The value of $\int_{\frac{1}{3}}^1 \frac{\left(x-x^3\right)^{\frac{1}{3}}}{x^4} d x$ is

The value of $\int_1^4 \log [x] \mathrm{d} x$, where $[x]$ is the greatest integer function less than or equal to $x$ is equal to

$$\int_1^e \frac{\mathrm{e}^x}{x}(1+x \log x) \mathrm{d} x=$$