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

Explanation

`int(x)/((x^(4)-x^(2)+1))dx`
यदि `t=x^(2) rArr 2x dx = dt,` तब
`int(x)/((x^(4)-x^(2)+1))dx=(1)/(2).int(dt)/((t^(2)-t+1))`
`=(1)/(2).int(dt)/({(t-(1)/(2))^(2)+((sqrt3)/(2))^(2)})`
`=(1)/(2).(1)/(((sqrt3)/(2)))tan^(-1).((t-(1)/(2)))/(((sqrt3)/(2)))+c`
`=(1)/(sqrt3)tan^(-1)((2t-1)/(sqrt3))+c`
`=(1)/(sqrt3)tan^(-1)((2x^(2)-1)/(sqrt3))+c`