📝 题目
例 3 求 $\displaystyle \int \frac{\mathrm{d}x}{\left( {x - \alpha }\right) \left( {x - \beta }\right) }$ .
💡 答案与解析
解 我们有
$$ \int \frac{\mathrm{d}x}{\left( {x - \alpha }\right) \left( {x - \beta }\right) } = \frac{1}{\alpha - \beta }\left( {\int \frac{\mathrm{d}x}{x - \alpha }-\int \frac{\mathrm{d}x}{x - \beta }}\right) $$
$$ = \frac{1}{\alpha - \beta }\left( {\ln \left| {x - \alpha }\right| - \ln \left| {x - \beta }\right| }\right) + C $$
$$ = \frac{1}{\alpha - \beta }\ln \left| \frac{x - \alpha }{x - \beta }\right| + C. $$