A rational function R(x) can sometimes be expressed as a sum of simpler fractional terms whose denominators are linear and non-repeating. In the context of integrating expressions of the form ∫R(x)dx, answer the following.
(a) Describe the algebraic conditions on R(x) that guarantee it can be written as a finite sum of fractions whose denominators are distinct first-degree factors.
(b) Explain how writing R(x) in the form described in part (a) affects the antiderivative that results from integrating R(x).
(c) Discuss how the integration strategy changes if the denominator of R(x) instead contains a repeated linear factor or an irreducible quadratic factor.