Primitive of Logarithm of x over x

Theorem

 * $\displaystyle \int \frac {\ln x} x \ \mathrm d x = \frac {\ln^2 x} 2 + C$

Proof
With a view to expressing the primitive in the form:
 * $\displaystyle \int u \frac {\mathrm d v}{\mathrm d x} \ \mathrm d x = u v - \int v \frac {\mathrm d u}{\mathrm d x} \ \mathrm d x$

let:

and let:

Then: