3.4 Integration of rational functions

1.

(a) $\displaystyle{\frac{1}{x-2} + \frac{-1}{x+5}}$ (b) $\displaystyle{\frac{-1}{x} + \frac{1}{x+1} + \frac{1}{x-1}}$ (c) $\displaystyle{1 + \frac{-4}{x-1} + \frac{7}{x-2}}$

(d) $\displaystyle{\frac{3/4}{x-1} + \frac{1/2}{(x-1)^{2}} + \frac{1/4}{x+1}}$ (e) $\displaystyle{x^{3} + 4x^{2} + 12x + 32 + \frac{80}{x-2} + \frac{32}{(x-2)^{2}}}$

(f) $\displaystyle{\frac{1}{x} + \frac{-x+1}{x^{2} + 1}}$