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Evaluate: int(x^4\ dx)/((x-1)(x^2+1))...

Evaluate: `int(x^4\ dx)/((x-1)(x^2+1))`

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Given,`int(x^4dx)/((x-1)(x^2+1))`
Let,`(x^4dx)/((x-1)(x^2+1))=(x^4-1+1dx)/((x-1)(x^2+1))=x+1+(1)/((x-1)(x^2+1))`
Let,`(1)/((x-1)(x^2+1))=A/(x-1)+(Bx+c)/(x^2+1)`
`1=A(x^2+1)+(Bx+c)(x-1)`
Equating coefficient of similar terms we get
`A=1/2` and `B=C=-1/2`
Thus,`intx+1+(1/2)/(x-1)-(1/2)(x+1)/(x^2+1)`dx
=`x^2/2+x+1/2log|x-1|-1/4int(2x)/(x^2+1)dx-1/2int(dx)/(x^2+1)`
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