I'm stuck on this one. I've tried integration by parts but to no avail:
$$\int_{0}^{4} x e^{ (x-2)^4 } dx = \left[ x \int e^{ (x-2)^4 } dx \right]_{0}^{4} - \underbrace{\int_{0}^{4} e^{ (x-2)^4 } dx}_{=k} $$
I suspect this is a dead end. I think there's some simple trick here I'm missing. Any hints are appreciated.