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

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

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`int (x^(2) +x+1)/((x-1)^(3)) dx " "underset(rArr dx =dt)("Let" (x-1) =t)`
`=int ((t+1)^(2) +(t+1)+1)/(t^(3)) dt`
`= int(t^(2)+3t+3)/(t^(3) ) dt`
` = int((1)/(t)+ (3)/(t^(3))+(3)/(t^(3)))dt`
`=log |t| -(3)/(t)-(3)/(2t^(2)) +c.`
` =log |x-1| -(3)/(x-1) -(3)/(2(x-1)) +c.`
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