📝 题目
例 5 求 $\displaystyle{\int {\sin }^{2}x\mathrm{\;d}x,\int {\cos }^{2}x\mathrm{\;d}x}$ .
💡 答案与解析
解 $\displaystyle{\int {\sin }^{2}x\mathrm{\;d}x = \int \frac{1 - \cos {2x}}{2}\mathrm{\;d}x = \frac{1}{2}x - \frac{1}{4}\sin {2x} + C}$ .
$$ \int {\cos }^{2}x\mathrm{\;d}x = \int \frac{1 + \cos {2x}}{2}\mathrm{\;d}x = \frac{1}{2}x + \frac{1}{4}\sin {2x} + C. $$