解答过程如下
let
1/[x(x-1)(x+1)]≡ A/x +B/(x-1) +C/(x+1)
=>
1≡ A(x-1)(x+1) +Bx(x+1) +Cx(x-1)
x=0 =>A =-1
x=1 =>B=1/2
x=-1 =>C=1/2
1/[x(x-1)(x+1)]≡ -1/x +(1/2)[1/(x-1)] +(1/2)[1/(x+1)]
∫ dx/[x(x^2-1)]
=∫ {-1/x +(1/2)[1/(x-1)] +(1/2)[1/(x+1)] } dx
=-ln|x| +(1/2)ln|x-1| + (1/2)ln|x+1| + C
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024