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Question
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Solution
Let `I = int 1/(x (log x)^m) dx`
Put log x = t
`1/x dx = dt`
`therefore I = int dt/t^m`
`= int t^(-m) dt = (t^(-m + 1)/(- m + 1)) + C`
`= (log x)^(- m + 1)/(1 - m) + C`
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