Evaluate the improper integrals in Exercises 53–62.
∫ from 3 to ∞ of (2 / (u² − 2u)) du

Which of the improper integrals in Exercises 63–68 converge and which diverge?

∫ from −∞ to ∞ of (2 / (e^x + e^(−x))) dx

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

133. ∫ (sin²x) / (1 + sin²x) dx

A brief calculation shows that if 0 ≤ x ≤ 1, then the second derivative of

f(x) = √(1 + x⁴)

lies between 0 and 8.

Based on this, about how many subdivisions would you need to estimate the integral of f from 0 to 1

with an error no greater than 10⁻³ in absolute value using the Trapezoidal Rule?

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

131. ∫ dx / (x√(1 − x⁴))

Evaluate the improper integrals in Exercises 53–62.

∫ from 0 to 3 of (1 / √(9 − x²)) dx

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

127. ∫ (ln x) / (x + x ln x) dx