How do you find the indefinite integral of $int (lnx)^2/x$ ?

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Answer 1 · 2016-11-04T00:46:24

$int (lnx)^2/x dx = 1/3(lnx)^3 + C$

This is a straight forward with the appropriate substitution

Let $u = lnx => (du)/dx=1/x$ , so #int ...du=int...1/xdx#

So Then,
$int (lnx)^2/x dx = int u^2du$
$:. int (lnx)^2/x dx = 1/3u^3 + C$
$:. int (lnx)^2/x dx = 1/3(lnx)^3 + C$

How do you find the indefinite integral of int (lnx)^2/xint (lnx)^2/x?