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

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

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