Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.
∫ [(4x) / (x³ + 4x)] 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.

121. ∫ (1 + x²) / (1 + x³) 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.

119. ∫ x³ / (1 + 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.

131. ∫ dx / (x√(1 − x⁴))

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

∫ (x + 1) / (x⁴ − x³) dx