PartialFracs.mws Rational Functions: Case 0. Case 1: The denominator of p(x)/q(x); is a product of distinct linear factors. Case 2: q(x); is a product of linear factors, some of which are repeated. e.g. find Int((9*x^2-20*x-2)/(6*x^3-18*x^2+24),x); Case 3: q(x); contains distinct irreducible quadratic factors. Three Preliminary e.g.'s The decomposition. Case 4: q(x); contains repeated irreducible quadratic factors. Some "rationalizing" substitutions e.g. Find I1 = Int(1/(x*sqrt(x+1)),x); using substitution: e.g. Find I1 = Int(x^3/((x^2+1)^(1/3)),x); using substitution: e.g. Find I1 = Int(1/(sqrt(x)+x^(1/3)),x);