Primitive of Logarithm of x over x

Theorem

 * $\ds \int \frac {\ln x} x \rd x = \frac {\ln^2 x} 2 + C$

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

let:

and let:

Then: