Lista de cálculo

MAT2455 - C´lculo Diferencial e Integral III para Engenharia a Lista de Exerc´ ıcios - Revis˜o de integrais a Calcule as integrais indefinidas abaixo (de 1 a 73): x7 + x2 + 1 dx x2 tg2 x dx sen3 x √ dx cos x x dx 1 + x2 x x2
5

1. 4. 7. 10. 13.

2. 5. 8. 11. 14.

e2x dx 7 dx x−2 tg x dx x dx 1 + x4 sec x dx 4x + 8 dx 2x2 + 8x + 20 ex dx 1 + ex ex √ 3 1 + ex dx

3. 6. 9. 12. 15.

cos 7x dx tg3 x sec2 x dx tg3 x dx x2 dx 1 + x2 1 √ dx x 1 + ln x √ ln x dx x sen 2x dx 1 + cos2 x √ sen x √ dx x x sen x dx (ln x)2 dx arcsen x dx sen2 x cos3 x dx 3x2 + 4x + 5 dx (x − 1)(x − 2)(x − 3) x5 + x + 1 dx x3 − 8
√

1 − x2 dx x3 + 1 dx

16. 19. 22. 25. 28. 31. 34. 37. 40. 43. 46. 49. 52. 55.

17. 20. 23. 26. 29. 32. 35. 38. 41. 44. 47. 50. 53. 56.

18. 21. 24. 27. 30. 33. 36. 39. 42. 45. 48. 51. 54.

dx √ (arcsen x) 1 − x2 ex x2 dx earctgx dx 1 + x2 ex cos x dx xe−x dx sec3 x dx sen2 x cos2 x dx 1 dx 2 + 8x + 20 2x √ x2 dx 1 − x2 1 + x2 ) dx
3

2x(x + 1)2006 dx xr ln x dx, r ∈ IR x arctg x dx cos2 x dx 1 − sen x dx cos x 3x2 + 4x + 5 dx (x − 1)2 (x − 2) x2 √ 1 − x2 dx

e √

x

dx

ln(x +

dx 5 − 2x + x2 x dx −4 1 dx + b2 x 2 x2 ) 1 √ 1 − x2 dx

x ln x dx

sen(ln x) dx a2 + b2 x2 dx 3 − 2x − x2 dx sen5 x dx

x2 √

x3

3x2 + 5x + 4 dx + x2 + x − 3 x2 − 2x + 2 dx

a2

(1 +

57.

cos3 x dx sen3 x x cos5 2 2

58.

59.

cos5 x dx sen3 x

60.

dx

1

61. 64. 67.

sen5

1 dx x cos3 x

62. 65. 68.

sen4 x dx cos6 (3x) dx 1−x dx 1+x arctg x dx x2

63. 66. 69.

sen2 x cos5 x dx cos2 x dx sen6 x √

sen2 x cos4 x dx 1 dx sen2 x cos4 x x+1 dx x2 (x2 + 4)2 4x2 − 3x + 3 dx (x2 − 2 + 2)(x + 1)

1 √ dx x− 3x √ (Sugest˜o: Fa¸a u = 6 x) a c 72. √ x2 dx dx 2x − x2

70. 73.

71.

74. Determine condi¸˜es sobre a, b, c, d ∈ IR para que as primitivas de co (x − a)(x − b) sejam fun¸˜es racionais. co (Resp.: d = c ou (a + b)(c + d) = 2(ab + cd)) f (x) = (x − c)2 (x − d)2 −1 x2 75. Calcule dx. Sugest˜o: Calcule a