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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\large\frac{(1+ \log x)^4}{x}$$dx$

\[\begin {array} {1 1} (a)\;\frac{(1+\log x)^3}{3}+c \\ (b)\;\frac{(1+ \log x)^4}{4}+c \\ (c)\;\frac{(1+\log x)^5}{5} +c \\ (d)\;\frac{(1+\log x)^6}{6}+c \end {array}\]

Can you answer this question?
 
 

1 Answer

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$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.
answered Dec 19, 2013 by meena.p
 
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