$\displaystyle\int_0^{\log 5} \dfrac{e^x\sqrt{e^x - 1}}{e^x + 3}\,dx =$

The integrating factor of the differential equation $(1 + t^2) + \left(x - e^{\tan^{-1}t}\right)\dfrac{dt}{dx} = 0$ is

The degree of the differential equation obtained from the equation $(y - a)^2 = 4(x - b)$ [where $a$ and b are arbitrary constants] is

The solution of the differential equation $\left(x + 2y^3\right)\dfrac{dy}{dx} - y = 0$ is