cac dang bai tap nguyen ham

<span class='text_page_counter'>(1)</span>Chương 3. NGUYÊN HÀM- TÍCH PHÂN VÀ ỨNG DỤNG 1. CÔNG THỨC THƯỜNG DÙNG . 0dx C. . dx x  C. .  x dx . x 1 C  1. 1. dx. . x dx  x. . e dx e. x. . x.    1. x a dx . ax C lna.  0  a 1. . sin xdx  cosx  C. . cosxdx  sin x  C. . cos x dx  cos x  tan x  C. . sin.  ln x  C. C. 1. dx. 2. 2. 1. . 2. dx dx   2  cot x  C x sin x. 1 dx  eax b  C a. ax b. . 1. cos ax  b dx  a sin  ax  b  C  a  0 . e.  a  0.  1. dx. 1. ax  bdx  ax  b  a ln ax  b  C. 1. sin  ax  b dx  a cos ax  b  C  a  0 2. LUYỆN TẬP Bài 1. Tìm nguyên hàm của các hàm số sau 1. 2.. f x  x3  4x .  . 3 x. 5.. f x  x  3x  4x.  . 6.. 2x4  2 f x  x2 3..  .  . f x  4.. 1 2 x. . 7. 3 3. x. . 5 5. x. 8. 9..  . f x . x 1 x2. f x  2sin2.  . x 2. f x  tan2 x.  . f x  cos2 x.  .  . f x . 1 sin2 x cos2 x.

<span class='text_page_counter'>(2)</span> 10. 11. 12..  e x  f x e  2   cos2 x   13..  . f x  sin4 x cos3 x.  .  . f x  2sin3x cos2x.  . x. . 14.. . x. f x e e  1. x.  . f x e3x 1. Bài 2. Tìm nguyên hàm F(x) của các hàm số f(x) sau thỏa mãn điều kiện tương ứng 1. 2.. f x  x3  4x  5.  .  . f x  3  5cosx. . F 1 3. 6..  . F  2. 3  5x2 f x  x 3..  .  . . .  . 5.. 1 x.  . f x . x3  3x2  3x  7. . F 1  2.  . Bài 3. Chứng minh rằng F(x) là một nguyên hàm của f(x).  .  . F x  5x3  4x2  7x  120;.  . . . f x 15x2  8x  7.  . F x  ln x  x2  3 ; f x . 2. 3. 4..   . . 5..   . x2  3. .  .  . F x  tan4 x  3x  5; f x  4tan5 x  4tan3 x  3.  x2  4   2x F x  ln  2 ; f x  2 x  4 x2  3  x  3.  . x2  x 2  1 F x  ln ; 2 x  x 2  1 6..  . Bài 4. Tính các nguyên hàm sau 1.. 1. F x  4x  5 ex ; f x  4x  1 ex.  .  5x  1. 11. xdx.  x  1. f x  sin2 9.. 1.. . 8.. x2  1 3 f x  F 1  x 2 4. f x x x .   F '  0  3. 3x4  2x3  5 f x  F 1 2 x2 7.. F e 1.  .  . f x  sin2x cosx. .  . f x . . . . . 2 2 x2  1 x4  1. x 2. 2.  . F 0 8.    F   2 4.

<span class='text_page_counter'>(3)</span>  2.. 2. dx.  3  2x. sin 10. . 5. sin x. dx  11. cos x 5. 5  2xdx. 3.. . 4..  2x. 5..  x. 2. 3. . tan xdx. 7.  1 xdx. . 4.  5 x dx. 2. exdx. 13.. 3x. dx. 5  2x3 dx. . . x 1 x. 9..  3. dx. ex. 15.. . x. x2  1. x2  1xdx. . e. xe 14. . 2. 8..  12. cos x. 2. x dx  2 6. x  5 7.. x cosxdx. . 2.  x dx. ln3 x  x dx 16..  17. e. dx 1. x. etan x  2 dx 18. cos x. Bài 5. Tính các nguyên hàm sau. .  1 x  2. 1.. 3. dx.  2.. x2dx. dx.  1 x  2. 3. 7..  1 x. 2. dx 2 8. x  x  1 3. 9.. x. x2  1dx. 2. 3.. 4..  1 x dx dx. . 2. 4 x 2. 5.. x2 x2  1dx 10. . x. 11.. . 2. 1  x dx. dx  2 6. 1  x. 12.. . x2 x2  4 1 x2  3. dx. dx.

