`int(x^(2)+1)/(x^(4)+x^(2)+1)dx` का मान ज्ञात कीजिए ।

Explanation

`int(x^(2)+1)/(x^(4)+x^(2)+1)dx=int(1+(1)/(x^(2)))/(x^(2)+1+(1)/(x^(2)))dx`
(अंश और हर को `x^(2)` से भाग देने पर )
`=int(1+(1)/(x^(2)))/((x-(1)/(x))^(2)+(sqrt3)^(2))dx" "{:("माना "x-(1)/(x)=t),(rArr(1+(1)/(x^(2)))dx=dt):}`
`=int(1)/(t^(2)+(sqrt3)^(2))dt=(1)/(sqrt3)tan^(-1)((t)/(sqrt3))+c`
`=(1)/(sqrt3)tan^(-1)((x-(1)/(x))/(sqrt3))+c`