So I was bored and decided to figure out the indefinite integral of the absolute value function, $|x|$. Using integration by parts ($u=|x|, dv=dx$, $dx = \text{sgn}(x)=\frac{|x|}{x}$), it can be shown that $\displaystyle\int |x| dx = \frac{x |x|}{2}+C$.
Now I decided to take the integral again, finding that $\displaystyle\int\left(\int |x| dx \right) dx=\frac{x^2 |x|}{3}+C$. Continuing, I found the pattern in the title, that the $n$th indefinite integral of $|x|$ is $\displaystyle\frac{x^n |x|}{n+1}+C$. Is there a way to prove this general result?