Verify the integration formulas in Exercises 37–40.
37. b. ∫sech(x)dx = sin⁻¹(tanh x) + C

Evaluate the integrals in Exercises 67–74 in terms of

b. natural logarithms.

71. ∫(from 1/5 to 3/13)dx/(x√(1-16x²))

80. Find all values of c that satisfy the conclusion of Cauchy's Mean Value Theorem for the given functions and interval.

b. f(x) = x, g(x) = x², (a, b) arbitrary

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

8. b. arccot(√3)

Evaluate the integrals in Exercises 67–74 in terms of

b. natural logarithms.

67. ∫(from 0 to 2√3)dx/√(4+x²)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

6. b. arccsc(-2/√3)

3. Use the properties of logarithms to write the expressions in Exercises 3 and 4 as a single term.

b. ln(3x² - 9x) + ln(1/3x)