In Exercises 69–80, determine whether the improper integral converges or diverges. If it converges, evaluate the integral.
∫₁^∞ (1 / x^(1/5)) dx

In Exercises 21–32, express the integrand as a sum of partial fractions and evaluate the integrals.

∫ (x² + x) / (x⁴ - 3x² - 4) 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.

∫ dx / (4 - x²)^(3/2) from 0 to 1

Evaluate the integrals in Exercises 33–52.

∫ tan⁴(x) sec³(x) dx

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

∫ (√2 - x) / √x dx

Evaluate the integrals in Exercises 23–32.

∫₋π^π (1 - cos²(t))^(3/2) dt

Exercises 59–64 require the use of various trigonometric identities before you evaluate the integrals.

∫ cos²(2θ) sin(θ) dθ