Primitive of Power of Logarithm of x

Theorem

 * $\displaystyle \int \ln^n x \rd x = x \ln^n x - n \int \ln^{n - 1} x \rd x + C$

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

let:

and let:

Then: