Integrate the functions`1/(x(logx)^m), x >0`

Explanation

To solve the integral \( \int \frac{1}{x (\log x)^m} \, dx \) for \( x > 0 \), we will use the method of substitution. Here are the steps:

### Step 1: Substitution
Let \( t = \log x \). Then, we differentiate both sides:
\[ dt = \frac{1}{x} \, dx \quad \Rightarrow \quad dx = x \, dt = e^t \, dt \]
This substitution is valid since \( x = e^t \).
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