$$\int_\limits0^{\pi / 4} \log (1+\tan x) d x=$$

If $$\int_\limits0^{\frac{\pi}{2}} \frac{d x}{5+4 \sin x}=A \tan ^{-1} B$$, then A + B =

$\int_\limits0^1 \tan ^{-1}\left(\frac{2 x-1}{1+x-x^2}\right) d x=$

The c.d.f, $F(x)$ associated with p.d.f. $f(x)=3\left(1-2 x^2\right)$. If $0< x<1$ is $k\left(x-\frac{2 x^3}{k}\right)$, then value of $k$ is