What is $int 1/(xlnx)dx$ ?

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Answer 1 · 2017-02-16T08:21:46

$int dx/(xlnx) = ln abs(lnx)+C$

Evaluate:

$int dx/(xlnx)$

Note that:

$dx/x = d(lnx)$

So:

$int dx/(xlnx) = int (d(lnx))/lnx$

Substituting $t = lnx$ we then have:

$int dx/(xlnx) = int (dt)/t = ln abs(t)+C$

And undoing the substitution:

$int dx/(xlnx) = ln abs(lnx)+C$

What is int 1/(xlnx)dxint 1/(xlnx)dx?