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Evaluate: int(x^3+x+1)/(x^2-1)\ dx...

Evaluate: `int(x^3+x+1)/(x^2-1)\ dx`

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To evaluate the integral \( \int \frac{x^3 + x + 1}{x^2 - 1} \, dx \), we will 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 will 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 \( (x^3 - x) \) from \( (x^3 + x + 1) \): ...
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