Two JEE problems together level 5.O

If $^{21}C_{1}+5.^{21}C_{5}+9.^{21}C_{9}+.........17.^{21}C_{17}+21.^{21}C_{21}=k$ ,then the number of prime factors of $k$ is/are $A$ .

$and$

The value of $\displaystyle \lim_{x \to - \infty}\frac{\int^{\sqrt{x^{2}+1}}_{2}[tan^{-1}y].dy}{\int^{x}_{-1}[1+\frac{1}{|y|}].dy}$ , (where [.] denotes greatest integer function) is $B$

Find $\color{#D61F06}{A+B}$