Evaluate the integrals in Exercises 97–110.
97. ∫ 3x^(√3) dx

In Exercises 59–86, find the derivative of y with respect to the given independent variable.

77. y = log₃(((x + 1)/(x − 1))^(ln 3))

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.

y = e^(-5x)

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

19. y = (sech θ)(1-ln(sech θ))

11. Show that if positive functions f(x) and g(x) grow at the same rate as x→∞, then f=O(g) and g=O(f).

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

21. y=arccos(x²)

81. Find the lengths of the following curves.

a. y = (x²/8) - ln(x), 4≤x≤8