Evaluate the integrals in Exercises 31–78.
77. ∫dt/((t+1)√(t²+2t-8))

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

93. lim(x→0) (csc(x) - cot(x))

110. Does f grow faster, slower, or at the same rate as g as x→∞? Give reasons for your answers.

a. f(x) = 3^(-x), g(x) = 2^(-x)

Evaluate the integrals in Exercises 31–78.

35. ∫sec²x e^(tan x)dx

109. Does f grow faster, slower, or at the same rate as g as x→∞? Give reasons for your answers.

b. f(x)=x, g(x)=x + 1/x

Evaluate the integrals in Exercises 31–78.

75. ∫(from -2 to -1)2dv/(v²+4v+5)

113. The function f(x) = e^x + x, being differentiable and one-to-one, has a differentiable inverse f^(-1)(x). Find the value of df^(-1)/dx at the point f (ln 2).