The graph of $\frac{e^x}{\Gamma(x+1)}$ is somewhat bell-shaped. I think the proof of the following requires an understanding of the integral of this function that I can't glean from either Mathematica or the usual assortment of Wiki entries. Can one show that
$$e^e< \int_{-1^+}^{10}\frac{e^x}{\Gamma(x+1)}dx~~~?$$
Thanks.