Indefinite integral problem: $\int_1^\frac{n+1}{1} \frac{(x - [x])^{[x]}}{[x]} dx$
Calculate $\int^{n+1}_1 \frac{(\{x\})^{[x]}}{[x]}dx$ where $n\in\mathbb{N}$, $[x]$ is the integer part of $x$ and $\left\{ x\right\} =x-[x]$.