If $\int_{2}^{e}\left[\dfrac{1}{\log x} - \dfrac{1}{(\log x)^2}\right] dx = a + \dfrac{b}{\log 2}$, then values of $a$ and $b$ are

If $\int_{0}^{k} \dfrac{1}{1 + 4^x} dx = \log_2\left(\dfrac{4}{3}\right)$, then $k = $ _____

The area bounded by the curve $y = x\left|\sin\left(\dfrac{x}{2}\right)\right|$ and the X-axis between the lines $x = 0$ and $x = 4\pi$ (in square units), is....

If the area enclosed between the curves $y^2 = 4kx$ and $y = kx, k > 0$ is $\dfrac{2k}{3}$ sq. units then $k = $