8. Definite Integrals

7–84. Evaluate the following integrals.

35. ∫ from 0 to π/4 [(tan²θ + tanθ + 1) sec²θ] dθ

Evaluate the following integrals.

65. ∫ from 0 to 1/6 1/√(1 - 9x²) dx

7–84. Evaluate the following integrals.

62. ∫ from 0 to π/2 √(1 + cosθ) dθ

7–84. Evaluate the following integrals.

56. ∫ from π to 3π/2 sin2x e^(sin²x) dx

9–61. Trigonometric integrals Evaluate the following integrals.

53. ∫ from 0 to π/4 of sec⁴θ dθ

9–61. Trigonometric integrals Evaluate the following integrals.

59. ∫ from 0 to π/2 of √(1 - cos2x) dx

9–61. Trigonometric integrals Evaluate the following integrals.

60. ∫ from 0 to π/8 of √(1 - cos8x) dx

9–61. Trigonometric integrals Evaluate the following integrals.

40. ∫[0 to π/6] tan⁵(2x) sec(2x) dx

9–61. Trigonometric integrals Evaluate the following integrals.

57. ∫ from 0 to π of (1 - cos2x)³ᐟ² dx

9–61. Trigonometric integrals Evaluate the following integrals.

19. ∫[0 to π/3] sin⁵x cos⁻²x dx

7–84. Evaluate the following integrals.

7. ∫ from 0 to π/2 [sin θ / (1 + cos² θ)] dθ

9–61. Trigonometric integrals Evaluate the following integrals.

22. ∫[π/4 to π/2] sin²(2x) cos³(2x) dx

2–74. Integration techniques Use the methods introduced in Sections 8.1 through 8.5 to evaluate the following integrals.

9. ∫ (from 0 to π/4) cos⁵ 2x sin² 2x dx

2–74. Integration techniques Use the methods introduced in Sections 8.1 through 8.5 to evaluate the following integrals.

68. ∫ (from -1 to 1) dx/(x² + 2x + 5)

2–74. Integration techniques Use the methods introduced in Sections 8.1 through 8.5 to evaluate the following integrals.

51. ∫ (from 0 to π/4) sin⁵(4θ) dθ