INSTITUTO SUPERIOR DE ENGENHARIA DE COIMBRA

DEPARTAMENTO DE FSICA E MATEMTICA

Plano de treino intensivo das regras

Primitivao imediata

A.Conhecimento

Reproduza a seguinte regra:

CCpf

ffp

p ,1

'1

1. dxx10

Nota: afaaf ,

2. dxx103

3. dxx10)2(

4. dxx 2)1(

5. dxx 3)12(

6. dxx 2)1(

7. dxx 4)12(3

Nota: qp

q p ff

8. dxx )52(

9. dxx 3 23

10. dxx 32

2

Nota: pp

ff

1

11. dxx 2)3(

1

12. dxx 2)12(

1

13. dxx

1

1

14. dxx

3 21

1

15.

dxx

31

16.

dxx

3

521

3

Nota: 1 pp ffpf

17. dxxx 42 )3(

18. dxxx 332 )1(

19. dxxx 543 )3(2

20. dxxx 5 2 2

21. dxxx 4 43 2)(

22. dxxx 5 32 2

23. dxxx

4321

24. dxx

x 23

2

)3(

2

25. dxx

x 34

3

)3(

2

26. dxx

x

3 2 2

27. dxx

x

5 3

2

2

2

28.

dx

x

x

5322

2

Nota: ff efe

29. dxee xx 2)1(

30. dxe

ex

x

2)2(

31. dxee xx 22 9

32.

dx

e

e

x

x

21

33.

dxe

e

x

x

1

2

34.

dx

e

e

x

x

3

1

1

35. dxx

ee xx

2)1(

Nota: f

ffln

36. dxxlnx2))((

1

37.

dxx

xln

1

))1(( 3

38. dxxlnx )(14

39. dxxlnx )(1

24

40. dxxlnx )(12

41. dxeln

xx )2(

24

42.

dxxlnx 1)(

1

2

43.

dxxlnx

31)(

1

Nota: )( fcosffens

)( fensffcos

44. dxxsenxcos )()(2

45. dxxsenxcos )2()2(

46. dxxsenxcosx )()(242

47. dxxsen

xcos )(

)(2

48. dxxsen

xcos )3(

)3(4

49. dxxcos

xens 2)2)((

)(

50. dxx

senx

cos 3 )2()

2(

51. dxx

cosx

sen 3 )3()

3(

52. dxxcosxens 5 )3(2)3(

53. dxxsenxcosx5 322 )()(

54. dxxcosxensx3

22 )()(

55. dxxsen

xcos

)3(

)3(

56. dxxsen

xcos

)1(

)1(3

57.

dx

xcos

xxsen

3 22

2

)1(

)1(

58. dxx

xsenxcos

)()( 3

59. dxesenecose xxx )()(3

60. dxesen

ecosex

x2x

)()(

23

2

61.

dxecos

eense

x

xx

23)(

)(

62. dxxlnsenxlncosx

)()(1 3

63. dxxlnxsen

xlncos )(

)(3

64. dxxlnsenx

xlncos

)(

)(

65. dxxlnsenx

xlncos

)(

)(

3

Nota: )(

1)(

fcosfsec

)(

1)(

fensfcosec

66. dxxcosecxcos )()( 2

67. dxxsec

xens )2(

)2(3

68. dxxsec

xens

)2(

)2(

3

69. dxxcosec

xcos

3 2 )3(

)3(

70. dxxcosecxcosx 3 222 )()(3

71. dxeseceense xxx )()( 31

72. dxxlnxcosec

xlncos )(

)(32

73. dxxxsec

xens

)(

)(

3

Nota: )(2 fecsfftg

)(2 fecscoffgcot

74. dxx

cotgx

cosec )2()

2( 42

75. dxxtgxsec )3()3(32

76. dxxtgxsec 22 )1)2()(2(

77. dxxtg

xsec )(

)(3

2

78. dxxcos

xtg )2(

)2(2

3

79. dxxtgxcos )2()2( 32

80. dxegcoteens

exx

x

)()( 32

2

81. dxxlngcotx

xlnsec2

))(())((

4

82. dxxgtx

xcosec 2

)(

)(5

Nota: 21 f

ffarctg

21 f

ffarcsen

83. dxxarctg

x

3

2))((

1

2

84.

dxx

xarcsen

2

2

41

))2((

85. dxearctg

e

e xx

x

)(1

22

86.

dxe

earcsene

x

xx

2

3

1

)(

87.

dxxarctgx

x

)(1 24

88.

dxxarcsenx

x 324

))((1

89.

dxxlnx

xlnarcsen

)(1

))((

2

90.

dxxxarcsen )1)((

4

2

91.

dxxarctgxx

x

32 1)(

92.

dxxlnarctgxlnx 32 ))(()(1

3

Nota:exerccios variados

93. dxxsen

xsen 22 )2)((

)2(

94.

dx

ecos

eense

x

xx

3

23)(

)(

95. dxexecossenxsenx 2)1(

96.

dxe

xecos

senx

senx

3 2

2

1

97. dxxcoslnxtg

)(

)(2

98.

dxxsenlnxcotg3

1))(()(2

99. dxxsenln-

xcotg

3 ))((1

)(2

100. dxecotgeeccose xxx )()(21