In Exercises 69–80, determine whether the improper integral converges or diverges. If it converges, evaluate the integral.
∫₋₂¹ (1 / x⁴) dx

Evaluate the integrals in Exercises 53–58.

∫ from -π/2 to π/2 of cos(x) cos(7x) dx

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

∫ dx / (x √(x + 4))

Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.

∫ √x e√x dx

Evaluate the integrals in Exercises 33–52.

∫ sec⁴(x) tan²(x) dx

In Exercises 35–68, use integration, the Direct Comparison Test, or the Limit Comparison Test to test the integrals for convergence. If more than one method applies, use whatever method you prefer.

∫ from 0 to 1 of ((e^(-√x)) / √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.

∫ tan^(-1)(√y) dy