.

3.4 Integration of rational functions

1.

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

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

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