7. Antiderivatives & Indefinite Integrals

7–64. Integration review Evaluate the following integrals.

40. ∫ (1 - x) / (1 - √x) dx

7–64. Integration review Evaluate the following integrals.

36. ∫ (t³ - 2) / (t + 1) dt

Evaluate the definite integral if it exists: ${\int }_1^3{x}^2+2x+4 dx$

Finding Indefinite Integrals

In Exercises 17–56, find the most general antiderivative or indefinite integral. You may need to try a solution and then adjust your guess. Check your answers by differentiation.

∫2x(1 − x⁻³) dx

Evaluate the indefinite integral: ${\int }_{}^{}{x}^{2}dx$

Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.

∫ [(4x) / (x³ + 4x)] dx

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ dx / (x² √(4x - 9))

Variations on the substitution method Evaluate the following integrals.                                                                                                        

 ∫ 𝓍/(∛𝓍 + 4) 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.

∫ (1 - x²)^(1/2) / x⁴ dx

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ dx / (x √(7 - x²))

Find the following indefinite integral.

$\(\int\)-300dx$

7–64. Integration review Evaluate the following integrals.

47. ∫ dx / (x⁻¹ + 1)

Finding Indefinite Integrals

In Exercises 17–56, find the most general antiderivative or indefinite integral. You may need to try a solution and then adjust your guess. Check your answers by differentiation.

∫(2x³ − 5x + 7) dx

Evaluate the integrals in Exercises 33–36.

∫ [1 / √(9 - x²)] dx

Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.

∫ e√x / √x dx