# How do you evaluate the integral int lnx/xdx?

Jan 11, 2017

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

#### Explanation:

We have that:

$\frac{d}{\mathrm{dx}} \left(\ln x\right) = \frac{1}{x}$

so:

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