Evaluate the integrals in Exercises 97–110.
109. ∫ (dx / (x log₁₀x))

In Exercises 5 and 6, solve for t.

6. ln(t-2) = ln8 - ln(t)

Find the values in Exercises 9–12.

11. tan(arcsin(-1/2))

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)

17. lim(x→∞)arcsec(x)

Each of Exercises 1–4 gives a value of sinh x or cosh x. Use the definitions and the identity cosh²x - sinh²x = 1 to find the values of the remaining five hyperbolic functions.

4. cosh x = 13/5, x>0

Evaluate the integrals in Exercises 33–54.

∫8e^(x+1) dx

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

y = ∫(from 0 to lnx) sin(e^t) dt