Identify the type of integral
Simplify the integrand
Use algebraic manipulation if needed
Apply basic antiderivative rules
Use substitution for composite functions
Use integration by parts for products
Use trigonometric identities when helpful
Use partial fractions for rational functions
Use trigonometric substitution for radicals
Use symmetry for definite integrals
Evaluate limits for improper integrals
Add the constant of integration for indefinite integrals
Differentiate the result to check your work