Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.
∫ [(x + 1) / (x² (x − 1))] 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.

117. ∫ dr / (1 + √r)

Evaluate the integrals in Exercises 1–8 using integration by parts.

∫ arccos(x / 2) dx

Evaluate the integrals in Exercises 1–8 using integration by parts.

∫ x² ln(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.

∫ x dx / √(2 − x)