In Exercises 21–32, express the integrand as a sum of partial fractions and evaluate the integrals.
∫ 1 / (x⁴ + x) dx

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ cos(θ / 2) cos(7θ) dθ

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ dx / (x² √(4x - 9))

In Exercises 27–40, use a substitution to change the integral into one you can find in the table. Then evaluate the integral.

∫ cos^(-1)(√x) / √x dx

Use any method to evaluate the integrals in Exercises 15–38. Most will require trigonometric substitutions, but some can be evaluated by other methods.

∫ (1 - x²)^(1/2) / x⁴ dx