If Rolle's theorem holds for the function $x^3+\mathrm{a} x^2+\mathrm{b} x, 1 \leq x \leq 2$ at the point $\frac{4}{3}$, then the values of $a$ and $b$ are respectively

$$ \int \frac{1}{\mathrm{e}^x+1} \mathrm{~d} x= $$

If $y=\tan ^{-1}\left(\frac{4 x}{1+5 x^2}\right)+\cot ^{-1}\left(\frac{3-2 x}{2+3 x}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

The differential equation $x \frac{\mathrm{~d} y}{\mathrm{~d} x}=2 y$ represents ________