7. Antiderivatives & Indefinite Integrals

69. Different substitutions

b. Evaluate ∫(tan x sec² x) dx using the substitution u=secx.

7–64. Integration review Evaluate the following integrals.

53. ∫ eˣ sec(eˣ + 1) dx

3. Describe the method used to integrate sin³x.

4. Describe the method used to integrate sinᵐx cosⁿx, for m even and n odd.

5. What is a reduction formula?

7. How would you evaluate ∫ tan¹⁰x sec²x dx?

9–61. Trigonometric integrals Evaluate the following integrals.

31. ∫ 20 tan⁶x dx

9–61. Trigonometric integrals Evaluate the following integrals.

32. ∫ cot⁵(3x) dx

9–61. Trigonometric integrals Evaluate the following integrals.

34. ∫ tan⁹x sec⁴x dx

9–61. Trigonometric integrals Evaluate the following integrals.

37. ∫ [sec⁴(lnθ)]/θ dθ

9–61. Trigonometric integrals Evaluate the following integrals.

38. ∫ tan⁵θ sec⁴θ dθ

9–61. Trigonometric integrals Evaluate the following integrals.

43. ∫ tan³(4x) dx

9–61. Trigonometric integrals Evaluate the following integrals.

45. ∫ sec²x tan¹ᐟ²x dx

9–61. Trigonometric integrals Evaluate the following integrals.

50. ∫ csc¹⁰x cot³x dx

9–61. Trigonometric integrals Evaluate the following integrals.

51. ∫ (csc²x + csc⁴x) dx