Evaluate the integrals in Exercises 41–60.
59. ∫(from -ln2 to 0)cosh²(x/2) dx

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

17. y = ln(sinh z)

Evaluate the integrals in Exercises 41–60.

51. ∫(from ln2 to ln4)coth(x)dx

In Exercises 73 and 74, repeat the steps above to solve for the functions y=f(x) and x=f^(-1)(y) defined implicitly by the given equations over the interval.

73. y^(1/3) - 1 = (x+2)³, -5 ≤ x ≤ 5, x_0 = -3/2

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

39. y=arctan√(x²-1) + arccsc(x), x>1

86. Use a derivative to show that g(x)=√(x² + ln x) is one-to-one.

Verify the integration formulas in Exercises 111–114.

111. ∫ (arctan x) / x² dx = ln x - 1/2 ln(1 + x²) - arctan x / x + C