integrate this`int ( x^2+1)/(x^2-5x+6)dx`

Explanation

To solve the integral \(\int \frac{x^2 + 1}{x^2 - 5x + 6} \, dx\), we will follow these steps:

### Step 1: Polynomial Long Division
Since the degree of the numerator is equal to the degree of the denominator, we perform polynomial long division.

1. Divide \(x^2\) by \(x^2\) to get \(1\).
2. Multiply \(1\) by the entire denominator \(x^2 - 5x + 6\) to get \(x^2 - 5x + 6\).
3. Subtract this from the numerator:
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