<span class='text_page_counter'>(4)</span> Bài 6. Tính các nguyên hàm sau 1.. x ln  1 xdx. 2..  x. 3.. x sin2xdx. . 2.  2x  1 exdx. 4..  1 x cosxdx. 5.. e. 6.. x. 12.. x xe dx. x. sin2xdx. 2. cosxdx. Bài 9. Tính các nguyên hàm sau x. 2. 1.. xe dx. 2.. x cosxdx. 3.. lnxdx. 4.. ln  x . 5..   x. 6.. x sin xdx. 7.. x sin 2x  1 dx. x cos xdx 18. . 8..  1 x cosxdx. sin xdx 19. . 9..  1  2x e dx. cos xdx 20. . 2. e x 13.  x.  x  1 cosxdx. . 1  x dx. .  3x  1 exdx. . x. dx 2. ex cosxdx 15.  x. e 16. . sin xdx. x2 cosxdx 17. . x. x ln 11. .  1 dx. 14. . . xe 10. . . 2. 2. x sin xdx 21.  xdx. Bài 10. Tính các nguyên hàm sau 1.. e. x. dx. lnxdx. 2.. 3. 4.. . . x. sin. x2 dx. 6..  x ln xdx. 7.. x. 8..  lnx. 2. lnx. lnxdx x 3. x. 5.. xdx. 5. dx 2. dx.

<span class='text_page_counter'>(5)</span> 2. 9.. x. sin xdx. . . ex sin 2x  1 dx 10. . . . x dx  2 sin x 15. esin x cosxdx 16. . cosx ln sin x dx 11. . 1 x x ln  1  x dx 12..  13.. x cosx.  1 sin x. 2. dx. x  sin x dx  2 cos x 14..  17.. x2exdx.  x  2. 2.  1 tan x  tan x e dx 18.  2. x. 2.  lnx   x  dx 19. x3. 20..  1 x. 2. dx. Bài 19. Tính các nguyên hàm sau 4. xdx. 4. xdx. 4. xdx. 1.. tanxdx. sin 12. . 2.. cot xdx. cot 13. . 3.. cos xdx. 4.. sin. 2. 5.. tan. xdx. sin6 xdx 16. . 2. 6.. cot. xdx. sin x sin 3xdx 17. . 3. 7.. sin. xdx. cos7x cos3xdx 18. . 8.. cos xdx. 9.. tan. 2. 2. tan 14. . 6. xdx. cos xdx 15. . 3. sin5x cosxdx 19. . 3. xdx. sin x sin2x cos5xdx 20. . 3. xdx. cosx cos2x cos3xdx 21. . cot 10. . 4. cos xdx 11. . cos5x cos4x sin 3xdx 22. . Bài 20. Tính các nguyên hàm sau 3. 1.. sin x cos xdx. 3. 2.. sin. x cosxdx.

