Evaluate the integrals in Exercises 33–52.
∫ sec³(x) tan³(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.

∫ (x^2 + 6x) / (x^2 + 3)^2 dx

The integrals in Exercises 1–34 converge. Evaluate the integrals without using tables.

∫₀¹ (−ln(x)) dx

Evaluate the integrals in Exercises 33–52.

∫ sec⁶(x) dx

Evaluate the integrals in Exercises 1–24 using integration by parts.

∫ e^(-y) cos(y) dy

Use the substitution u = tan x to evaluate the integral

∫ dx / (1 + sin² x).

Expand the quotients in Exercises 1–8 by partial fractions.

(t⁴ + 9) / (t⁴ + 9t²)