7. Antiderivatives & Indefinite Integrals

Use the given substitution to evaluate the following indefinite integrals. Check your answer by differentiating.                                                                                              

 ∫ 8𝓍 cos (4𝓍² + 3) d𝓍, u = 4𝓍² + 3

9–61. Trigonometric integrals Evaluate the following integrals.

50. ∫ csc¹⁰x cot³x dx

9–61. Trigonometric integrals Evaluate the following integrals.

13. ∫ sin⁵x dx

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ (cos 7ω) /(16 + sin² 7ω) dω 

Evaluate the integrals in Exercises 37–44.

∫ tan³(x) sec³(x) dx

Use reduction formulas to evaluate the integrals in Exercises 41–50.

∫ 8 cot^4(t) dt

9–61. Trigonometric integrals Evaluate the following integrals.

10. ∫ sin³x dx

Use any method to evaluate the integrals in Exercises 15–38. Most will require trigonometric substitutions, but some can be evaluated by other methods.

∫ dx / √(1 - x²)

7–84. Evaluate the following integrals.

41. ∫ cot^(3/2)x · csc⁴x dx