<span class='text_page_counter'>(6)</span> 3. x cos4 xdx. 4. x cos4 xdx. 3.. sin. 4.. sin. dx  20. cosx sin x cos3 xdx  1  cos2 x 21.. sin3 x  4 dx 5. cos x. 22.. sin3 x  2 dx 6. cos x. . . cosxdx.  23. 6  5sin x  sin. 2. 5. 7.. 3. 2 sin2x 1  sin x dx. sin xdx. x. cos3x. dx  24. sin x. 5. 8.. cos xdx. 9.. sin x cosx 1 cosx dx. . . x. . 2. 25..  1 tan x tan 2  sin xdx. 3. cos xdx. sin3x  sin3 3x  1 cos3x dx 26..  10. 1  sin x. 4sin3 xdx  11. 1  cosx. cos2xdx.  27. 1  cosx. sin2x dx  2 4  cos x 12. sin2x cosx.  13. 1  cosx cosx. e 14.  15.. cos2x dx 2 x cos2 x.  28. sin. dx. dx.  29. sin. 3. sin2xdx. . dx. . sin x  tan x  e cosx dx. e. 16. . sin x. . x.  cosx cosxdx.  30. sin. 4. x. dx  3 3 31. sin x cos x dx x cos4 x. 1  2sin2 x dx  1  sin2 x 17..  32. sin. sin2xdx  2 18. 4  cos x.  33. cosx sin. dx  19. sin x.  34. 1  cosx. 4. dx. 3. dx. x.

<span class='text_page_counter'>(7)</span> dx  35. 1  sin x. sin x cosx dx  4 4 sin x  cos x 37.. 1  cosx. sin2xdx. dx  36. 1  cosx.  38. 4  cos 2x 2. Bài 1. Tính các tích phân sau 2.  x. 1.. 3. .  2x  1 dx. 1. 2. . 2. 2.. 3 3x1   e  dx x . . 1. 2. e. x. 1. . 1 2. 6.. 1. . . 7..   x2  dx . x 1 x . 1. 2. x dx  2 x  2 4. 1. dx.  x  x  x 2. 1. 2. 2. 2. x 1 dx 2. x. 3.. . x4  4. . 5..  x. . 1. 2.  x. 2. 8.. .  x x  3 x dx. 1 4. . 9.. . x  23 x  44 x dx. 1. Bài 2. Tính các tích phân sau. 1.. 2. 4.  x  1dx. x. 5. 2.. 6.. 1. . x2 x 2. 2. 2.  x. 2. 3.. 3x2dx.  1 x 3. x 2 x 3. 3. 2x  1. x  x  1 dx 1. 2 2. 0. 0. 8.. xdx.  1 x 2. 5.. . dx.  2.  x x  x dx. 1. 2. 4.. 3. 7.. 3. Bài 3. Tính các tích phân sau. 9.. x2  9dx. 0. 4. dx. x 1. . x  1 dx. dx 5  x3.

<span class='text_page_counter'>(8)</span> .   sin 2 x    dx  6  0 1..  2. 7..  2. 2..  2sin x  3cosx  x dx   3. 3.. 0.  4. 8.. 4.. 0. 9.. 10.. 2 3tan xdx. 6..  2cot  . 2. x cos2 xdx. 0. .   tan x  cot x. . 11.. x  5 dx.   sin   x  4      dx  sin   x  2 4   4. 6. 12.. 4. cos xdx 0. Bài 4. Tính các tích phân sau 1. ex  e x dx  x x e  e 0 1. 2. 2.. 1. ex dx  x 2 0 6..  x  1 dx. x. 2. 1.  x ln x.  2. 7.. 1. e2x  4 dx  x e  2 3. 0 ln2. 4.. e dx x 1. 2. 9. x.  e  x e 1    dx  x 1  5.. ex.  x dx 1.  1. e. 10.. sin xdx. 0. e. e 0. 8.. cosx. e 4. x. 2. 6.  2.  4.  4. 2. sin  3.  3. 5.. 1  cosx dx  1  cosx 0.  2. tan xdx cos2 x. . 0.  2.  6.  sin3x  cos2x dx. dx. 1  sin x. 1  ln x dx x. ln x. x 1. dx. dx.

