Question

求不定积分，这题有什么方法

求不定积分，这题有什么方法过程

Answer 1

解答过程如下

Answer 2

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