Evaluate each of the following integral: `int_e^(e^2)1/(xlogx)dx`

Explanation

To evaluate the integral \( I = \int_e^{e^2} \frac{1}{x \log x} \, dx \), we will use the substitution method. Let's go through the steps in detail.

### Step 1: Choose a substitution
We will let \( t = \log x \). This means that \( x = e^t \). Now, we need to find \( dx \) in terms of \( dt \):
\[ dx = e^t \, dt \]

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