Find the Definite Integrals : `int_1^2 dx /x(1+logx)^2`

Explanation

To solve the definite integral \( \int_1^2 \frac{dx}{x(1+\log x)^2} \), we will use the method of substitution. Here’s a step-by-step solution:

### Step 1: Choose a substitution
Let \( z = 1 + \log x \).

### Step 2: Differentiate the substitution
Differentiating both sides, we have:
\[
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