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  "body": "\n## Summary\n\nIntegration by partial fractions is a method to integrate [[rational functions|0WCZH4AFMT]]. We write the rational function as a polynomial plus a sum of simple fractions. Each simple fraction has a known antiderivative.\n\n## Remarks\n\nOver $\\mathbb{R}$, the simple fractions have the forms $\\frac{A}{(x - r)^k}$ and $\\frac{B x + C}{(x^2 + p x + q)^k}$, with $p^2 \u003c 4 q$.\nTheir antiderivatives use powers, the [[logarithm|0K1N1Y4EGZ]], and the [[arctangent|065XW2V6C3]].\nFor example, $\\frac{1}{x^2 - 1} = \\frac{1}{2} \\Big( \\frac{1}{x - 1} - \\frac{1}{x + 1} \\Big)$.\nSo every rational function has an elementary antiderivative.\n\n## Explanations\n\n### L1 human\n\nA complicated fraction of polynomials splits into a sum of simple fractions.\nWe can integrate each simple fraction by a standard formula.\n",
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