Primitive of Power

Theorem
Let $n \in \R: n \ne -1$.

Then:
 * $\ds \int x^n \rd x = \frac {x^{n + 1} } {n + 1} + C$

where $C$ is an arbitrary constant.

That is:
 * $\dfrac {x^{n + 1} } {n + 1}$ is a primitive of $x^n$.

Proof
When $n = -1$ we have $n + 1 = 0$, and $\dfrac {x^{n + 1} } {n + 1} = \dfrac {x^0} 0$ is undefined.

Also known as
Some sources refer to this as the reverse power rule, as it is the "reverse" of the Power Rule for Derivatives.

It is even suggested that it could be called the anti-power rule, but this appears to be unlikely to catch on.

Also see

 * Primitive of Reciprocal for the case where $n = -1$