Chapter 7 - Techniques of Integration - 7.4 Integration of Rational Functions by Partial Fractions - 7.4 Exercises - Page 541: 3

a) $\frac{A}{x}+\frac{b}{x^{2}}+\frac{Cx+D}{1+x^{2}}$ b) $1+\frac{A}{x}+\frac{B}{x-1}+\frac{C}{x-2}$

a) $\frac{1}{x^{2}+x^{4}}$ = $\frac{1}{x^{2}(1+x^{2})}$ =$\frac{A}{x}+\frac{B}{x^{2}}+\frac{Cx+D}{1+x^{2}}$ b) $\frac{x^{3}+1}{x^{3}-3x^{2}+2x}$ = $1+\frac{3x^{2}-2x+1}{x(x^{2}-3x+2)}$ = $1+\frac{3x^{2}-2x+1}{x(x-1)(x-2)}$ = $1+\frac{A}{x}+\frac{B}{x-1}+\frac{C}{x-2}$