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

You need to use the following substitution `ln x = u` , such that:

`ln x = u=> (dx)/x = du `

`int ((ln^2 x)dx)/x = int u^2 du`

Using the formula `int u^n du = (u^(n+1))/(n+1) + c ` yields

`int u^2 du = (u^3)/3 + c`

Replacing back ` ln x` for `u ` yields:

`int ((ln^2 x)dx)/x = ((ln x)^3)/3 + c`

Hence, evaluating the indefinite integral, yields `int ((ln^2 x)dx)/x = ((ln x)^3)/3 + c.`