<span class='text_page_counter'>(9)</span> 1. 11.. xe dx 0. 14.. 1. 12..  4. x2. dx. 1  2sin2 x dx  1  sin2 x 0  2. 1 e. x. 0. 15.. 3. dx x 13. 1 e  1.  e. sin x. .  cosx cosxdx. 0. Bài 5. Tính các tích phân sau 1. 1.. x  1  x.  1 x . 0. 1. 2. 11.. 3. 12.. x dx 2 1. 13.. xdx. . 5.. 1  x2dx. 1. 6.. x. 2. 1  x dx. 0. 2 3. 7.. x 5. 3. 8.. 0. 15.. dx. 17.. exdx  x 9. 0 1  e. 0. 10.. 18.. cosx  sin x cosx dx 2  sin x 0. . . ex  1. 3. 19.. sin2xdx. 1  cos x 2. 0.  4. exdx. . 0.  2. ln2. . sin2xdx 2 x  cos2 x. 2sin.  2. 3. 1  x2. ln 3. cos2 x  4sin2 x.  4. x2  4. x  2x. . 0. sin2xdx. sin3 x dx  2 cos x 16. 0. dx. 5. .  6. 0. 3. 1. 1  3ln x ln x dx x. cosx sin3 x dx  2 1  sin x 0 14.. 1. x. . 2  ln x dx 2x.  2. 2x  1. 0. 1.  2. x 0.  e. 5. 1. 4.. dx. x3dx. . 3.. e. 0. 1. 2.. 19.  0. 2.  tan x  1 dx cos2 x.

<span class='text_page_counter'>(10)</span>  2. 20.. 3cot x  1 dx sin2 x.   4.  4. 21.. cos2xdx. sin x  cosx  2 0. Bài 6. Tính các tích phân sau 1. 1 2. 1.. dx.  1 x. 0. 2. 0 1. 2..  12.. x2dx.  2. 2. 3.. 4  x2dx. 3. 14.. dx  2 4. 0 x  3. 15.. dx  2 5. 0 x  9. 6.. 0. . 1. 7.. x 0. 1.  8.. 0.  9.. . .  1 x2  2. xdx  x2  1 dx.  2 x . 1. 0. 4. 2. 2. 16.. 17.. 11..  1. x. 2. 2x  x2dx. 0.  0. 1 x dx 1 x.  0. dx x3 x 1. 1. 18.. 3. dx. x  1 0. . . dx. 2. x 1 dx x3. Bài 7. Tính các tích phân sau.  0. 20..  0. 2x  1  3 2x  1 dx x 1 x. 2 3. 21.. x 5. 1  x2 dx. 1. 2 10.  1 x  2x  2 2. 1  x2. 1. 19..  1 x . . 0. x2dx. 4. dx. 0. . 2 2. dx. 2. x2  1. 2. 2. 1. x. 5. dx. x 2 2. 1. 1. 2. 3. 13.. x.  1 x . 2. 4  x2. 0. dx. dx x2  4.

<span class='text_page_counter'>(11)</span> 1.. 2.. 2. 2. lnxdx. x. 15.. 1. e. ln  1  x dx. x. 2. 16.. 0. . . ln. 17.. 2. ln  x. 18.. 1. e. . 19.. 2. 0. 20.. 1. 21..  2x  1 ln xdx. 1. 9.. .  1 dx. 0. x ln  x. 2. 10.. .  x  1 dx. 0.  1  ln x. ln2 x dx  x 1. 2. 13.. 25.. 14..  x  2. x. 3. .  5 dx. . ln 1  x 2. x.  dx.  dx. 2. ln2 xdx. 1. ln2 x dx  x 1. 1 e. . ln x. . x 1. 26.. x ln 0. 1.  1. 0.  2. 0. 2. . ln x  1. . lnx dx  2 x 12. 1. x ln  x. dx. 1. e. 2. 3. 2. e. 24.. e. 11.. dx. e. 23.. 1. 2. 1.  22.. x ln  x. dx. 3  ln xdx x.  x ln x. 1. 1. 2. . 2. e.  x  2 ln xdx. 1.  x  1.  2x . 2. 8.. 3  ln x. e.  2x  7 ln  x  1 dx 2. 7.. 0. .  x dx. 2. ln  1  x dx 3. x 1 dx x 1 2. 6.. ln xdx. 1. 2. 0. 3. 5.. dx. 1. ln 2x  1 dx 3. 4.. 3. 1. 1. 1. 3.. lnx. 2. 27.. x 0. 2. dx. 1  x2 dx 1  x2.  1 ln  1   dx x .

