Identify the type of integral
Simplify the integrand
Choose an appropriate method
Use substitution if a composite function is present
Use integration by parts if the product of functions is present
Use partial fractions if the integrand is a rational function
Use trigonometric identities if trigonometric expressions are present
Use trigonometric substitution for square roots of quadratic expressions
Use standard integral formulas
Integrate term by term when possible
Add the constant of integration for indefinite integrals
Evaluate the antiderivative at the bounds for definite integrals
Verify the result by differentiating the antiderivative