$$\int \frac{\mathrm{e}^{2030 \log x}-\mathrm{e}^{2029 \log x}}{\mathrm{e}^{2028 \log x}-\mathrm{e}^{2027 \log x}} \mathrm{~d} x=\ldots$$

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

The order and degree of differential equation of all tangent lines to the parabola $x^2=4 y$ is respectively.

The probability distribution of a discrete random variable X is

$\mathrm{X}$	0	1	2	3	4
$\mathrm{P(X=}x)$	$\mathrm{2k}$	$\mathrm{k}$	$\mathrm{2k}$	$\mathrm{4k}$	$\mathrm{k}$

If $\mathrm{a}=\mathrm{P}(x<3)$ and $\mathrm{b}=\mathrm{P}(2 \leq \mathrm{X}<4)$, then