Partial Fractions

Use partial fractions to integrate rational functions.

适用情况

基本步骤

1. Decompose into partial fractions.
2. Integrate each piece.
3. Combine results.

例子

例 $\int \dfrac{1}{x^2 - 1} dx$
$\dfrac{1}{(x-1)(x+1)} = \tfrac12\bigl(\dfrac{1}{x-1}-\dfrac{1}{x+1}\bigr)$ → $\tfrac12\ln\left|\dfrac{x-1}{x+1}\right| + C$.

Summary

中英对照