Find `int[log(logx)+1/((logx)^2)]dx`

Explanation

To solve the integral \( \int \left( \log(\log x) + \frac{1}{(\log x)^2} \right) dx \), we can break it down into two parts and use integration by parts where necessary.

### Step-by-Step Solution:

1. **Split the Integral**:
\[ \int \left( \log(\log x) + \frac{1}{(\log x)^2} \right) dx = \int \log(\log x) \, dx + \int \frac{1}{(\log x)^2} \, dx \]
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