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int1/((x)(6(logx)^2 +7logx + 2)) dx...

`int1/((x)(6(logx)^2 +7logx + 2)) `dx

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`I = int 1/(x(6logx)^2+7logx+2)dx`
Let `logx = t,` then, `dx/x = dt`
`:. I = int 1/(6t^2+7t+2) dt`
Now, `6t^2+7t+2 = 6t^2+4t+3t+2 = (3t+2)(2t+1)`
`:. I = int 1/((3t+2)(2t+1))dt`
Now, `1/((3t+2)(2t+1)) = A/(2t+1)+B/(3t+2)`
If we put, `t = -1/2, A = 1/(3(-1/2)+2)=> A = 2`
If we put, `t = -2/3, B = 1/(2(-2/3)+1) =>B = -3`
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