Identify the type of integral
Simplify the integrand
Look for algebraic expansion or factoring
Use substitution when a composite function appears
Use integration by parts for products of functions
Use trigonometric identities when trigonometric terms appear
Use partial fractions for rational functions
Use standard integral formulas
Rewrite expressions to match known forms
Apply symmetry when appropriate
Use trigonometric substitution for radicals
Use u-substitution for inner functions
Use definite integral limits carefully
Compute the antiderivative
Add the constant of integration for indefinite integrals
Verify by differentiating the result