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

Nov 4, 2016

$\int {\left(\ln x\right)}^{2} / x \mathrm{dx} = \frac{1}{3} {\left(\ln x\right)}^{3} + C$

#### Explanation:

This is a straight forward with the appropriate substitution

Let $u = \ln x \implies \frac{\mathrm{du}}{\mathrm{dx}} = \frac{1}{x}$, so $\int \ldots \mathrm{du} = \int \ldots \frac{1}{x} \mathrm{dx}$

So Then,
$\int {\left(\ln x\right)}^{2} / x \mathrm{dx} = \int {u}^{2} \mathrm{du}$
$\therefore \int {\left(\ln x\right)}^{2} / x \mathrm{dx} = \frac{1}{3} {u}^{3} + C$
$\therefore \int {\left(\ln x\right)}^{2} / x \mathrm{dx} = \frac{1}{3} {\left(\ln x\right)}^{3} + C$