Identify the type of integral
Check for a basic antiderivative
Use substitution when a composite function appears
Use integration by parts for products of functions
Use trigonometric identities for trig integrals
Use trigonometric substitution for radicals with quadratic expressions
Use partial fractions for rational functions
Simplify the integrand before integrating
Apply symmetry when the interval or function allows it
Use definite integral properties to split or combine intervals
Evaluate improper integrals by taking limits
Verify the result by differentiating the antiderivative
Use numerical methods if no elementary antiderivative exists