Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.
∫ [(x³ + 1) / (x³ − x)] dx

2. When applying the formula for integration by parts, how do you choose the u and dv? How can you apply integration by parts to an integral of the form ∫ f(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·sec²x dx

Use the substitutions in Equations (1)–(4) to evaluate the integrals in Exercises 33–40. Integrals like these arise in calculating the average angular velocity of the output shaft of a universal joint when the input and output shafts are not aligned.

∫ dx / (1 + sin x + cos x)

7. What is the goal of the method of partial fractions?

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

∫ θ·cos(2θ + 1) dθ

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

∫ cotx·csc³x dx