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Evaluate: int(x^2)/((x-1)^3(x+1))\ dx...

Evaluate: `int(x^2)/((x-1)^3(x+1))\ dx`

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Given:`int(x^2)/((x-1)^3(x+1))\ dx`
`I=int(x^2)/((x-1)^3(x+1))\ dx`
`(x^2)/((x-1)^3(x+1))=A/(x-1)+B/((x-1)^2)+C/((x-1)^3)+D/(x+1)`
`x^2=A(x-1)^2(x+1)+B(x+1)(x-1)+C(x+1)+D(x-1)^3`
`A=1/4, B=5/8, C= 1/2,D=1/-8`
`I=int (x^2)/((x-1)^3(x+1))=1/4int 1/(x-1)dx+5/8int 1/((x-1)^2)dx+1/2int 1/((x-1)^3)dx-1/8int 1/(x+1)dx`
`I=1/4log|x-1|+5/8((x-1)^(-1))/(-1)+1/2((x-1)^(-2))/(-2)-1/8log|x+1|+c`
`I=1/4log|x-1|+5/8((-1)/(x-1))-1/4(1/((x-1)^2))-1/8log|x+1|+c`
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