The area of the region bounded by the curve $y = 2^{kx}$ and $x = 0, x = 2$, in first quadrant is $\dfrac{2}{\log 2}$, then the value of $k$ is

The area of the region bounded by the curve $y = x^3$ and the lines $y = 8$ and $x = 0$ is ... square units.

The differential equation of $3y = \sqrt[3]{x+c}$ is

The general solution of the differential equation $(x+y)\dfrac{dy}{dx} = 1$ is