Integration of Rational Functions (Complete Square & Improper)

Integration of rational functions extends the Further integration topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-04). This subtopic integrates rational functions by completing the square on a quadratic denominator, and handles improper rational functions where the degree of the numerator is not less than the degree of the denominator.

Students and teachers will cover how to use polynomial division and algebraic manipulation to rewrite an integrand into a form that can be integrated — often producing logarithmic or inverse-trigonometric results — in the HSC Extension 2 course.