$$\int {{{dx} \over {\cos x + \sqrt 3 \sin x}}} $$ equals

Let $$F\left( x \right) = f\left( x \right) + f\left( {{1 \over x}} \right),$$ where $$f\left( x \right) = \int\limits_l^x {{{\log t} \over {1 + t}}dt,} $$ Then $$F(e)$$ equals

The solution for $$x$$ of the equation $$\int\limits_{\sqrt 2 }^x {{{dt} \over {t\sqrt {{t^2} - 1} }} = {\pi \over 2}} $$ is

The area enclosed between the curves $${y^2} = x$$ and $$y = \left| x \right|$$ is :