Evaluate the integrals in Exercises 31–78.
45. ∫(ln x)^(-3)/x dx

5. Which of the following functions grow faster than ln(x) as x→∞? Which grow at the same rate as ln(x)? Which grow slower?

a. log_3(x)

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

1. y = 10e^(-x/5)

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

4. Use the properties of logarithms to write the expressions in Exercises 3 and 4 as a single term.

a. ln secθ + ln cosθ

Use l’Hôpital’s Rule to find the limits in Exercises 85–108.

102. lim(x→0) (x sin(x²))/(tan³x)

In Exercises 79–84, solve for y.

83. ln(y-1) = x + ln(y)