Integration with Partial Fractions 1, Single Variable Calculus

(1 of 2) In this video we look at several examples of integrating rational functions by first breaking them into smaller pieces with partial fraction decomposition. No examples in this video have repeated factors (see part 2 for that!). Part 2 here: https://youtu.be/mI0WtGfEXjY Note around 23:29: you CAN factor x^4 + 1 (though you don't need to for the antiderivative, the form we use is fine). It factors into quadratics (x^2 - sqrt(2)x + 1)(x^2 + sqrt(2)x +1). The Fundamental Theorem of Algebra implies that any polynomial with real coefficients can be factored into linear and irreducible quadratic factors. #calculus #mathematics #integration #partialfractions #partialfractiondecomposition