MAT 148 Integration of Rational Functions with examples -...

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Chapter 7 Techniques of Integration7.4 Integration of Rational Functionsby Partial FractionsM148 7.4 Integration of Rational Functions by Partial Fractions
IntroductionIntegrals of the following form:ZP(x)Q(x)dxwhereP(x) andQ(x) are polynomials.M148 7.4 Integration of Rational Functions by Partial Fractions
IntroductionIntegrals of the following form:ZP(x)Q(x)dxwhereP(x) andQ(x) are polynomials.ExampleZx5+x-1x3+ 1dxM148 7.4 Integration of Rational Functions by Partial Fractions
ReviewStep 0Ifdeg(P)dep(Q), it is an improper fraction. First need toreduce it by long division.P(x)Q(x)=S(x) +R(x)Q(x)wheredeg(R)<dep(Q).M148 7.4 Integration of Rational Functions by Partial Fractions
ReviewStep 0Ifdeg(P)dep(Q), it is an improper fraction. First need toreduce it by long division.P(x)Q(x)=S(x) +R(x)Q(x)wheredeg(R)<dep(Q).ExampleZx5+x-1x3+ 1dxM148 7.4 Integration of Rational Functions by Partial Fractions
ReviewStep 1Factor the denominatorQ(x) as far as possible.M148 7.4 Integration of Rational Functions by Partial Fractions
ReviewStep 1Factor the denominatorQ(x) as far as possible.TheoremAny polynomial Q(x)can be factored as a product of linear factors(of the form ax+b) and irreducible quadratic factors (of the formax2+bx+c, where b2-4ac<0).

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