Evaluate : `int_(1)^(2) (cos (log x))/(x) dx `

Explanation

To evaluate the integral \( I = \int_{1}^{2} \frac{\cos(\log x)}{x} \, dx \), we can use a substitution method. Here are the steps to solve the integral:

### Step 1: Substitution
Let \( t = \log x \). Then, we differentiate to find \( dx \):
\[ dx = e^t \, dt \]
Since \( x = e^t \), we can also express \( \frac{1}{x} \) as \( e^{-t} \).
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