Verify the integration formulas in Exercises 37–40.
37. a. ∫sech(x)dx = tan⁻¹(sinh x) + C

Evaluate the integrals in Exercises 31–78.

47. ∫(1/r)csc²(1+ln(r))dr

In Exercises 1–4, show that each function y=f(x) is a solution of the accompanying differential equation.

1. 2y' + 3y = e^(-x)

a. y = e^(-x)

In Exercises 41–44:

a. Find f⁻¹(x).

43. f(x) = 5 − 4x, a = 1/2

23. What roles do the functions e^x and ln(x) play in growth comparisons?

10. True, or false? As x→∞,

a. 1/(x+3) = O(1/x)

In Exercises 41–44:

a. Find f⁻¹(x).

44. f(x) = 2x², x ≥ 0, a = 5