Partial Fractions

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The integral ∫1/(x² - 1) dx can be evaluated using

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1. **Identify Denominator Type**: $x^2 - 1$ is a factorable quadratic $(x-1)(x+1)$.
2. **Decomposition Method**: The integrand can be split into 'Partial Fractions':
   - $\frac{1}{(x-1)(x+1)} = \frac{1}{2(x-1)} - \frac{1}{2(x+1)}$.
3. **Evaluation**: Integrating each simpler term yields logarithms.
   - $\frac{1}{2} \log|x-1| - \frac{1}{2} \log|x+1| + C$
4. **Combined Result**: $\frac{1}{2} \log \left| \frac{x-1}{x+1} \right| + C$.

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Partial Fractions

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