`int (ln(x))^2/x dx` Find the indefinite integral.

`int (ln(x))^2/xdx`

To solve, apply u-substitution method. 

Let,

`u= ln x`

Then, differentiate it.

`du=1/xdx`

Plug-in them to the integral.

`int (ln(x))^2/xdx`

`= int (ln(x))^2 * 1/xdx`

`=int u^2 du`

Then, apply the formula, `int x^ndx=x^(n+1)/(n+1)+C` .

`=u^3/3+C`

And, substitute back `u=lnx` .

`= (ln(x))^3/3+C`

Therefore, `int (ln(x))^2/x dx = (ln(x))^3/3+C` .