Evaluate the integrals in Exercises 41–60.
47. ∫sech²(x - 1/2)dx

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

25. y=arcsec(2s+1)

Indeterminate Powers and Products

Find the limits in Exercises 53–68.

57. lim (x → 0⁺) x^(-1/ln x)

Evaluate the integrals in Exercises 91–102.

93. ∫(arcsin x)²dx/√(1-x²)

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

8. y = ln kx, k constant

Evaluate the integrals in Exercises 53–76.

59. ∫(from 0 to 1)4ds/√(4-s²)

In Exercises 57–70, use logarithmic differentiation to find the derivative of y with respect to the given independent variable.

59. y = √(t/(t+1))