2                                                                                                     π
219/I =                         dx                   247/I =                        dx                             1     x 3  2x 2  10x  1
0 1 e
x                                          0       4  x2
274/I =                                                dx               2    cos x
0                 x 2  2x  9                    301/I =                  dx
1                                                        2                                                                                                               0   cos x  1
1
220/I =  x 1  x dx                                  248/I =                             dx
275/I = 
1             x3
dx                                π
0                                                       2     x x 1   2
0 (x
2
 1)3                                       2     cos x
1                                                         3                                                                                                  302/I =                  dx
221/I =  x 2  1dx                                                                                                  1             3                                               0   2  cos x
1
0                                           249/I =  x5 (1  x3 )6 dx                          276/I =                          dx                                     π
π                                                     0
0     x3  1
2     sin x
π                                                              x 14                                   303/I =                  dx
222/I =
2
 (cos x  sin x) dx
3       3
277*/I = 
1
dx                                 0   sin x  2
2 sin x
0                                           250/I =                         dx                                  0   x6  1                                              π
0 1  sin x                                                                                                             cos3 x
3   x2  1                                                                                      278/I =
1    x                                            304/I =
2
             dx
223/I =             dx                                         π                                                                               dx
0    x 1                                                                                                  0 (2x  1)
3                                                  0   cos x  1
2         cos x
251/I =                     dx                                                                                                 π
224/I =
1
 (1  x) .e
2 2x
dx                       0       7  cos 2x                        279/I = 
7            1
dx                                            2            1
2  x 1                                305/I =                               dx
0
252/I =
4

1
dx
2
0    2cos x  sin x  3
π
1 (1  x)x
2                                            3                                                              π
2          cos x                                                                                             2                   1
225/I =                                   dx                   2 x 1                                    280/I =                                      dx             306/I =
2

cos x
dx
0      cos 2 x  1                          253/I =                        dx                               1       x 1  x2                                                π   (1  cos x)2
0 3x  2
3
7                                                                                                            2                                                               3
3 x 1                                                    π
π
281*/I =  x ln(x  1  x ) dx
1               2
254*/I =  cos x  sin x dx
226/I =           dx                                          3
0 3x  1
3                                                                                                                                                                      4
π 3  sin 2x                                             0                    1  x2                 307/I = tg 3x dx

π                                                                                                                                                                        0
4
2 1  sin 2x  cos 2x                                                                                      4
227/I =                                        dx               π                                        282/I =  (x  1)2 ln x dx                                   308*/I =
1

1
dx
π    cos x  sin x                                     2                                                   1
1 3  e
2x
 cos x cos x  cos xdx
3
6                                           255/I =                                                        3 2

π                                       283/I =     x ln(x  1) dx                                                   π sin 2 x
1 (1  e x ) 2                                          2                                                  0                                                 309*/I =                  dx
228/I =                             dx                                                                                                                                                π 3  1
x
0 1 e
2x
5

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