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Evaluate: int[ln(lnx)+1/(lnx)^(2)]dx...

Evaluate: `int[ln(lnx)+1/(lnx)^(2)]`dx

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Verified by Experts

Let I `=int[ln(lnx)+1/(lnx)^(2)]dx ("put" x=e^(t) rArr dx=e^(t)dt)`
`therefore I=inte^(t)(lnt+1/t^(2))dt inte^(t)(lnt-1/t+1/t+1/t^(2))=dt`
`e^(t)(lnt-1/t)+C=x[ln(lnx)-1/(lnx)]+C`
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