Wikipedia gives this evaluation:
$ \int x^ne^{cx}\,\mathrm dx=\frac1cx^ne^{cx}-\frac nc\int x^{n-1}e^{cx}\,\mathrm dx=\left(\frac{\partial}{\partial c}\right)^n\frac{e^{cx}}{c}$
But I have no idea how I should exactly understand the partial part: $\left(\frac{\partial}{\partial c}\right)\frac{e^{cx}}{c}$
EDIT
Thanks for your responses so far. I should add that $n$ is not necessarily an integer. Can be for example $n = 1.2$. I'll see how far I get on learning about fractional derivatives.