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

Answer

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Explanation

माना `I=int (x^(2)+x+1)/((x-1)^(3)) dx`
`implies x-1=t`
`dx=dt`
`:. I=int ((1+t)^(2)(1+t)+1)/t^(3) dt`
`=int (t^(2)+3t+3)/t^(3) dt`
`=int 1/t dt +3 int 1/t^(2) dt + 3 int 1/t^(3) dt`
`=log_(e) |t|+(3t^(-1))/(-1) +(3t^(-2))/(-2) +c`
.`=log_(e)|x-1|-3/((x-1))-3/(2(x-1)^(2)) +c`.