7. Antiderivatives & Indefinite Integrals

Use Table 5.6 to evaluate the following indefinite integrals.                                                                                                               

 (f) ∫ d𝓍/√36 ―𝓍²

Use Table 5.6 to evaluate the following indefinite integrals.                                                                                                               

 (e) ∫ d𝓍/(81 + 9𝓍²) (Hint: Factor a 9 out of the denominator first.)  

Indefinite integrals Use a change of variables or Table 5.6 to evaluate the following indefinite integrals. Check your work by differentiating.                                                                                  

 ∫ 2𝓍(𝓍² ― 1)⁹⁹ d𝓍

Indefinite integrals Use a change of variables or Table 5.6 to evaluate the following indefinite integrals. Check your work by differentiating.                                                                                  

 ∫ 𝓍eˣ² d𝓍

Indefinite integrals Use a change of variables or Table 5.6 to evaluate the following indefinite integrals. Check your work by differentiating.                                                                                  

 ∫ [ 1/(10𝓍―3) d𝓍

Indefinite integrals Use a change of variables or Table 5.6 to evaluate the following indefinite integrals. Check your work by differentiating.                                                                                  

 ∫ 𝓍³ (𝓍⁴ + 16)⁶ d𝓍

Indefinite integrals Use a change of variables or Table 5.6 to evaluate the following indefinite integrals. Check your work by differentiating.                                                                                  

 ∫ (𝓍⁶ ― 3𝓍²)⁴ (𝓍⁵ ― 𝓍) d𝓍

Indefinite integrals Use a change of variables or Table 5.6 to evaluate the following indefinite integrals. Check your work by differentiating.                                                                                  

 ∫ d𝓍 / (√1 ― 9𝓍²)

Variations on the substitution method Evaluate the following integrals.                                                                                                        

 ∫ 𝓍/(√𝓍―4) d𝓍

Variations on the substitution method Evaluate the following integrals.                                                                                                        

 ∫ y²/(y + 1)⁴ dy

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

3. ∫ (3x)/√(x + 4) dx

7-56. Trigonometric substitutions Evaluate the following integrals using trigonometric substitution.

23. ∫ 1/(25 - x²)^(3/2) dx

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

35. ∫ x³/√(4x² + 16) dx

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

40. ∫ (x² - 4)/(x + 4) dx

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

54. ∫ dx/√(9x² - 25), x > 5/3