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

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

$$\int_\limits0^{\frac{\pi}{2}} \frac{\sqrt[7]{\sin x}}{\sqrt[7]{\sin x}+\sqrt[7]{\cos x}} d x=$$

$\int_\limits0^1\left(1-\frac{x}{1!}+\frac{x^2}{2!}-\frac{x^3}{3!}+\ldots\right.$ upto $\left.\infty\right) e^{2 x} d x=$