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

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

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we have `int(x^4dx)/((x-1)(x^2+1)` = ` (x+1) + 1/(x^3 -x^2+x-1)`
using partial fraction
= ` (x+1) + 1/((x-1)(x^2+1))` ....(i)
now express
`1/((x-1)(x^2+1))` = `A/(x-1) + (Bx+c)/(x^2+ 1)` .....(ii)
so `1 = A(x^2+1) +(Bx+C)(x-1)`
...
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