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$$$\frac{\ln\left(2\right)}{x}$$$ 的积分
您的输入
求$$$\int \frac{\ln\left(2\right)}{x}\, dx$$$。
解答
对 $$$c=\ln{\left(2 \right)}$$$ 和 $$$f{\left(x \right)} = \frac{1}{x}$$$ 应用常数倍法则 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$：
$${\color{red}{\int{\frac{\ln{\left(2 \right)}}{x} d x}}} = {\color{red}{\ln{\left(2 \right)} \int{\frac{1}{x} d x}}}$$
$$$\frac{1}{x}$$$ 的积分为 $$$\int{\frac{1}{x} d x} = \ln{\left(\left|{x}\right| \right)}$$$:
$$\ln{\left(2 \right)} {\color{red}{\int{\frac{1}{x} d x}}} = \ln{\left(2 \right)} {\color{red}{\ln{\left(\left|{x}\right| \right)}}}$$
因此，
$$\int{\frac{\ln{\left(2 \right)}}{x} d x} = \ln{\left(2 \right)} \ln{\left(\left|{x}\right| \right)}$$
加上积分常数：
$$\int{\frac{\ln{\left(2 \right)}}{x} d x} = \ln{\left(2 \right)} \ln{\left(\left|{x}\right| \right)}+C$$
答案
$$$\int \frac{\ln\left(2\right)}{x}\, dx = \ln\left(2\right) \ln\left(\left|{x}\right|\right) + C$$$A