7. Antiderivatives & Indefinite Integrals

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ sinx·cos²x dx

Evaluate the integrals in Exercises 53–58.

∫ sin(2x) cos(3x) dx

Evaluate the integrals in Exercises 41–60.

41. ∫sinh(2x)dx

7. How would you evaluate ∫ tan¹⁰x sec²x dx?

Evaluate the integrals in Exercises 37–44.

∫ cos⁵(x) sin⁵(x) dx

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

22. ∫ tan³ 5θ dθ

9–61. Trigonometric integrals Evaluate the following integrals.

16. ∫ sin²θ cos⁵θ dθ

4. What substitutions are made to evaluate integrals of sin(mx)sin(nx), sin(mx)cos(nx), and cos(mx)cos(nx)? Give an example of each case.

Evaluate the integrals in Exercises 33–52.

∫ tan⁴(x) sec³(x) dx

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

∫(1 + 3 cosΘ) dΘ

7–84. Evaluate the following integrals.

27. ∫ sin⁴(x/2) dx

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ (tan²x + sec²x) dx

3. Describe the method used to integrate sin³x.

Evaluate the integrals in Exercises 37–44.

∫ sec²(θ) sin³(θ) dθ

Explain why or why not. Determine whether the following statements are true and give an explanation or counterexample.

d. ∫2 sin x cos x dx = −(1/2) cos 2x + C.