Evaluate the integrals in Exercises 87–96.
91. ∫₁^(√2) x·2^(x²) dx

In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then evaluate the limit using a method studied in Chapter 2.

3. lim (x → ∞) (5x² - 3x) / (7x² + 1)

Evaluate the integrals in Exercises 41–60.

43. ∫6cosh(x/2 - ln3)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)

81. Find the lengths of the following curves.

a. y = (x²/8) - ln(x), 4≤x≤8

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

75. y = x³ log₁₀ x