Identify the integrand and the variable of integration
Determine whether it is an indefinite or definite integral
Simplify the expression if possible
Choose an appropriate integration method
Use the power rule for simple polynomials
Use substitution for composite functions
Use integration by parts for products of functions
Use partial fractions for rational functions
Use trigonometric identities when helpful
Use trigonometric substitution for certain radicals
Use standard integral formulas when applicable
Integrate term by term when allowed
Add the constant of integration for indefinite integrals
Evaluate the antiderivative at the bounds for definite integrals
Simplify the final result
Check the result by differentiating if needed