7. Antiderivatives & Indefinite Integrals

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

22. ∫ tan³ 5θ dθ

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

29. ∫ cos⁴ x/sin⁶ x dx

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

32. ∫ csc²(6x) cot(6x) dx

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

48. ∫ sin(3x) cos⁶(3x) dx

7–84. Evaluate the following integrals.

82. ∫ 1/(1 + tanx) dx

90–103. Indefinite integrals Determine the following indefinite integrals.

∫ dx / (1 - sin² x)

90–103. Indefinite integrals Determine the following indefinite integrals.

∫(1 + 3 cosΘ) dΘ

1. State the half-angle identities used to integrate sin²x and cos²x.

9–61. Trigonometric integrals Evaluate the following integrals.

10. ∫ sin³x dx

9–61. Trigonometric integrals Evaluate the following integrals.

11. ∫ sin²(3x) dx

9–61. Trigonometric integrals Evaluate the following integrals.

13. ∫ sin⁵x dx

7–84. Evaluate the following integrals.

27. ∫ sin⁴(x/2) dx

7–40. Table look-up integrals Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table.

8. ∫ sin 3x cos 2x dx

9–61. Trigonometric integrals Evaluate the following integrals.

15. ∫ sin³x cos²x dx

9–61. Trigonometric integrals Evaluate the following integrals.

16. ∫ sin²θ cos⁵θ dθ