Integrate the rational functions`(x^3+x+1)/(x^2-1)`

Explanation

To integrate the rational function \(\frac{x^3 + x + 1}{x^2 - 1}\), we can follow these steps:

### Step 1: Polynomial Long Division
Since the degree of the numerator (3) is greater than the degree of the denominator (2), we perform polynomial long division.

1. Divide \(x^3\) by \(x^2\) to get \(x\).
2. Multiply \(x\) by \(x^2 - 1\) to get \(x^3 - x\).
3. Subtract this from the original numerator:
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