`int 1/(x( 6 ( log x)^2 + 7 log x + 2) dx`

Explanation

`logx=t`

`1/xdx=dt`

`intdt/(6t^2+7t+2)=1/6intdt/(t^2+7/6t+2/6)`

`1/6intdt/((t+7/12)^2-(1/12)^2)`

`ln((t+1/2)/(t+2/3))+c`

`ln((2t+1)/(3t+2))+c`

`=log((2logx+1)/(3logx+2)*3/2)+c`

`=log((6logx+3)/(6logx+4))+c`.