Which of the following best explains why writing an improper rational integrand as the sum of a polynomial and a proper rational function can simplify the process of finding an antiderivative?
(a) It guarantees that the integral of the remainder is zero, eliminating any additional work.
(b) It eliminates the need for any partial-fraction decomposition because the derivative of the denominator inevitably appears in the numerator after division.
(c) It separates the integrand into a portion that can be integrated term-by-term with the power rule and a remainder that is typically simpler to integrate.
(d) It ensures the proper fraction that remains will always integrate to a single logarithmic function, no matter the denominator’s factorization.