Iintegration of rational functions

Exercise

1.

Find the following integral．

(a)

$${\int{\frac{7}{(x-2)(x+5)}}\ dx}$$

(b)

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

(c)

$${\int{\frac{x^2 + 3}{x^2 - 3x + 2}}\ dx}$$

(d)

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

(e)

$${\int{\frac{dx}{(x^2 + 16)^2}}}$$

(f)

$${\int{\frac{x^5}{x^9 - 1}}\ dx \ \ (x^3 = t)}$$

(g)

$${\int{\frac{dx}{x(x^4 + 1)}} \ \ (x^4 = t)}$$