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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 Answer

$(1)\;f_{n+1}(x) +c$
answered Nov 7, 2013 by pady_1
 
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