Find the Definite Integrals : `int_1^2 e^x((x-1)/x^2) dx `

Explanation

To solve the definite integral \( \int_1^2 e^x \left( \frac{x-1}{x^2} \right) dx \), we will break down the problem step by step.

### Step 1: Break Down the Integral
We start by rewriting the integral:
\[ \int_1^2 e^x \left( \frac{x-1}{x^2} \right) dx = \int_1^2 e^x \left( \frac{x}{x^2} - \frac{1}{x^2} \right) dx = \int_1^2 e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx \]

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