7. Antiderivatives & Indefinite Integrals

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ (sec² x - 1) dx

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ (sec² Θ + sec Θ tan Θ)dΘ

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ y² (3y³ + 1)⁴ dy

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ 𝓍⁷ √(𝓍⁴ + 1d𝓍)

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ (1/2y)dy

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ (6/√(4 - 4x²))dx

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ sec Θ(tan Θ + sec Θ + cos Θ)dΘ

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ (1/x√(36x² - 36))dx

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ (4/x√(x² - 1))dx

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ (eˣ⁺²) dx

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ ((e²ʷ - 5eʷ + 4)/(eʷ - 1))dw

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ ((1 + √x)/x)dx

23–68. Indefinite integrals Determine the following indefinite integrals. Check your work by differentiation.

∫ (√x(2x⁶ - 4³√)dx

Evaluating integrals Evaluate the following integrals.                                                                                                                                         

 ∫ d𝓍/[(tan⁻¹ 𝓍) (1 + 𝓍²)]

7–64. Integration review Evaluate the following integrals.

7. ∫ dx / (3 - 5x)^4