# Integrate : $\large\frac{(1+ \log x)^4}{x}$$dx $\begin {array} {1 1} (a)\;\frac{(1+\log x)^3}{3}+c \\ (b)\;\frac{(1+ \log x)^4}{4}+c \\ (c)\;\frac{(1+\log x)^5}{5} +c \\ (d)\;\frac{(1+\log x)^6}{6}+c \end {array}$ ## 1 Answer 1+ \log x =t=> \large\frac{1}{x}$$dx=dt$
$\int t^4 .dt$
=> $\large\frac{t^5}{5}+c$
=> $\large\frac{(1+ \log x)^5}{5}+c$
Hence c is the correct answer.