<span class='text_page_counter'>(12)</span> 1. 28..  1 x. 2. x. 2. .  1 ln x. . 41.. 42.. . . 1. 44.. x lg xdx. 1. cos ln x dx 1.  2. 1. 10. 45.. 2 x logxdx 1. .  sin x ln  1 cosx dx 2.  4. 2. lnx dx  5 x 1 34. e. 35.. cos  ln x dx e. 2. 2. 33.. 0. 2. x log xdx 10. 32.. cosx ln  1  cosx dx. e2. 43.. 2. 31.. 1. . 2 ln x  1 x dx 1. sin  ln x dx  2. dx. x. 1. 2. 30.. e.  dx. 0. e. 29.. . ln 1  x. 46.. ln  1  tanx dx 0.  4. 3. x 1 ln xdx x 1. . 47.. cosx ln  tan x  dx   6. 1.  1 x  x ln   dx  1 x   0 36. 1. 37.. 2. 38.. 39..  dx. 2. x ln x  x  1.  0. .  3. x2  1. 48.. 0. x. 49.. x ln 1 x dx.  6. 1.  2.  4.  . . . cos2x ln cosx dx. 50.. 2. cos x. . ln cosx. . sin2 x.  dx  dx. . cosx ln sin x 2. sin x. 6. 0.  3.  2. 40..   4. . ln cosx. cosx ln  sin x  dx   6. 51..   4. . ln tan x 2. cos x.  dx.  dx.

<span class='text_page_counter'>(13)</span> Bài 8. Tính các tích phân sau ln2. 2 x. 1.. xe dx 1. 2.. 12.. 0. . x e  1 dx 0. 13..  2x. xe. dx. 0. 14.. 1.  x  2 e. 2x. 4.. 0. 15.. x e dx 0. 16..  x. 2. .  2x exdx. 0.  x. 2. 8.. 0.  0. 2. x3e x 1 x2  1 2x. 1.  18.. 3 x2. x e dx. .  3 x  1 dx.  1  x. 2.  x  1. 2.  x  3 e. 2x. 19.. dx. 0. 2x. e dx. 0.  xe. 0. xexdx. 1. 0. 2. x2  1 dx  3x e 20. 0. x. dx. 0. 1. 11.. 0. x  e. . 1. 10.. x2 dx. 0.  2x  1 e xdx. 1. 9.. 2. 17.  1. 1. 1.  1  x x1  1  x   e dx  x 1. 3. 1. 7.. 0. x. 2 x. 6.. 2. 3 x x e dx. 1. dx. 1. 5.. dx. 0. 2. ln2. 3.. xe. x 2. 1. . x. . 3. 1. x2  2 dx  x e 21. 0. 5 x x e dx 0. Bài 9. Tính các tích phân sau  2. 1..  x 0. 2. .  2.  1 sin xdx 2.. 2.  2x  1 cos xdx 0.

