有理関数の積分法(integration of rational functions)

演習問題

1.: 次の積分を求めよう．
(a): $\displaystyle{\int{\frac{7}{(x-2)(x+5)}} dx}$
(b): $\displaystyle{\int{\frac{x^2 + 1}{x(x^2 - 1)}} dx}$
(c): $\displaystyle{\int{\frac{x^2 + 3}{x^2 - 3x + 2}} dx}$
(d): $\displaystyle{\int{\frac{x^2}{(x - 1)^2(x + 1)}} dx}$
(e): $\displaystyle{\int{\frac{dx}{(x^2 + 16)^2}}}$
(f): $\displaystyle{\int{\frac{x^5}{x^9 - 1}} dx (x^3 = t)}$
(g): $\displaystyle{\int{\frac{dx}{x(x^4 + 1)}} (x^4 = t)}$