`int(x^(2)+x+1)/((x-1)^(3))dx` का मान ज्ञात कीजिए ।

Explanation

`int(x^(2)+x+1)/((x-1)^(3))dx`
`=int((t+1)^(2)+(t+1)+1)/(t^(3))`
`=int(t^(2)+3t+3)/(t^(3))" "{:("माना "x-1=t),(rArr" "dx=dt):}`
`=int((1)/(t)+(3)/(t^(2))+(3)/(t^(3)))dt=log|t|-(3)/(t)-(3)/(2)+c`
`=log|x-1|-(3)/(x-1)-(3)/(2(x-1)^(2))+c`