11. Integrals of Inverse, Exponential, & Logarithmic Functions

Evaluate the integrals in Exercises 1–14.

∫ (2 dx) / (x³ √(x² - 1)), where x > 1

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

∫ (x² dx) / (4 + x²)

The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫ (dx / ((2x + 1)√(4x + 4x²)))

In Exercises 39–48, use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

∫ √(x) / (1 - x³) dx (Hint: Let u = x³/2)

Evaluate the integrals in Exercises 1–14.

∫ dx / (8 + 2x²) from 0 to 2

Evaluate the integrals in Exercises 1–14.

∫ (2 dx) / √(1 - 4x²) from 0 to 1/(2√2)

Evaluate the integrals in Exercises 53–76.

53. ∫dx/√(9-x²)

Evaluate the integrals in Exercises 53–76.

55. ∫dx/(17+x²)

Evaluate the integrals in Exercises 53–76.

57. ∫dx/(x√(25x²-2))

Evaluate the integrals in Exercises 53–76.

59. ∫(from 0 to 1)4ds/√(4-s²)

The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫₁² (8 dx / (x² - 2x + 2))

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

∫ x arctan(x) dx

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

∫ tan^(-1)(x) / x² dx

In Exercises 27–40, use a substitution to change the integral into one you can find in the table. Then evaluate the integral.

∫ cos^(-1)(√x) / √x dx

In Exercises 27–40, use a substitution to change the integral into one you can find in the table. Then evaluate the integral.

∫ tan^(-1)(√y) dy