Evaluate the integrals in Exercises 53–76.
59. ∫(from 0 to 1)4ds/√(4-s²)

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

25. y=arcsec(2s+1)

In Exercises 115–126, use logarithmic differentiation or the method in Example 6 to find the derivative of y with respect to the given independent variable.

117. y = (√t)ᵗ

Indeterminate Powers and Products

Find the limits in Exercises 53–68.

57. lim (x → 0⁺) x^(-1/ln x)

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 41–60.

47. ∫sech²(x - 1/2)dx

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))