7. Antiderivatives & Indefinite Integrals

Evaluate the following integrals.

∫ (1 - cosx)/(1 + cosx) dx

Evaluate the integrals in Exercises 31–78.

43. ∫tan(ln v)/v dv

Exercises 59–64 require the use of various trigonometric identities before you evaluate the integrals.

∫ cos²(2θ) sin(θ) dθ

9–61. Trigonometric integrals Evaluate the following integrals.

28. ∫ 6 sec⁴x dx

9–61. Trigonometric integrals Evaluate the following integrals.

37. ∫ [sec⁴(lnθ)]/θ dθ

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

6. ∫ (2 − sin 2θ)/cos² 2θ dθ

Evaluate the integrals in Exercises 1–22.

∫ sin⁴(2x) cos(2x) dx

Evaluate the integrals in Exercises 33–52.

∫ eˣ sec³(eˣ) dx

9–61. Trigonometric integrals Evaluate the following integrals.

38. ∫ tan⁵θ sec⁴θ dθ

Use Table 5.6 to evaluate the following indefinite integrals.                                                                                                               

 (d) ∫ cos 𝓍/7 d𝓍

76-81. Table of integrals Use a table of integrals to evaluate the following integrals.

79. ∫ sec⁵x dx

Evaluate the integrals in Exercises 37–44.

∫ eᵗ √[tan²(eᵗ) + 1] dt

Evaluate the integrals in Exercises 41–60.

43. ∫6cosh(x/2 - ln3)dx

Find $g\(\left\)(\(\theta\]\right\))$ by evaluating the following indefinite integral.

$g\(\left\)(\(\theta\[\right\))=\(\int\)^{}\(\left\)(5\(\sec\)^2\(\theta\)-2\(\csc\)^2\(\theta\]\right\))d\(\theta\)$

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ sin 𝒵 sin (cos 𝒵) d𝒵