# If $f_n(x)=\log \;\log\; \log\;......... \log\;x$ ($\log$ is repeated n-times ), then $\int ( x f_1(x)f_2(x).......f_n(x))^{-1}dx=$

$\begin {array} {1 1} (1)\;f_{n+1}(x) +c & \quad (2)\;\frac{f_{n+1}{(x)}}{n+1}+c \\ (3)\;nf_n (x)+c & \quad (4)\;\frac{f_n(x)}{n}+c \end {array}$

$(1)\;f_{n+1}(x) +c$