$$$\frac{\sec^{2}{\left(x \right)}}{2}$$$ 的積分
您的輸入
求$$$\int \frac{\sec^{2}{\left(x \right)}}{2}\, dx$$$。
解答
套用常數倍法則 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$，使用 $$$c=\frac{1}{2}$$$ 與 $$$f{\left(x \right)} = \sec^{2}{\left(x \right)}$$$：
$${\color{red}{\int{\frac{\sec^{2}{\left(x \right)}}{2} d x}}} = {\color{red}{\left(\frac{\int{\sec^{2}{\left(x \right)} d x}}{2}\right)}}$$
$$$\sec^{2}{\left(x \right)}$$$ 的積分是 $$$\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}$$$：
$$\frac{{\color{red}{\int{\sec^{2}{\left(x \right)} d x}}}}{2} = \frac{{\color{red}{\tan{\left(x \right)}}}}{2}$$
因此，
$$\int{\frac{\sec^{2}{\left(x \right)}}{2} d x} = \frac{\tan{\left(x \right)}}{2}$$
加上積分常數：
$$\int{\frac{\sec^{2}{\left(x \right)}}{2} d x} = \frac{\tan{\left(x \right)}}{2}+C$$
答案
$$$\int \frac{\sec^{2}{\left(x \right)}}{2}\, dx = \frac{\tan{\left(x \right)}}{2} + C$$$A