11. Integrals of Inverse, Exponential, & Logarithmic Functions

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

Evaluate the integrals in Exercises 53–76.

65. ∫3dr/√(1-4(r-1)²)

Evaluate the integrals in Exercises 53–76.

67. ∫dx/(2+(x-1)²)

Evaluate the integrals in Exercises 53–76.

71. ∫(from -π/2 to π/2) 2cosθ dθ/(1+(sinθ)²)

Evaluate the integrals in Exercises 53–76.

73. ∫(from 0 to ln√3) e^x dx/(1+e^(2x))

Evaluate the integrals in Exercises 53–76.

75. ∫y dy/√(1-y^4)

Evaluate the integrals in Exercises 77–90.

79. ∫(from -1 to 0)6dt/√(3-2t-t²)

Evaluate the integrals in Exercises 67–74 in terms of

a. inverse hyperbolic functions.

67. ∫(from 0 to 2√3)dx/√(4+x²)

Evaluate the integrals in Exercises 67–74 in terms of

a. inverse hyperbolic functions.

69. ∫(from 5/4 to 2)dx/(1-x²)

Evaluate the integrals in Exercises 31–78.

67. ∫(from -2 to 2)3dt/(4+3t²)

Evaluate the integrals in Exercises 31–78.

69. ∫dy/(y√(4y²-1))