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Integrate the rational functions1/(x^4-1...

Integrate the rational functions`1/(x^4-1)`

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Given` 1/(x^4-1)`
`=1/[(x^2-1)(x^2+1)]`
`=1/[(x-1)(x+1)(x^2+1)]`
`Let 1/[(x-1)(x+1)(x^2+1)]=A/(x+1)​+B/(x−1)​+(Cx+D)/(x^2+1)​`
`⇒1=A(x−1)(x^2+1)+B(x+1)(x^2+1)+(Cx+D)(x^2+1)`
`⇒1=A(x^3+x−x^2−1)+B(x^3+x+x^2+1)+Cx^3+Dx^2−Cx−D`
`⇒1=(A+B+C)x^3+(−A+B+D)x^2+(A+B−C)x+(−A+B−D)`
Equating the coefficient of `x^3,x^2,x`, and constant term, we obtain
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