`int(1)/(x[6 (logx)^(2)+7log x +2])dx` का मान ज्ञात कीजिए ।

Explanation

माना `log x = t rArr (1)/(x)dx=dt`
`therefore" "int(1)/(x[6(log x)^(2)+7log x+2])dx=int(1)/(6t^(2)+7t+2)dt`
`=(1)/(6)int(1)/(t^(2)+(7)/(6)t+(1)/(3))dt`
`=(1)/(6)int(1)/((t+(7)/(12))^(2)+(1)/(3)-(49)/(144))fy`
`=(1)/(6)int(1)/((t+(7)/(12))^(2)-((1)/(12))^(2))dt`
`=(1)/(6).(1)/(2.(1)/(12))log[(t+(7)/(12)-(1)/(12))/(t+(7)/(12)+(1)/(12))]+c_(1)`
`=log((t+1//2)/(t+2//3))+c_(1)`
`=log((3(2t+1))/(2(3t+2)))+c_(1)`
`=log((2logx+1)/(3log x+2))+log (3)/(2)+c_(1)`
`=log((2log x+1)/(3logx+2))+c" जहाँ "c=c_(1)+log(3)/(2)`