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Q14  Integrate the functions  \frac{1}{x (\log x )^m} , x > 0 , m \neq 1

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Given function  \frac{1}{x (\log x )^m} , x > 0 , m \neq 1,

Assume the \log x =t

 \therefore \frac{1}{x}dx =dt

\implies \int\frac{1}{x(logx)^m}dx = \int\frac{dt}{t^m}

=\left ( \frac{t^{-m+1}}{1-m} \right ) +C

= \frac{(log x )^{1-m}}{(1-m)} +C, where C is any constant value.

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Divya Prakash Singh

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