<span class='text_page_counter'>(14)</span> 1. 2.  cos 3..  4.      3. 2. 3. xdx. 16.. 0. cos. xdx. 0. 17.. x sin2xdx 0. 18.. 2. x cos xdx 0. 19.. 2. x. 2. sin xdx 20.. 0.  2. 9.. 10..  x  1 sin2xdx 0. 21.. 2. 0. xdx 2 x.   sin 4. x  sin x.  cos x 2. dx. 0. x  2cos x  1 dx 2. 0. 0. 1  cos2x.  x  1 sin xdx. 22.. 0. . 0. 2. 23.. x. sin2  xdx. 0.  3. x sin xdx. 0. x sin x.  cos x dx 2. 24.. . 3.  2.  x  sin x cosxdx 2. 0. 25.. x  sin x dx  1  cos x  3. 2. x cos2xdx 0. xdx. 1.  2x  1 cosxdx.  2. 14.. xdx. cos x.  4.  2. 13.. 4.  2. 2. 12.. xdx.  4.  2. 11.. 2. x tan . 1. . 8.. 0.  3.  2. 7.. x cos xdx. .  3.  4. 6.. cosxdx. 0.  3. 2 4. 5.. x 2 4.  sin. 4.. 15.. 2. 1. 2. 1  xdx. 2. 26.. x 0. sin2 xdx.

<span class='text_page_counter'>(15)</span> Bài 11. Tính các tích phân sau 1. 1.. . 1. x2  1dx 3.. 0. 1 2. 2.. x. 0. 4.. 1.   sin. 4. 5..  4.  3dx. 0. .  2. x2  4dx. 1. cos x dx 0. 6.. dx. 4.  4. 4. x. 1. cos x dx 6. 0. Bài 12. Tính các tích phân sau 2. 1.. 2.. 2. x  1 dx 0. 7.. 2. 8.. 2x  1 dx 0. x. 2. x.  1 dx. 3. 4. 12..  x  3 . . x  4 dx. 4. 2. 2. 5.. x. 10.. x. . x  2 dx. 3. 0. 2. 6..  x  2 .  x dx. 2.  6x  9dx. 3.  2x  xdx. 1. x 0. 14. 5. 2. 2. 2. x 4. 13.. 3. 4..  2 x dx. 2. 11.  1. 0. 9.. 2 x  3x dx. x.  4x  3 dx. 6. 3. 3.. 1 2. x 2  4 dx. 3. x. 3.  4x2  4xdx. 0. 1. 0. . 4  xdx. 15.  1.  2x  3 dx. 0. Bài 13. Tính các tích phân sau. 1.. .  sinx dx.  cos2x dx. 2..  1  cos2xdx 0. 8.. 2. 5.. . 6.. 1  cos2xdx 9.. 0. cosx sin xdx. . 1  sin2xdx. 7.. 1  sinxdx. . 1  cosxdx. 0. 10..  2. 0. .  2. .  4. . 3.. 4.. 2. 3 4. . .  2.  0. 1  sinxdx.  3.   6. tan2 x  cot2 x  2dx.

<span class='text_page_counter'>(16)</span> 11.. 12..  2. .  cosx. cosx  cos3 xdx. 2.  3.   6. dx 1  cot2 x  1 2 cos x. Bài 14. Tính các tích phân sau 2. 1.. 1 dx  x x  1 1. . 2 3. 2.. . 3.  6.. 3. 7.. 1. dx  2 3. 0 x  5x  6 x3dx 2 4. 0 x  2x  1. 5.. 0. . 4. 9.. xdx.  1 2x. dx  2 1 x 1 x. 12.. . dx. x  x  1. 10.. 0. 2x3  6x2  9x  9 dx  2 x  3 x  2 1 3. 3x2  3x  3 dx  3 x  3 x  2 13. 2 1. x. 2. 1. 3. x3  x  1 dx  x 1 0. 11.. x3dx 2 8. 0 x  3x  2. 3. . 9. 1 2. 1. 1.  1 x. 4. dx. x  x. 2. 1. x2dx. x. 4x  11 dx  5x  6. 2. 0. 2. 14.. 0. 2x  7 dx  7x  14. 15. 1. x. 2. 0. 4x  8 dx  4x  2014.

<span class='text_page_counter'>(17)</span> ỨNG DỤNG TÍCH PHÂN TÍNH DIỆN TÍCH, THỂ TÍCH.

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