If the plane $\frac{x}{2}+\frac{y}{3}+\frac{z}{6}=1$ cuts the co-ordinate axes at points $A, B, C$ respectively, then area of the triangle ABC is

The number of positive integral solutions of $\tan ^{-1} x+\cos ^{-1}\left(\frac{y}{\sqrt{1+y^2}}\right)=\sin ^{-1}\left(\frac{3}{\sqrt{10}}\right)$ are

If $\int \frac{\mathrm{d} x}{x^4+5 x^2+4}=\mathrm{A} \tan ^{-1} x+\mathrm{B} \tan ^{-1} \frac{x}{2}+\mathrm{c}$ where c is a constant of integration, then

$$ \int \frac{\sqrt{\tan x}}{\sin x \cdot \cos x} d x= $$