Integrate the functions`(x+3)/(x^2-2x-5)`

Explanation

To integrate the function \(\frac{x+3}{x^2-2x-5}\), we will follow these steps:

### Step 1: Set up the integral
Let \( I = \int \frac{x+3}{x^2-2x-5} \, dx \).

### Step 2: Decompose the numerator
We can express the numerator \(x + 3\) in terms of the derivative of the denominator \(x^2 - 2x - 5\). The derivative of \(x^2 - 2x - 5\) is \(2x - 2\). We can write:
\[
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