The value of the definite integral $\int_0^{\log_e 5}\dfrac{e^x\sqrt{e^x-1}}{e^x+3}\,dx$ is equal to...

If $[\cdot]$ denotes the greatest integer function, then $\int_0^{\pi/3}[\tan x]\,dx = $

The area (in square units) bounded by the line $y = x$, the X-axis and the lines $x = -2$ and $x = 4$ is...

The equation of the curve whose slope is $\dfrac{y-1}{x^2+x}$ and which passes through the point $(1, 0)$ is