What is the indefinite integral of $1/(xlnx)$ ?

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Answer 1 · 2016-05-30T01:58:40

$ln(abslnx)+C$

We have the integral:

$int1/(xlnx)dx$

Use substitution. Let $u=lnx$ so that $du=1/xdx$ . Note that both of these are currently present in the integral.

$int1/(xlnx)dx=int(1/lnx)1/xdx=int1/udu$

This is a common integral:

$int1/udu=ln(absu)+C$

Since $u=lnx$ :

$ln(absu)+C=ln(abslnx)+C$

What is the indefinite integral of 1/(xlnx)1/(xlnx)?